Class 12th Physics Part I CBSE Solution
Exercises- A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current…
- A long straight wire carries a current of 35 A. What is the magnitude of the field B at a…
- A long straight wire in the horizontal plane carries a current of 50 A in north to south…
- A horizontal overhead power line carries a current of 90 A in east to west direction. What…
- What is the magnitude of magnetic force per unit length on a wire carrying a current of 8…
- A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its…
- Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the…
- A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The…
- A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil…
- Two moving coil meters, M1 and M2 have the following particulars: R1 = 10Ω, N1 = 30, A1 =…
- In a chamber, a uniform magnetic field of 6.5 G (1 G = 10-4 T) is maintained. An electron…
- In Exercise 4.11 obtain the frequency of revolution of the electron in its circular orbit.…
- A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended…
- Would your answer change, if the circular coil in (a) were replaced by a planar coil of…
Additional Exercises- Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the…
- A magnetic field of 100 G (1 G = 10-4 T) is required which is uniform in a region of…
- For a circular coil of radius R and N turns carrying current I, the magnitude of the…
- A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm,…
- A magnetic field that varies in magnitude from point to point but has a constant direction…
- A charged particle enters an environment of a strong and non-uniform magnetic field…
- An electron travelling west to east enters a chamber having a uniform electrostatic field…
- An electron emitted by a heated cathode and accelerated through a potential difference of…
- A magnetic field set up using Helmholtz coils (described in Exercise 4.16) is uniform in a…
- A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two…
- The wires which connect the battery of an automobile to its starting motor carry a current…
- A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its…
- A uniform magnetic field of 3000 G is established along the positive z-direction. A…
- A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10…
- A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A…
- A galvanometer coil has a resistance of 12 and the metre shows full scale deflection for a…
- A galvanometer coil has a resistance of 15 and the metre shows full scale deflection for a…
- A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current…
- A long straight wire carries a current of 35 A. What is the magnitude of the field B at a…
- A long straight wire in the horizontal plane carries a current of 50 A in north to south…
- A horizontal overhead power line carries a current of 90 A in east to west direction. What…
- What is the magnitude of magnetic force per unit length on a wire carrying a current of 8…
- A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its…
- Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the…
- A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The…
- A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil…
- Two moving coil meters, M1 and M2 have the following particulars: R1 = 10Ω, N1 = 30, A1 =…
- In a chamber, a uniform magnetic field of 6.5 G (1 G = 10-4 T) is maintained. An electron…
- In Exercise 4.11 obtain the frequency of revolution of the electron in its circular orbit.…
- A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended…
- Would your answer change, if the circular coil in (a) were replaced by a planar coil of…
- Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the…
- A magnetic field of 100 G (1 G = 10-4 T) is required which is uniform in a region of…
- For a circular coil of radius R and N turns carrying current I, the magnitude of the…
- A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm,…
- A magnetic field that varies in magnitude from point to point but has a constant direction…
- A charged particle enters an environment of a strong and non-uniform magnetic field…
- An electron travelling west to east enters a chamber having a uniform electrostatic field…
- An electron emitted by a heated cathode and accelerated through a potential difference of…
- A magnetic field set up using Helmholtz coils (described in Exercise 4.16) is uniform in a…
- A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two…
- The wires which connect the battery of an automobile to its starting motor carry a current…
- A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its…
- A uniform magnetic field of 3000 G is established along the positive z-direction. A…
- A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10…
- A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A…
- A galvanometer coil has a resistance of 12 and the metre shows full scale deflection for a…
- A galvanometer coil has a resistance of 15 and the metre shows full scale deflection for a…
Exercises
Question 1.A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?
Answer:Given:
Number of turns, n = 100
Radius of coil, r = 8 cm
Current through the coil, I = 0.40 A
Magnitude of magnetic field at centre of coil, B = ?
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)
Using Biot Savart law, we find that magnetic field at the centre of a coil is given by,
…(1)
Where,
B = Magnetic field strength
n = total number of turns
I = current through the coil
μ0 is the permeability of free space.
μ0 = 4 × π × 10-7 TmA-1
r = radius of coil
Now, by putting the values in equation (1), we get
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZkAAAAtCAYAAAB8iRYZAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABgZSURBVHhe7V1NbBtHln7dmuMCztna26jbsKzLHrRYUTpOrBUZ7GQPFrDKQR7EoryXYTMTXcYaWqLtyyqxfi4RKQOxDysDdhaRAVO0B9hTRAWIfPBgZCki6dtkzqsAPgXs3q+q2CS72RS7KckSySrAMMSuqn7v66p6Ve+vfjU/P0+ySAQkAhIBiYBE4DQQ+NVpdCr7lAhIBCQCEgGJAENAChk5Ds4cgURiwloe1sjYdpES3aT53h3lzAk8YQIYv9npSQrTbEfyd8Jwye7aHAEpZNr8A3YO+UtUsGK0nkwqQuhMEs2M0eH6TuewCE4mLvxkDU8v0MAuJOpAR7EmmZEIeCIghYwcGGeOQDK5rtAoMQEjaMku0JOBWRpdT3bcKWb9sFcZ7YWw6Q9Z6b0zh14SIBE4dQS6SshMXHhpaQbRUiGHHXLnLWCnMVomBi9YC3efUP8jb8z4qQOqHyMtdF2h0BLNPorRTov42qeY8UepI08x4lu69WtuBKK0aaVoB6ejk8KmotojnLxy4uR1Un2fVT/gySxmM8rCXYPKnxEfMkpL+AZGH6nzyaR1VrS18l6MWfOLe0+Uy19vUUxT1KSLfsbv8s3rSjyVI8ZYKLRItx4aFNbIUZfVW0E9w1Evhnr1fbZC53HaVGhLgwcwIXiI0bvXSs/+ftL00/cnF16WtDip9w+2qNfVLpH4pLRyc1I1fPbP649oqmHdpx+3YqQrSg9w53R0jZBJTFywhjW2KIX84N/1dRITg9b0ZJi02wwKLNZ9RG7FlWPBtXLUV8zSMtqEtT22uFtscU8k0I8SpnQDRKObFvXu1CzUOMUYOMXM+xJSocqGQQidAS5UxqhI3ObR6KXH+bqMPi7bnlCmGKv0FJjP49Bwwm1fTGs0Bqyim3miMU21itnStB5RDI0oY6bMcCJRt1CfMAkn0h3GrHnzekTRbjPREaUMxqy7cAEzoitxLIYH5hZpbzFmr0foI32fnpurZqLMK1/EUY8tmgfmd6j3glY86p0I4QE7cdBWqqVtj56XUqXLaqJnv7zAN+o68cmF0oj2vWpZQx4YVQXGgd/+s/9FccwLy3pKm4UY/UWvdtsVQsZeAAaiUdpO7wb8pES8/fAGfZzz3hWLBbnx88AvDNDgNGjjAnkhjxOJRTOZYWKnP8/CF1y20Fd39InZqGVgdd/IpghaIUomd5ReuMk3dJTfKavIUNc+xbAdtB9bTGjpkeeJlKnfEqlZK5reCICkv6rZjTRFl5Zo1zDoSabItHy8BOHT35vecy04WaTDuoqQBgtfRJ1ZGjLXYmnlWXaVImGl8fdrgUyMWfPmyIby2+9WaUzxOGlwYdH4udcrMWbNkYW88sevTfp8c4T0eOMxG98eovsHMdIUnFzWd6zErSkzHrF5JcErH9t2PdBYrme46zXh/zR4JSzo9bTdMI3IA2XjxSp9+O7owzVoKt3siahXbtyg7Qdv6jngAkPw/vobpefx/o4JjErxyJraqH82L6YWF+mv8c/o6WaBtiFl7DnfFUImOx2m3aUC5fQFSre0u9WoH3vx8DDRZk7s0O0vYwuwXUzSXp+qE7eKqdE4DYHm0UPYK44sJ0sbXzDXD7ndACov0i5wjYK3jMHAYjtGvfaUM/YxfklTeiMLz6mAK1CAU8z64agySusNXyAW/V6mKqPE4E+WUj7WsJPTTH6aJo008XMtvtsoPNiYQd79m7tz8a2j9LEVof4nBhlPMvQol7CCqsyEdxk7IuZpIhG8fUBUm1b/oXdenWfn1JqYuT4NXglKVR3JTwDTk4qtFm08ZvO0bWgQVkep2DS6TGsUHsFJaat6emB98kVZjSh/nXpOKVVp0k+VCoxZ9SrG26vHSdIvWExN4zlv2GJIlhizlcLH7BqlnmUJEpVLGb/1moJLbH6uUWTEoudbqcpJycHrDfAKYetXLZn9dg3Np1w8/Dt4eIB594LWPnx35KaAr4f38/Sd/iU9eOAhY4CRxfr/NdE7nGaJ7QOB0ZSy5tm/EFrT6r/9EqHLT/9A8aebdLCllXQlwVVmHS9k2AIz/HKJHqUwqjCGWil8Z5wrWAQ32/BwP3TxYmGoqEgCutoyVQ7NQJc6s4wu92i2bDcQKj2DBmwV0mHjRdTm46Rp84uPOHVgoQz1YxrVq9JoFwtoyv8CGvQU45dOVi+506tYhSWO7e7dacrgpDQKA/wjrmLDohKKWhdmZ2h03v7tLo0Xcpbbbldcvkvp6Cw2E+vKxHjIMow9KgQhBHWZWk9RuA4SxSAtbRA2E1bzzUTAFx2zur3I/nZMoRT6EmN2C2N2hUb0PbpVgloSJwEqrpRG9Jhy5bmJk5CijsL+MdokvhtjVk1s5U10pERG+im/FeOLL95SYgImBQGDznwLGL+sClXZnEKhyxizHjIIYzZvjpmaMkErI3MYF6yeR6nUa65GrOX1I/B64OI1DQFjMV592r2Eqgw8DIl5V1fegIdUrPQaNhEvlRnWw9LIn5fUr1f7SHlR31zYVuZU3j8geu2u4tH/WzYvbtyi1P+87ilc+5dfPovvq0VsTf9ShrijhYwQAi+xYKSEa+xg4115s4Fau5hrONEUHjEVGmwNEDCF1Bj69+9qu9M7qqABW3FOxKB6krQ1w6H5c+zcWjB7CQ8z7mLW/BXHqDEwy1Rx4iTaFxmnEDOwjM/Q4Y44MYrfDNqD9Kg9iNlCNTo7Bom6U6lnqwX9ksROYPPztpKt3MrHZsJv/ydRLzHxgTmikzKVgaoMgoQvgL2jKq3fwZj9oOEpIci7axdfHSea/EPd/OJ3EUpDwORXYQuEZLOdDYP021pdnKwwZpWms1GM7eb1nFTU8noJvB48vGR+Web1gPGK6scf9eV5dwQP4sTxZ/Xaj6tcDab9g/ULXg3h7qfo1M/MN67+baE09cd/pd+8UzEv/k5Dn8Xp2Yuv8LeQMh0rZGyjNFOT9XoYkdmOckHPOY3OTbB2LOZsZMCTSgiYs/cwOs+0+RnCZ1lnwKHva0BJMQNTP07EkDE8dKcvQuMhqMxaUQueJbNN3m0bxq3FPKUj/tVVrbDkEDQ6c5FaEgKG2Up87uxbee9ZtHEIGvBqwRssvzr23ni1vb92vzyg1Otveub3900arCLxT38fKf3v4HeQIW+DwfP2OebFIn2NY+1rLlMwL4Y+I+PZC0r/RqjtOlbICMMdONzWmO6dy9+KkgKj2MDfOITIcuIIFGiP4R7Vz4XwPSn2ipkntL29jUWBjRyybt8uj6btDRose9Kd1LvOqh9bwBhXoK5qalc5KypP470F2meLxJROOuxAcAku4S0e+jQxtu16R9udToPOo/osz7sb4OGbshCprV72/jJz3O2rxEavvR7GdZWYn8RU5qijXJ72vkelT539v30u5oWu8nnBcBMlt0GZr1Kld6rS07FChunh3ck/hQF4txonU+PZ5GdIOFx2CzotMBdfpjprwfjr531B6rxv2tjJaXAAwhsRhV52iVA/jnqH/lWIQXh933VttStMJw5vNtuhIKjK7H3T7/d9zJU5fiUDnf77UVdVhJqFXX1eJ6Yu02Egz28ZDgO5X/qb1WOnicErcApI7ysFDF23XSZ0GRtSrLPOelRn+7DrBdFxOdyO85eIqcu46qxso/F7cuO09YOHB3vgoZ62Icy77XpLCrNL9tyem3NAxOwzPZFd9Us7TuZV0rzziggYlWhtT8VwrxO1tf3b6rfFA5Mu1sTZiH6rnmgdK2SaDbigz72C8FI5WOgRA6JN61Cb+TdyV95d2OMeTsctp0KbD6I0bnypuivzJtkNHhMT9aOC8vGOc1GF8RQapwJ8RxyuGMfxpDsXjFWJmPjgpam/XFIOtriNgKursFiYI/kZJWf0VY3whTd8zDY1XzThzyFgELzHVGSprUxJgeFfv6kztdmpCBo+ZpU0Cdds212ZjVn4U2HM2vPRbz0/n9EhYDiviroKXgm8XsLacZAKxqt2hc27NR4mEAYPYt59y+fdDbiEGXAJ2w8iAV1M6Hxeo/9ad2jMgTV89E9r+2e/DV2jHzEvXtcallyeaF0lZIr54DEyDP9GUd7MTTZllQUNsWSOfoZctY6gpz6B1W6+SClE2i9rsaaZCU6LNicnuwSS6kpfbJai8M5K313mp7k+BEGyRJdMt460Y8J28Z5KgevoYED2oJM/KAt0r3RhDG/3p7N/s/GFy19j9R/icdpZZcYM/cMw9C8iLkIvG/rZwpid1hWr/3PHFywWMGYtjzFbKJKZ3TRXJhJNswR4CZjyTl5dNTMmW3x14h5mtV7VAUeSGLOI4ncUPmbjEUrdW6b8mGFqiQlCcCbR0CJ9XvakY0Z4Z70Yr4fgzHI94h53foz1XgLGzesl8AoPM9+xSDZtafAwM8Y882za7uNvYRtJkIiFSX+Kvj98J2wwrvIW64/XZuHXDKPP4IRxbwUOhbHSNe5tp5M1VNu/CNi0oFr1VM+xd61BZbaaKnWNkBGqDbEQGdBxIbVMnYtqw1FchL5zgBn569OIcEED91hC8GLQmAexMNZMWNuYbEzSNAINHZHwjYg7BdrsOJ4nyDFSa8dC7gorOg66yrE7gncIWaY2FLYKeAN74xRwhQhUffCn25YIg9n2/LbCNVxwAjdb2OIsK6Ux93FD7FwR2g63cY/fNuGdqIlsBdthuh1asuxUMs4If8RQYWLbWQ4CEX8OKr9YiHE10TYkDIrJ9fVlmxP2C45SeOMes2G6xhwgjOt0E2MWa2Vz12OM2f0ri1RYjVGfy8iPMaWu5hdNWigon5tk9inN3YQZgVxwIQXME6SAcdgaQiEzOv6Q0jHE7uB0JvqHIENmAF0VEZuh6CIdrMKdvIaWxvXEScSveov4/ET/X/2+rl2F1y8Kyh8sC4LMH6+1tF0CD0xQhKbwDqxPFddluNIeVYRKi0X8WxSHe99ifqt0mZApAClp0H8PMCrRZET16v8aZX/hAsyEA0MuQrS7WPqPrT/xdzuesfignrLh396tPRn3E/znTfpJ9HGa881to4Ebq+/XIdpX6cVWt5LA0dWSBS8e9bzRi3Z652E3gkds2VdTuPEiOp55uPp0az0N2jgdvaMgBf/cxLvo4u+3aeZ1Dxvi5BvwgBVtHO1m7m/Lg0sBdIUX2OKYx3nz30SAYjXso8qbV4S//R0Dkn/m1XkwZqPYlsPHbEhWCrBW5/D3qztJgvqeFZWuztH8VTFm/dyBiDGjXmTzCX14FRZYedRzzzawVdDFq6AV/+rG7GOar3kVf79NM6/7Mz32oMW7Hty4AxTex0VC/97tOK9HPG/0Kpu2OYZ7hYfqO5iguHh7jubYV9qv78Vto/n58R2gUC3J/0Z7YOTVP6As913/7vpnnexdFmAgyKoSAYmAREAicDoINFSXVXT9npbpEI6Ys4iiPx8xIqcDjexVIiARkAhIBI6LQEMhI4L7Nq09lkG3Jm0Kz7u0jAy3MPhqLRi7j0uwbC8RkAhIBCQC7YNAE8N/fYoQLnwSyHDLvIoC5qdqH1gkpRKB84lAIvHP5vTwtwrLCA7v1bqcV4kJPJ9s/Px8ciWp6mQEjuddNtBZUd2d/KElb52CQB/P6lvOCM7verGTK3IBpI4pu1NI28+y+iJtf6dwLfloXwQCC5nEBLsJEW6duDlvEzaZnQCJIdsXJkm5ROB8IMBzYOWQwXhYV1hG8HyOxXCwDMYvSkzApCFgRAZjKWDOxxeTVPgTMnB+h++5yP/F/OfhPL/Jrtg9gcSQ1RiHZh+jegtis5ryuUSgkxGoFTQ60hrlHyGDMWKVmIDJY+OnpSykRvHvot/JWEnezh4Bf0LGbfjHSSasISdtkIDGBry6YxyOgiRIbAuEoVQVnP34khQEQACnjyYX1FU7cwgarZzBmAmYckoYv6/FPDmR1P1+3yfrdR8C/oRMDS7iattNXG0bJmNSpBM5D6nu3Z8uyITtvs8uOZYICAQwT3zeJyIRkwi0hkBgISNeU/Y62w5+M6CbTKkua+3DyVbdjQBPowK7jIG7PPLICM7UZVx1BhsNu2XSd9qT7oZRcv8eEGhRyJTvLmh09W4Awk9LXRaABFlVItBWCDgETA65tKAiS+WyyOo7pujI6gu7jBQ0bfVFO5vYJkKmLExqcjjyYEzmXQZcQuORjrqYqrM/teSuExDwEjB2Vt+UmUUGYwgaBEmLDMaNEpJ1AhKSh3ZBoGlaGZ6Bts67LIRMtixLsLgXXRaJgETgPSFQLPKsviwjOK7xcKjFkskf1FR+GRmM88oMsvq6n78nCuVrJAIOBI5MK1PJCOwF2o7j+iYJawciMHHhpYVs+NWbRDuQx3ZjKbn+g3p0RvD/O/J5u/HbKr126v84Uv/zVPihRbr10GD3yxxpr+L3v+DKAMPRLoZ2zvT+E7jQ7fq9tJLL2RRi4734kFK4tlraw5xfrUWbTKufXrZrFwTEHSwsOyq7JU8WiUD7IGBfiha37tOBuUXa2ywtX4/QR/o+PTdXG9qrHBeMmd+h3Qta8WiHzZepR0iZep6nXFjcU8OEjh7RFVyVZm7XZGFoH9ROj1IpZE4P27bt2b6QayAape10a7eJti3zkvD2RyC7QPHtIbqPmz75RWTrO1bi1pQZj6QVx7XLbk7Rzqi0w8ml3M6oaWexk87InEJTzykdgYCZT/J4vPWdXjUzRWbkaUbJx0QWBnmiEQBzIWNfljXq86Isr1F4En20/+juDA6y02HaXSpQTl+gNDfKVYt9a6aBWzOPKiG0x3iSNrvOGBJtxUV2A4PWipIOo1Sl4N75KHK+pZ5liSJILerhE+GrXbMQb+Rz1JE3zspGS3NzDxR28+QULuKcKfwn/S6ephz+Dk1lsHkLq4XlaOl6/IFS+5udh66tAG9CrDzJdNLXPAFe2DXVwy+XcFcQZijmY91mb3qSaAZ67hl2ffEezVopnl5IqNcMdo2xuDb6GBuWE2BDdtGlCAhVGU4aoctw7fbY4yBzfN4Mm5rrWmdnOw/weLsxZEfoU39/a6pkRCJKNJM3b4dFglKuLpsLKfcPxshgG/edf1RNXCM9oseVN/emafNhirZiq2pxebikxyNK6M2Umbk1Q1tmuvzbPWVxZsw0OvAEJIVMl05GL7aFmuwljRdS3DUd14TX7dt2ekcVPCSCUJHQSQTaBwGNLsO8qAQetSLwvLYdri5W85kl83rkkkLw4kM2R+R2DNFifosMl4MAw2fgVopi5d8TE+MUin9P1rUZMmDPOYSAEr/Fab+Aygh66rQihUynfdEW+bFvQmVqst51nERchXmaLeg5cUqRRSLQxQjg1M5PKNb9A4JUEScZ5gxwSVX2nptm2sdpZAC6POaY1g1pTKWQ6eLJ4mCdGz3xy7ZG+E9k3C5XwO6MqwCQJ1UWiUCbIlCgfTawp2AzUXHZW9lg35wZEZAu2sHWYhVLK9fjyvYQPNdiffzgwQRFX+wRLT3Vybi3TDNjIrUPFZebd98FNaSQ6YKP7IdFqAAUd4Q4s88o4d1qnMxON+y7/KAl65xXBFh26sErlknpfaWAvZLbLhO6jE0U20K5hrKzXb3WqtKOnELHFlaV9mt7eG9Har1a/uRSyLQMXZc3LOyxE48sEoFzh4DGjShpcrgrZzeQCgueXlBTNRq3/tqVbTRwBDiAI4DbgYCG+jvRrHKsbyyFzLHg6+zGxXzjGBnxrCapXRmK3XyRUoMXrGUtBgczab/p7BFyPrnri81SNB6hFFRX+TEDMSsTtDyiEw0t0udjCqUY2YlB86YaUVKIdxE3iSYtZzsW6zJBK5V2xNuxE8vEtSHTiMeV68s6PYyFuWqsmJ0u6XOkDN2PcBdmZqdJDP6NC7R+D5jYPFGQfqDWk9rrt/OJcDCqpJAJhlfX1BaqMrHnM7ThugvqCkxRXStk+iI0HjLIMCZpeonltZMCpmsGyzljNJncUVfzCE65HlF0Nc6pC0UX6WDVEMGZTADAddJdGrdjQZ3VtDLrh6PwLhtAWhn0L7o38QJaRAYA5jHG++fOAXM8TmYtgit7MqaZmviARnSDx8pQXMepyjT/5PFbp13VIIXMOZsg54Uct43GfSupfUUDYmQ4yXYw7vwo/pAxMuflM3YtHYjWVy9enaP5qzYEP9PjO1VDDBMoF+fwnF4hMBP/ysW73Z06HFmE/9Wr83S10j/Rz68eU7LcVXL9UL2K/iuPX92hO3jm5ze7j075eFLIdMqXlHxIBCQCEoFziMD/A60LEe4eHvqfAAAAAElFTkSuQmCC)
⇒ |B| = 3.14 × 10-4T
∴ Magnitude of magnetic field at the centre of the coil is 3.14 × 104T.
Question 2.A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?
Answer:Given:
Current through the wire, I = 35 A
Distance of point P from the wire, d = 20 cm
![](data:image/jpeg;base64,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)
Using Biot Savart law we can find magnetic field at a distance d from a current carrying conductor.
It is given by:
…(1)
Where,
B = Magnetic field strength
I = current through the coil
�0 is the permeability of free space.
�0 = 4 × π × 10-7 TmA-1
d = distance of point P
By plugging the values in the equation (1), we get
⇒ ![](data:image/png;base64,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)
⇒ |B| = 3.5 × 10-5T
In this case the magnetic field at 20 cm away from a current carrying conductor is found to be 3.5 × 10-5T.
Question 3.A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.
Answer:Given:
Current through the wire, I = 50 A (North to South)
Distance of point P East of the wire, d = 2.5 m
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Using Biot Savart law we can find magnetic field at a distance d from a current carrying conductor.
It is given by:
…(1)
Where,
B = Magnetic field strength
I = current through the coil
�0 is the permeability of free space.
�0 = 4 × π × 10-7 TmA-1
d = distance of point P
By plugging the values in the equation (1), we get
![](data:image/png;base64,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)
⇒ |B| = 4 × 10-6T
Direction of magnetic field,
The point is in a plane normal to the wire and the wire carries current in north to south. Using Right hand thumb rule we can conclude that the direction of magnetic field is vertically upwards, or out of the paper.
The magnitude of the magnetic field is 4 × 10-6T and its direction is upwards or out of paper.
Question 4.A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?
Answer:Given:
Current through the wire, I = 90 A (East to West)
Distance of point P below the wire, d = 1.5 m
![](data:image/jpeg;base64,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)
Using Biot Savart law we can find magnetic field at a distance d from a current carrying conductor.
It is given by:
…(1)
Where,
B = Magnetic field strength
I = current through the coil
�0 is the permeability of free space.
�0 = 4 × π × 10-7 TmA-1
d = distance of point P
By plugging the values in the equation (1), we get
⇒ ![](data:image/png;base64,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)
⇒ |B| = 1.2 × 10-5T
Direction of magnetic field,
We know that wire carries current in east to west direction. Using Right hand thumb rule, we can conclude that the direction of magnetic field is from north to south as indicated in the figure.
The magnitude of the magnetic field is 1.2 × 10-5T and its direction is from north to south.
Question 5.What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30° with the direction of a uniform magnetic field of 0.15 T?
Answer:Given:
Current through the wire, I = 8A
Strength of magnetic field = 0.15T
Angle between direction of magnetic field and current, θ = 30°
![](data:image/jpeg;base64,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)
Force on a current carrying conductor of length L carrying current I, due to a uniform magnetic field of strength B is given by,
F = IL × B …(1)
In the equation we assume length to be unity (L = 1) to calculate the force per unit length.
From equation (1) we have,
F = IB×sin(θ) …(2)
Now by putting the values in equation (2), we get
F = 8A × 0.15T × sin30°
⇒ F = 0.6 Nm-1
Hence, the magnitude of force per unit length of the wire is 0.6 Nm-1
Question 6.A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?
Answer:Given:
Current through the wire, I = 10A
Strength of magnetic field inside the solenoid = 0.27T
Angle between direction of magnetic field and current, θ = 90°
Length of the wire = 3 cm
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASEAAACXCAYAAABa+e3HAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAABPnSURBVHhe7d1bjBRV/gfw32gQ3EDWrAq6mQfEaSQgbsJyyb8ncVeND9MjiiaMEVAjmh4u/zBjongDZYUQRRMbDAodMKAOBiTZSfgz82JgY9L9NOFBEZAe0UQeWAQkgSwgcft/fqdO9VRVV1fXtau75/tJCrpq6nLq9utzTlWf01IUCMDJlStEN9+sRkCqcEwGBgaos7OT+vr6aNGiRWoqOLlB/Q9QGQJQORyT0CAIAUCsEIQAInT58mX67bff1BjYQRACCCifz9Phw4fl/0eOHJHTjh07RgcOHKBPP/2UTp06JaeBPVRMAwTU0tKiPtk7ePAgpVIpNQZWCEIAAXEQmvy3ydT6P61qiubs0bN08v9OIghVgeIYQAgmzpxIf3n6LzRz0Uw58Oc/z/mz+is4QRCqd9evE124QHTmDNHp09r//I6Kjj/zPDp9fqi5//7+X/r9t9/lwJ/DcFqcc65rambNF4SMNyTjces0ZryRmXWcWZe1G9eX488cJOzWU4lxXYyDB6/DaMwYoj/9iejWW4kmTdL+N76jwp95Hp0+vzWtukrTWbVljIORdVxXad5K89uxzu+0rN263U5jbs+d/qUgDA0Nyf+jsm3bNlq9ejXt2bNHTWk+zReEjDck43HrNGZ92czu5TPrsnbjQV5aM66L8aPcP/xBjVjo27YuU0mleZ3WUW0Z42BkHddVmrfS/Has8zsta7dut9OYm3PJwYvP0003qQnRuuuuuyiXy9ELL7zQtIEIxbEw2X27usXL8jdxkKAG0eCcDw+XLhGdP6+dpwkT1B+j9eSTT9KWLVvEJq/IQPTRRx/Jd4+aCYJQWPib9Y9/9B9EeHleFkGofvEXBeeAWltLOamxY8fK/53cHOCcjh8/nrq7u2nHjh1yfOXKlZTJZJoqEJke0Z84cYL2799PV69eVVPAE74wxEXjW9DlIRrWG95wjs6cOUM7d+6kuf87l/6a/quslGY33nQjHf/ncfrXW/+ihQsX0tSpU+V0vy5evEiffPKJzBFxUFu6dCndcsst6q+VPfTQQ/TAAw+osfpkCkL6L4ABwBunIBSnN954g1599VWZo6pXpiDEWTx+JAgA7hQKBXr00UcdgxAXpdrb2+V0v66LouC8efNkTohxPdHDDz8sPzvh4DNx4kRRiqxNRbofeGMaIIBvv/2W7rvvPscgFPSNac4YrFu3Thb7br/9dtq7dy/NmTOnrnM3XqBiGiCAa9euqU/R4F/gP/744zIAsf7+flnH0ywBiCEIAdSxs2fPyhciOQf0888/UzKZVH9pHghCAHWstbWVLl26JJsD4c/NCEEIoM5x0auZil9WCEIAECsEIQCIFYIQAMQKQQgAYoUgBACxQhACgFghCAFArBCEAEa54c3tsscQ69A9qGaIGIIQAAhJyhSKxL9n56GQSVI2VZtAhCAEAGXaOrtEWCI6enJYmxAhBCGAOse/pG/m/uwRhADq3GeffSabXT537pyaEr3B93opT2la09OmpkQHQQigznEvG4sXL5Z9kEUXiPLUmxiplE5lxaT0AurQ/hgpBCGAOtfX1yfbE1q7dq0MRNE0wWyumC4WMpTMpqilBjXTCEIAAUTd5Q9btGiR7OZn9uzZMhC99tprsmecSLX10O5Mkii7gTZHXDdtamOas3rcZq7emDYAOPvhhx9o1apVjm1Mr1+/nmbNmiWn+8WBbOPGjfTVV1/Jce5GaPny5VXv1SlTptC0adPUmD1+TyjRSyInlCNTFdBgN7WIcll6oEjboyyXcRDSHTp0iAMSBgwYPA4iCBWXf7O8mB5Ky4E///0ff7edt5aDCIDFS5cuqTvcXiGTFPMmi6I4ZlJpethMOSEua3799ddqDACq4WZXuYjklBPivr+mT58upwfxwQcfyPamGXchtGLFCvnZyeTJk2VvIE4tM9rmhIY3U7uYmE8PUDHSbBC6/AEIxE2XP6KEEbgX1D179tC7775L33zzDT3//PO0bNkyWUcUBi0I5dXYiGSmQDk8ogeob266/AlSx8r1tB9++KF8RM8BiHNVL730UmgBiLX15EaeihmGWgQghiAEUMf4qRhXfDPuyZVzQNUqmhsNghBAHZs0aRLNnz9fFumefvrppuz2B0EIoI499dRTtGnTJlmnVM/9yQeBIARQx2677bamK35ZIQgBQKwQhAAgVghCABArBCEAiBWCEADECkEIAGKFIAQAsUIQAoBYIQgBQKwQhAAgVghCABArBCEAiBWCEECDuXz5shyapVdWBCGABsLBh5v1mDBhguyVtRkgCAE0EG5T6LHHHpOfX3nlFdn2dKPniBCEABoIB6HVq1fLtqa5dxwORJwjauRAhCAEEICbHljDxoFow4YNslPF8+fP05tvvtnQgcjU5Q+XNzm6Xr9+XU0BgErGjBlDR44ckT1hOHX5s3XrVnrwwQdDva942xcuXJC5olwuRzNmzKAXX3xR9kdm3M6dd94pW2esZ6YgdPjwYXmwAMAbpyAUJ+6hg/spq2emIMQdue3du5fGjRunpgCAkzNnzsicjlMQWrJkCd1zzz1yeph27dol+8LnfuofeeQR2Qmj0dWrVymVSlEymVRT6hN6YAUIoFY9sFoNDAzQW2+9Rd999x2l02mZ25k5c6b6a2NBxTRAAFH3wGrFlc/8WL6zs1MGoNdff132yNqoAYghCAE0mP7+frr77rvp/ffflz2yNnqHiAhCAA2EH8/39vbSli1b6Jlnnqn7J19uIAgBNBiuaOYK5/Hjx6spjQ1BCABihSAEALFCEAKAWCEIAUCsEIQAIFYIQgAQKwQhAIgVghAAxApBCKCB8A9mud2vZoIgBNAghoaGaN68ebR06VI6d+6cmtr4EIQAGsS0adPkL/K//PJLWrdunZra+BCEABoE/1bs+PHj8jM3pMY/ZG0GCEIAAbj5ESm3fBgWzg1xm9Ism83KBu8bnallxXw+L5sH4CYjAcA9tDHtnykndPHiRQQggCby448/1n0ltikIcRslnDHCgAGDu0Gvo3HCbUzbLRtk4EbNWE9Pj+3f9YGLa/Xe8BnqhAACcPPOTphtTDNu5H7VqlW0cOFCWrNmjZrauBCEABrIiRMnZCP3s2fPlk/H0LwrANQM97TBPa7y07bnnnuu7vsTcwtBCKCBTJkyRXbzs2LFCjWl8SEIATQI7mkjk8k0RT2QEYIQQEhuuPEGarmhRQ78GdzBkQIIwZXzV+jfR/9N5wvn5cCf//PLf9RfnXFdz2iGvugBAuBfts+ZM0eNlZsxY4b8eUWlSmR+2nXkyBGaNWuW/EnGaIQgBBDA6dOnadeuXfLz999/T59//jnNnz+f5s6dS1evXpXB5/7776/4G7Ouri75q/iVK1fSO++80zQdGnrCQQgAgjt06BB/oRf7+vrUlOrWr19fbG9vL+7YsaN47do1NdWrQjGTJLnt9ICaVGagmBZ/53n0ofK8Yu60ms9pppCgTgggZF7ekF62bJl84sU/MuWnX54NdlNLS4J682rczvBmam9J0dFMofRzjoKIWtlUC3UPqnlMBqk/q3U3Tdl+MRatCILQMG1ub6GW9s3ik1tulxmk7pYWat9caS4/23YjrPQFM7y5XVxw3ZFfFP5Fdfy9qI9z5dZPP/1EZ8+e9Vc5zcEllaUkBxeRdalk8L1eyicztLunTU0hauvZTSIOUXaDzXEa7KcspWnN7i4SoYr6I77gvAchGXnFSS4b6vnmAKg/HHg2bdokf4Zx6tQpNdWDth7KiVxNzhBcyqlcTVcnmedqo84uEYXy++igKQqJIL5BLJBeQB1tncSzZCOOQr5zQqKoWMraacN26pB/aaOenBjP9Vh2uhai2naN90kG+naK+Uu6QcV5/XnDOaBff/1Vfo6s8frhk3RU/Hfv1PKj0Tb1XvFvno4VtHFp+CDtE0W79AK+m1Wgym6I9FpEnRBATIyBx/RUTNbh2JU2tMFTEbJwTIQZ94YP7hPzp0nGIKGtk4tkedpnzi6FqnZ1QtZinH2NmJlpGTc5g/Jty3oUOa7VAejrKz+RatnSPMbipZt9ckif631X2xHlfP6G6k1Umr/avgiej7fT/is2N4eb01gtLe7PkVA1DQHPVQ1xENIrsU1BSBWzzCWNkcG5+BXEMB3kbFByOiXUFJFdIplf2nfQfDxDVJucEF8A4sYqFeEKGUpmU84RvWyZLtqXSBHfnp7leynR0k8L1EnkJwP53oTh4uULN0G99w6UTnRxgCjldIe5TZ+nfVdFCVnJmKRMQS2zXX0tSVlKOe6L4Pl4u9h/Xmeil0SiDPOkHZ6wKG7TUvUcCaGlIcC1FCKuE7p27Zr8PG7cOPl/6BLTxZXkkiqKmeuPOmgBX45ldUchEifFm4F0lXcM1DsLyYz4ZBi3LCAuMrGedFGb6m4ZsVBRHNBiUtyd9qzr0beTLJoX0d6ZGFmPddzKb/rs5zPvuw15jK1p1perti9+tuly/637K8j3SazHxdO518f97Rfzkwax0SrXknf6e0L8zo8buVyuOHv2bLnML7/8oqYKKm083W6wTXOl+9JhP63HXRu33yYPYR4rI985If72MWaJy7K/OlNF1witUuwonbRdqEDHZK6wlCnUqKyhd/eSuV4uQdPFmcmXauTUuPjmdcydlbhMn699r6bKvvjaZpX9178hrfsrJOSCFb4lPaXF3X55TkPo11K4xo4dqz4ZhFkcU0+4yotTetGrizrl6vTxDIlQY9lmQT7Oj6pIFt7TsSpPI8qClsgeV6Rq9GtHKwZxKYhvRC2NDq8ceEyfp30Pibdtutv/yk9YnIW5/57TENG1xD/X4PabuYcav4wvJ/JPPKIhzu0aeWLpWcMXzPDmZ6k3L4r8u9V9O/iefOExvcbuPtYf5/fSe07FXp9q9nSsLGjJIUe2QT2mb6mO7SpdXG8h614qBCKP6fO07yHxs81q+3/UJhs1fLL6LR7m/ntOQ0TXUqFQoLVr18rfex0+fFhNrWxoaEgOxpcS77jjDvXJZ52QsZJeBfZSwDeWTDq2y7qzkS+YFtKq1kbOwSC/TGR4KmalPSUT64/gnaHog5C6COwunsqsxSWlVjkkzg5ztqCsyKBzmT5f+x5QGNu07r+epbfur1CQZR09S28R5v77TUNE11IikZA/tThw4IBscpX/t6PnmJYvX07btm2T7wbpWltb6eOPP5Y9dvhqK9qp2GYtmXAgMs1j/hLQvoD0d/1s6NsyPSQJRw1yQh30sihQchQue9JRqR5Jz/5lUyPLcNQX4dt/5tdBWVqGtbdGK17YbtPnZ98F+UTD77sZPrZZdf9t9lfgR+v8BWyfhWc+99+W3zREcy1xAOH+4NevXy9zOG+//TZt3LhR/o3bgOYcz86dO2Vb0Jxj4kfxTzzxBE2cOFHOo5s5c+aobcKjRERFbzw/HVPUcqXB9Hf7Zcy19fw0RZuvci19+Xq0dVifCpU/MTFvy7wOu/Uy1+lz3Hd7pnWrdLrdF8njNp33X7Gus+yJlv1xqpaWQPvlMg2uz5VH/FRry5YthnVTcf78+cUlS5aUxrdu3Srn8/8r+eaG9oQAAuIeTr/44gvZF5gRd0zIv5If9TmdKhCEAELAxa/9+/fT4sWLqb29Xf4wtVm65IkaghAAxKpmj+gBAOwgCAFArBCEACBWCEIAECsEIQCIFYIQAMQKQQgAYuUxCFVoOjM2FdJjagLUoUmOplaLLm38XA/1dg1B3JowJyQu8md7KZ/Wmyp1+GUwAMTOYxCqt+5U7NJToSU9iEC9XQ/QiJovJ1SrNocAIBQh1AmpaS7rYAa77eYpr79w1w2MOT1y3aqdmFIrcubGZ6p2WSO3y+kzzKtvU66ft2VZj74Obd/Myzgxzm+3jKeucLiNntI87ru0cUqDdiwsx0jtuzafff1Otf0CMOEfsLpnbavFps0Xbu/F2gaMwQD3jFDWdkx5bw8j7b+MzKtPG1m9TdsxlXoXUO3QmKaracbkjmzX2k6NnnZzmkamGdZjs14rXs59WpyOgWBd1tBbg1N7OdXToI5vafsVzr/h+Ltep6W9Hxi9Agahal3FlNNuWrdByGU3MFWDkJrPdOdqZHoMy+s3ud0+2aZd3WTm+bV0OgXjcuXLeDoG1m05dPVSmU26jeuR+2pMj5uAYl2nm2VgNAlYJ1Slq5jAqnXV45Ln7mKS1GXfrms51bmcuRcILZ3eVFqm2jEIs0sbmzS09ZDWWYMo3mrtqHpsoN7PsYDRJGAQctdVTL3w22VNNKx1aQnZ5YpngSri3aWhY/sAiVMsJCnzcrUXHkLaLxg1Qnk65rqrnJh57i4mMnyjipuTjB3NaR3MeeYrx8Pcp2GwO0XZZFI2vt/7rLkS2izE/YJRI9xH9FW7yhGZc7u8edSP1X13FxMRvXho6vPbL2vxTKl2TN2mYbBb9WaR086tUwd4oe4XjBbBglDVrmLKaZ2oZWmDXofEj3yj6sqnxG93MRFRuRdj4Bjs9lts8dmljas0DFK3PEADJLub6nhZ5mqyqQo5XZ/7ZfsqAIwawYJQx3YqdO2jhLH8z1lxpzdoRW5pt7iSS3VIiWO0pgZZ9raenOyF0tglsbhPKVMoajdYTXXQdi66isChp2XD9IKsW/OD960gDmBp31wd0+ppkMUwUz1QG/XsVkVu24gR7n7B6ICG7gEgVuHWCQEAeIQgBACxQhACgFghCAFArBCEACBWCEIAECsEIQCIFYIQAMQKQQgAYoUgBACxQhACgFghCAFArBCEACBWCEIAECsEIQCIFYIQAMQKQQgAYkT0/4ted5VFyNkVAAAAAElFTkSuQmCC)
Force on a current carrying conductor of length L carrying current I, due to a uniform magnetic field of strength B is given by,
F = IL × B …(1)
Now by plugging the values in the equation (1), we get,
F = 10A × 0.03m × 0.27T × sin90°
⇒ F = 8.1 × 10-2 N
Hence, the magnitude of force per unit length of the wire is 8.1 × 10-2 N.
Note: The direction of magnetic field inside the solenoid is parallel to its axis.
Question 7.Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.
Answer:Given:
Current in wire A, IA = 8.0 A
Current in wire B, IB = 5.0 A
Distance between the conductors A and B, d = 4 cm
Length of conductor on which we have to calculate force, L = 10cm
![](data:image/png;base64,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)
Intuitively we can break the problem into two parts,
1) the magnetic field due to wire A, at a distance d.
2) Then we introduce a current carrying conductor B, at distance d and find the force on it due to field created by wire A.
1) Field at distance d due to current IA in conductor A is given by,
…(1)
Where,
B = Magnetic field strength
I = current through the coil
�0 is the permeability of free space.
�0 = 4 × π × 10-7 TmA-1
d = distance of point P
By plugging the values in the equation (1), we get
![](data:image/png;base64,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)
⇒ |B| = 3.18 × 10-6T
2) Force on a current carrying conductor due to a magnetic field is given by
F = B × IB × L …(2)
Now by putting the values in equation (2) we get,
F = 3.18 × 10-6T × 5A × 0.1 m
⇒ F = 2 × 10-5N
So, the force on the 10 cm section on wire A is 2 × 10-5N. Since the current is flowing in the same direction the force will be attractive in nature.
Note: The force will be same on both the wires, we can use Newton’s third law of motion to such conclusion.
Question 8.A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.
Answer:Given:
Length of solenoid, L = 80cm
Number of turns = number of layers × number of turns per layer
Number of turns, n = 5 × 400 = 2000
Radius of solenoid, r = Diameter/2 = 0.9 cm
Current through the solenoid = 8.0A
We know that, magnetic field strength near the centre of solenoid is given by,
…(1)
Where,
B = Magnetic field strength
n = total number of turns
I = current through the coil
�0 is the permeability of free space.
�0 = 4 × π × 10-7 TmA-1
r = radius of coil
Now, by plugging the values In equation (1), we get,
![](data:image/png;base64,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)
⇒ |B| = 2.512 × 10-2T
Hence the magnetic field strength at the centre of the solenoid is 2.512 × 10-2T.
Question 9.A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30° with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?
Answer:Given:
Length of side of square, L = 10 cm
Number of turns, n = 20
Current through the square coil, I = 12 A
Angle between the normal to the coil and uniform magnetic field, θ = 30°
Magnitude of magnetic field, B = 0.80 T
![](data:image/png;base64,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)
The torque experienced by the coil in a magnetic field is given by,
T = n × B × I × A × sin(θ) …(1)
Where,
n = number of turns
B = Strength of magnetic field
I = Current through the coil
A = Area of cross-section of coil
A = L2 = 0.1 × 0.1 = 0.01m2 …(2)
θ = Angle between normal to cross-section of coil and magnetic field
Now by plugging the values in equation (1), we get
T = 20 × 0.80T × 12A × 0.01m2 × sin30°
⇒ T = 0.96 Nm
∴ the magnitude torque experienced by the coil is 0.96 N-m.
Hence the torque experienced by the square coil is 0.96 Nm.
Question 10.Two moving coil meters, M1 and M2 have the following particulars:
R1 = 10Ω, N1 = 30,
A1 = 3.6 × 10–3 m2, B1 = 0.25 T
R2 = 14Ω, N2 = 42,
A2 = 1.8 × 10–3 m2, B2 = 0.50 T
(The spring constants are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M2 and M1.
Answer:Given:
For moving coil meter M1
Resistance of wire, R1 = 10Ω
Number of turns, N1 = 30
Area of cross-section, A1 = 3.6 × 10-3 m2
Magnetic field strength, B1 = 0.25 T
For moving coil meter M2
Resistance of wire, R2 = 14Ω
Number of turns, N2 = 42
Area of cross-section, A2 = 1.8 × 10-3 m2
Magnetic field strength, B2 = 0.50 T
Spring constant, K1 = K2 = K
a) Current sensitivity is given by,
For M1,
…(1)
By putting the values in equation 1, we have
⇒ ![](data:image/png;base64,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)
For M2
…(2)
By putting the values in equation 2, we have
⇒ ![](data:image/png;base64,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)
Now finding the ration of I1 and I2
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASIAAAAwCAYAAAC113eSAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABEFSURBVHhe7V2/cyJHFn5Dbb4bH+EBAUuqrTLa2DpQspfoqkhwYtjoNK6yopPRwuKIwMjRgpMj4cpKrMBCu7nhqiyHOlVZKN3c+gN25r7Xw/BjmGF6hkEg3FO1waKe7ve+7nnz+r03/T2pVqukLoWAQkAhsE4EnqxzcDW2QkAhoBBgBJQhUutAIaAQGCNQePbRKP7Y1gYD/ilLpWaH2noiVq3WzChgKhR2jMYX+1q7b3WXLV3QoJ2PKUMUBbqqD4XAFiBQqRSM05dF7eB4SINcIja8LH9K7Re15u0vhp6sxKq15YxRpbJjvI7VtfTPvxPlk6P+v0X/OUMZoi1YQFGpUHj60bzYb9F9t6ZF1afq5/EgUKt1Y/T5HtFVl6pXRInCc/hE15EpUKtdxf7yZo/uf/sPVX+b7f8JrKB5upskXbhiuEo9qsavHu1CZH3uLhtUrLfJci+F/0fNzvwDJnQvF0lvWw2z2SYddw4xD+t/EMPIZul+QY26TiOVXHWvFJ6au0mdbHjslXaCZdfcd193hacfzOR4kXitzRL1zBZd1R4evyDz7iU993GJ9VAHeAOshWH/kLpr0MVNvsKLZ0bj7Y9autMnPUFz3onwZspFzbmW8y5tZSxLBVuo00Zde37RIT2pLe0NuY151/uR6Lt/k57SYk9gBbVKv2feaHlqP3IjxMpelpOUb+OB6g1p7wq6FXbM02IeYF5Tc9g37bf92AATFpzZp8TdJXG7fPKGHyZzHQ+TPVlhZbN053fJEG80S/dyknUnV51KPZPiV7NGA/gsWKfAddgXHpNlmDLC8OToDrgXxdjrumTn3dMI7Xw0dzUAhWegM8xRFzrCCK1LnfG4lcILo1zMackT4SVQ76/zIgkjtJvSdPqObrGWk9Nr2WgZ+UolZtL7T+VYTmt7RHpKPYPaeRgcxIJ2Pp4YsSRpZhYxolergaCw89H44vxY67eTYszR1ixJ6exqBlxLr6VjuseDyGPXulda4SBr6nCPboZEcVsgeE36gB+syVuvclwydTxN55etSTsfBbDvNcu75/Sq7+4JCGNQ9P67a/fLyIYHKT6l+1Eza7b1YDp5qZxF4NJt2yZeZq1js9Q+l5rulWAmnlOJeXeRsMJGCPOegQFn7Lpd7EsCXqvQqVJ4Zuw2fteOOyYdXexSSvcQ6n2Dvhp8Rs3bQ0oRvKXulVn5pmR8lWtr5+/fIR6jUa36ayz+pkqexTpXb8mu5LmKV2NoSoWdZ0ZxP6mVfjaMExizZWNEtvSFZx9GRig3DoJvXYwIIGpVml1IwxvehJToVQ7b39GfLs/59V2iVAK/2QjlXuGXNrXPL7E9lV2JMOK4J78Lr6M/60mJxQlP85qNQwAXP6xsbronUhko4tyEyeo2ade939P2qOt5I/b/WhygwZOU6Dx6zGTn3SmcNUcnNMAcsQctIbxHk+h1qnX/iO1hHSJUQMlnZGBgV/ne/9Qmc7SWx8L97e/0pcZr+T1+yuOff71gpQLvK/ZWS//+i9iOVe6+nxsQRtuI7bc1E55V6cKgo+FrKuJFxyvMzoANT8ufvjhsa/2p3+ysG9//UnhClhHi/7+md9rWGaLpVSK2ZY061bH96sHzsbdb1tYHvm42TXDGHWYLP1zfUqFVMWXiA9bWdmgS4mz53TTiCtZ9thEKut2NUjbGwjZq00Y4/MMWzZ1RYzZnXDzm3VX6y3O8RvBQLQnQqnXyQt7alr3ReC0nYKZ45zXzKsBavjVNA+s8VvPJetVqv8aOmhmjmIqxwTPQKdL3Q2rvW1s2lqF2FY8Zt6fGy9Shdv3ta7pA7HVw2IoNv9/9lDrc17LZknGRPKK+af9mZcU462bS5afXsTda3xR7eOMEjyDvOEsX77azjsg2AnjRiStbOqDktOfj+TyF26JOL8IkPKNhh7drVsxt2EK8oRbc1Z8XMbhsVlCawx7u28brepmuB23TKhlxD+hHY3rme1kFZmHm3TbUaTqlmw8nph3kz3KsSMydfOB9FTqFxz9B6c+CO3jdP+KxPezRkDuzrntk0Dycqcy/3o0D54nCPyiLZIZ58DXpeavuyPrtUIRE+I1vZc3ezPtmv73dTkNkbROs/XBh56lZzOuUbK82CD2zCNnN4qxLwIUcftHN32kHvBEEmwtIU2KfDrJndHN8hL/Ftb5HQD9Kedz6ihqzoPM+9j7hE53dwvCgyI630NaayVMxjYRHQBCi1ing8GtvnsEbfzDnlvmLtdVbM1a/e3Wv9XslU0Mwsn565LOwhmSFk1KB3oT+MEfRQl62cdYtg1KM+/m4Bz8stLfHgVkhGAf0K52meYaU/tnFXeCHLwrtou4j0LzjpdE5nHg/fO9xicz82QWMk9wWPWr5l+/vjm7+C4vwZYpSGm+tqpFURi8vl3sPoQ2RXXORp+PNrztKprHbnVz8IO5ksJ2Gl8Reo/PKpuHS3AfbTs2k3IcpaqAUQGzTAi7kKGTjVLYOIxRoW5hIEYe12/CjOUD6EFdUmHnK6pj3IDolOY3ssT4W9bNynRyDcxHii4yJ3PuNdgdTk8JubHonlU3DQ5mPHAWB4kHahjJEXIG7W25Q5hruA6/eDbnsRXB2gIdp2hMY3oiofmkqRSYWGlzymVS9HbicSaX5Kzez+EZFcC3UZhEyZslyCgYh2Ft1GdlEfc8HLsabvOFFevoW3uAIE9SJmHXedkxjdHcramjDGGF/hOZbRIlZkHmflmSR0ReZ1ixii7hB9pUUpU5BME08zyK7hbU8StULS/T+J/pBOERsiDb/GhmikdvvMCpscOzUHKvCEfQ4Fm/3Pq7xW7OQRo3KzeYpOdCLdDAqXrQKGjlD1qQjpO/tEpHE4TGVdASU66fCa0mgKI8rzJ3t/LRzW3x8D8crWubIGBFXq/v1NPm7jGxuWTk7OD1TGyWqhaFX+mhGgHmM8liwKJg7TCC76C+rVRJBdHvn39bZYhWY8Rh+8+6GWe6oSdm2Tvnyq/ELA8V2JhcQlnryldWr0mkWu2sLb7aOU1fin9/Ql3oOa/l7ZMgOkSErYC2nyMSa/zqnUQsGSaqqQnYqh/8Txu25S/vrIQTkwtApt8ztN+et4088REKtnacTlNvyJx7Wov6AIi8T9RVWJW0RTQI8T7JqRdZOBAo7EBgp+7OkxmCZnCLkDIgzcCwMxRBteQuFmlS+siUOMMsvPnHTHYx4xv0+a4wm5EE5QEXeKwor22XD+mxjAN1xiZjACQPAujUnMOeOelS6rnOtiGhnYYQSB/68RSJLxB6VVUU9QB+7MxXrUpMZMWZB5t0pX62LGCLmqCzWgfirecIZRBQ33juqzhfqFrFOPJb92cYZUnmjBDB/DsHfIhkfDyZfxXPavXV7aRAqsLm+enotI1nsm7aXmrNRIy6yfJk6EXVE7f0Y1xIZsBWEdD5S9mikp8Rv36TmfzvJexdFik88aA8ZpnF6YOSIisyKjlTcLjyhY5MOK7QnsUiDKLWKthx4pfgeVMK/8QBXril0bhuf0f2eg9SBxBJ9wDp73ccLfdHfvQbzk22SIZpsHERRn1fdGtKw9mX1vYc5n84J3YvCOZnLOc7iz0Lme1wFZjLz7oYZSyfmaGYdcIjQu3jTDaOV6MQfoc6t5dHojrR6rYvK6SXXsszcc5Hl5yi7/txujNR7DR+wOn976/Ibf+jqdXnGiGwDxTUxIvCqo7ip1zed3ybJCK/aKAQUAgqBRQh4GiIOcGr1NLYUOWr1h5RG/OQMG1R7a2ZlzdhhDLbtUNOhEFAIKAScCCzImiHlPUAh4GjPyZW3diCT40WaXbZMXCyoIwYxNGeyMAprhYBCQCEgiYD31gxFXTOl3ujQ/qCRP4CsToJK1lBTMQjJsVUzhYBCQCEgEAhVR6SwUwgoBBQCUSKgDFGUaKq+FAIKgVAIrM0QTWpR/OSenAro11L9XSGgEHicCDxBwVukH8Ph4zqpswcW1rw4sJStU4lal8c5pUpqhcCjQyD2RNZwPAbVtkmXx4C3klEhEBUCamsWFZKqH4WAQiA0AmszRKvYmoVGQd2oEFAIrBWBtRmitWqtBlcIKAQ2CgFliDZqOh5OGMXq+nBYb+pI6+K5tw/in8Zl65heZSbdIgekMVmgfY8sU6rMGKtoE4r9dQtZXaex5fOlG/UzYgZUGapsPmtohgVYMFV0xDlbq5izMH1O67QqVleL/WPEc4/D7gXPfe5heO6Z0cPJkbZ1TK9+E2+dsyRYmOaaBmVK9Rsryr+HZX+1ZdgmVlfWySKuxKkQNgOqBEuLeAGB4ouZcG0OM3EIWj65Ed9KzukUktVVhghR8NzzMTDMc4+jYxKJ5/SZ9jA8927PxXYyvXpYAPuEvkypRIO2B+gRMKWugvWTlmF/DWERN5nVVbxMcNiczYDK3q3fNWbsmJpfvqcLFpNewIPyVzG/0jpJsLpKcCnOwMW01qeNt1rmgXjuXbdmfhO4TX+/LIN1Fcfd9lMNarvwtEfHlBo962dY9tcw87fprK58kNmYAfWpdRLl0lcmCHNL9PMrq5MMq2ulcgnGVjme+xfgucfJruBSnOe5l2V1LYLVdZrp1WlonDz3Czyipadx4zsQB8jjUPlOCz78pby4YZhSo2b9jJr9VV775VtGjUVYiYQcxyVTB1/Zx94QB/xZMSHrfGr+jCiHGJPcMfnr0kmW1RVqMc+9KcNz/yt47nlrVngBnvsceO5xzKvNcy/L6jpwYXW1t4duPPd/WkNkbck+4ED9luArq+zIvUX9mFIXPRQPw/opz/66bayuYQwSHixt2GuCPDHJNNPWmd6IFTaHcoHu6TEfZn5ltQzO6jrhue/j3HESPPdzRPdTwwdldeVbvXjuWznwrDnor7c+fW8HeXlLFu/O0wdzALOR6s+xoS5kSpVcHxvB+rmlrK6SU+CIhXCiQud06Zh4UgSwcWo+gvmBj0HeiPkNAwTumfDca548935dL2J1xcvf8OK5/3N6RCLIC9UHScHqYb0FrYtZLLAssQhnofFjSvWboIf7uz/765+B1VUGb3tOB0wFDsokmycgcdih5hkIKUe0UkG47mXGfZg24Vhdg/DcB9VjEc+92yH6oTyiAlKnfKA+WE7ExXQ9e6AgCirsQ7Rndxwfw86+Gfk87vz1xCV3EHmFYkp1USYq1s8o2F9nxNtGVlffxeRutP2wXdRtVPPrK/qowbawukbiEVnxljqlUYtRRcDPqsOojwkNZUHd1HYyTKkyskfN+hmW/XXbWF1lsHdvM4qnXYPswY15N5tWrK7hwV36zsBMr/wGieO8apv3KSH4xaMrhFpaI4kO7m7d5Q3ClCr9phxRUHP7dbC/8rjbyOo6i/+IAXXqRyerK6/bwkHW1HWdiqcp6owIL21W12xzXyQyJJYPEx+azAqsE1N7Twg5l5nf+XG3l9XV1SOyQQ3L9Hp3cYbgX0eqvF5mklfdRtAk5a09pZOlVJYp1VfGFbB+hmV/3TZWV8be/tRlhgGVaVqzWbMEBlSvzzW4PmrYy+ATD+bpE7M4xeoa4BOPFcyvq06PhNW1EpDV1dUQLcP0Kr7bOT9GfCjAJPo+xatt4IwZTZ/+KMuU6ifhKlg/hUflw0zrxmS6layuzE68gAHV9j7jiA1WabY2iCup98CIOk1yuyGsrgt1mg5zbhqrqxvT6yJWV1dD5PVQ+TG9cizFMkKbGaT2Mxbq7woBhcDmIBCK6VVUKU8ZIf5/mVpztTibo6aSRCGgENhkBAIzveaIs2YnqMlpz9TllHqtTdZTyaYQUAhsMAKBmV55x23tvR2XoxZng3VWoikEFAIbhsD/AVlCH4Y4NiGXAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
Hence, the ratio of current sensitivities is 1.4.
b) Voltage sensitivity is given by,
For M1,
![](data:image/png;base64,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)
⇒
…(3)
For M2
![](data:image/png;base64,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)
⇒
…(4)
By dividing equation 3 by 4, we get
⇒ ![](data:image/png;base64,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)
Hence, the ratio of voltage sensitivity of M1 and M2 is 1.
Question 11.In a chamber, a uniform magnetic field of 6.5 G (1 G = 10–4 T) is maintained. An electron is shot into the field with a speed of 4.8 × 106 m s–1 normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. (e = 1.5 × 10–19 C, me = 9.1 × 10–31 kg)
Answer:Given:
Magnetic field strength, B = 6.5 G = 6.5 × 10-4T
Initial velocity of electron = 4.8 × 106 ms-1
Angle between the initial velocity of electron and magnetic field, θ = 900
![](data:image/png;base64,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)
Force on the electron,
Fe = e × V × B × sinθ …(1)
Where,
e = charge on electron
V = velocity of electron
B = Magnetic field strength
θ = angle between direction of velocity and magnetic field
By putting the values in equation (1), we get
⇒ Fe = 1.6 × 10-19 C × 4.8 × 106 ms-1 × 6.5 × 10-4T × sin 90
⇒ Fe = 4.99 × 10-16N
This force serves as the centripetal force, which explains the circular trajectory of the electron.
Centripetal force Fc = mv2/r …(2)
By equating equation (1) and equation (2) we get,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
r = 4.2 cm.
Hence the radius of the path of electron shot into the magnetic field is 4.2 cm.
Question 12.In Exercise 4.11 obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.
Answer:Given:
Magnetic field strength, B = 6.5 G = 6.5 × 10-4 T
Initial velocity of electron = 4.8 × 106 ms-1
Angle between the initial velocity of electron and magnetic field, θ = 900
We can relate the velocity of the electron to its angular frequency by the relation,
V = rω …(1)
Where,
V = velocity of electron
r = radius of path
ω = angular frequency
![](data:image/png;base64,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)
We understand that, magnetic force on the electron is equal to the centripetal force on it, hence we can write,
Fe = Fc
e × V × B = mV2/r …(2)
From equation (2) we can write,
⇒ eB = mV/r …(3)
Now, by putting value of V from equation (1) in equation (3)
![](data:image/png;base64,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)
⇒ e × B = m × ω …(4)
We know that, ω = 2πν
Putting in equation (4), we have
…(5)
Now, by putting the values in equation (5) we get,
⇒ ![](data:image/png;base64,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)
⇒ v = 18.2 × 106Hz
Hence, the frequency of rotation is 18.2 × 106Hz.
Note: The frequency of rotation is independent of the initial velocity of the electron.
Question 13.A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field lines make an angle of 60° with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.
Answer:Given:
Number of turns in the coil, n = 30
Radius of coil, r = 8 cm
Current through the coil, I = 6.0 A
Strength of magnetic field = 1.0 T
Angle between the direction of field and normal to coil, θ = 60°
We can understand that the counter torque required to prevent the coil from rotating is equal to the torque being applied by the magnetic field.
Torque on the coil due to magnetic field is given by,
T = n × B × I × A × sinθ …(1)
Where,
n = number of turns
B = Strength of magnetic field
I = Current through the coil
A = Area of cross-section of coil
A = πr2 = 3.14 × (0.08 × 0.08) = 0.0201m2 …(2)
θ = Angle between normal to cross-section of coil and magnetic field
Now, by putting the values in equation (1) we get,
⇒ T = 30 × 6.0T × 1A × 0.0201m2 × sin60°
T = 3.133 Nm
Hence, the counter torque required to prevent the coil from rotating is 3.133 Nm.
Question 14.Would your answer change, if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)
Answer:From equation (1) we can understand that, torques depends on the total area of cross-section and has no relation with the geometry of cross-section. Hence, the answer will remain unaltered if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area.
A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?
Answer:
Given:
Number of turns, n = 100
Radius of coil, r = 8 cm
Current through the coil, I = 0.40 A
Magnitude of magnetic field at centre of coil, B = ?
Using Biot Savart law, we find that magnetic field at the centre of a coil is given by,
…(1)
Where,
B = Magnetic field strength
n = total number of turns
I = current through the coil
μ0 is the permeability of free space.
μ0 = 4 × π × 10-7 TmA-1
r = radius of coil
Now, by putting the values in equation (1), we get
⇒ |B| = 3.14 × 10-4T
∴ Magnitude of magnetic field at the centre of the coil is 3.14 × 104T.
Question 2.
A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?
Answer:
Given:
Current through the wire, I = 35 A
Distance of point P from the wire, d = 20 cm
Using Biot Savart law we can find magnetic field at a distance d from a current carrying conductor.
It is given by:
…(1)
Where,
B = Magnetic field strength
I = current through the coil
�0 is the permeability of free space.
�0 = 4 × π × 10-7 TmA-1
d = distance of point P
By plugging the values in the equation (1), we get
⇒
⇒ |B| = 3.5 × 10-5T
In this case the magnetic field at 20 cm away from a current carrying conductor is found to be 3.5 × 10-5T.
Question 3.
A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.
Answer:
Given:
Current through the wire, I = 50 A (North to South)
Distance of point P East of the wire, d = 2.5 m
Using Biot Savart law we can find magnetic field at a distance d from a current carrying conductor.
It is given by:
…(1)
Where,
B = Magnetic field strength
I = current through the coil
�0 is the permeability of free space.
�0 = 4 × π × 10-7 TmA-1
d = distance of point P
By plugging the values in the equation (1), we get
⇒ |B| = 4 × 10-6T
Direction of magnetic field,
The point is in a plane normal to the wire and the wire carries current in north to south. Using Right hand thumb rule we can conclude that the direction of magnetic field is vertically upwards, or out of the paper.
The magnitude of the magnetic field is 4 × 10-6T and its direction is upwards or out of paper.
Question 4.
A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?
Answer:
Given:
Current through the wire, I = 90 A (East to West)
Distance of point P below the wire, d = 1.5 m
Using Biot Savart law we can find magnetic field at a distance d from a current carrying conductor.
It is given by:
…(1)
Where,
B = Magnetic field strength
I = current through the coil
�0 is the permeability of free space.
�0 = 4 × π × 10-7 TmA-1
d = distance of point P
By plugging the values in the equation (1), we get
⇒
⇒ |B| = 1.2 × 10-5T
Direction of magnetic field,
We know that wire carries current in east to west direction. Using Right hand thumb rule, we can conclude that the direction of magnetic field is from north to south as indicated in the figure.
The magnitude of the magnetic field is 1.2 × 10-5T and its direction is from north to south.
Question 5.
What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30° with the direction of a uniform magnetic field of 0.15 T?
Answer:
Given:
Current through the wire, I = 8A
Strength of magnetic field = 0.15T
Angle between direction of magnetic field and current, θ = 30°
Force on a current carrying conductor of length L carrying current I, due to a uniform magnetic field of strength B is given by,
F = IL × B …(1)
In the equation we assume length to be unity (L = 1) to calculate the force per unit length.
From equation (1) we have,
F = IB×sin(θ) …(2)
Now by putting the values in equation (2), we get
F = 8A × 0.15T × sin30°
⇒ F = 0.6 Nm-1
Hence, the magnitude of force per unit length of the wire is 0.6 Nm-1
Question 6.
A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?
Answer:
Given:
Current through the wire, I = 10A
Strength of magnetic field inside the solenoid = 0.27T
Angle between direction of magnetic field and current, θ = 90°
Length of the wire = 3 cm
Force on a current carrying conductor of length L carrying current I, due to a uniform magnetic field of strength B is given by,
F = IL × B …(1)
Now by plugging the values in the equation (1), we get,
F = 10A × 0.03m × 0.27T × sin90°
⇒ F = 8.1 × 10-2 N
Hence, the magnitude of force per unit length of the wire is 8.1 × 10-2 N.
Note: The direction of magnetic field inside the solenoid is parallel to its axis.
Question 7.
Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.
Answer:
Given:
Current in wire A, IA = 8.0 A
Current in wire B, IB = 5.0 A
Distance between the conductors A and B, d = 4 cm
Length of conductor on which we have to calculate force, L = 10cm
Intuitively we can break the problem into two parts,
1) the magnetic field due to wire A, at a distance d.
2) Then we introduce a current carrying conductor B, at distance d and find the force on it due to field created by wire A.
1) Field at distance d due to current IA in conductor A is given by,
…(1)
Where,
B = Magnetic field strength
I = current through the coil
�0 is the permeability of free space.
�0 = 4 × π × 10-7 TmA-1
d = distance of point P
By plugging the values in the equation (1), we get
⇒ |B| = 3.18 × 10-6T
2) Force on a current carrying conductor due to a magnetic field is given by
F = B × IB × L …(2)
Now by putting the values in equation (2) we get,
F = 3.18 × 10-6T × 5A × 0.1 m
⇒ F = 2 × 10-5N
So, the force on the 10 cm section on wire A is 2 × 10-5N. Since the current is flowing in the same direction the force will be attractive in nature.
Note: The force will be same on both the wires, we can use Newton’s third law of motion to such conclusion.
Question 8.
A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.
Answer:
Given:
Length of solenoid, L = 80cm
Number of turns = number of layers × number of turns per layer
Number of turns, n = 5 × 400 = 2000
Radius of solenoid, r = Diameter/2 = 0.9 cm
Current through the solenoid = 8.0A
We know that, magnetic field strength near the centre of solenoid is given by,
…(1)
Where,
B = Magnetic field strength
n = total number of turns
I = current through the coil
�0 is the permeability of free space.
�0 = 4 × π × 10-7 TmA-1
r = radius of coil
Now, by plugging the values In equation (1), we get,
⇒ |B| = 2.512 × 10-2T
Hence the magnetic field strength at the centre of the solenoid is 2.512 × 10-2T.
Question 9.
A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30° with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?
Answer:
Given:
Length of side of square, L = 10 cm
Number of turns, n = 20
Current through the square coil, I = 12 A
Angle between the normal to the coil and uniform magnetic field, θ = 30°
Magnitude of magnetic field, B = 0.80 T
The torque experienced by the coil in a magnetic field is given by,
T = n × B × I × A × sin(θ) …(1)
Where,
n = number of turns
B = Strength of magnetic field
I = Current through the coil
A = Area of cross-section of coil
A = L2 = 0.1 × 0.1 = 0.01m2 …(2)
θ = Angle between normal to cross-section of coil and magnetic field
Now by plugging the values in equation (1), we get
T = 20 × 0.80T × 12A × 0.01m2 × sin30°
⇒ T = 0.96 Nm
∴ the magnitude torque experienced by the coil is 0.96 N-m.
Hence the torque experienced by the square coil is 0.96 Nm.
Question 10.
Two moving coil meters, M1 and M2 have the following particulars:
R1 = 10Ω, N1 = 30,
A1 = 3.6 × 10–3 m2, B1 = 0.25 T
R2 = 14Ω, N2 = 42,
A2 = 1.8 × 10–3 m2, B2 = 0.50 T
(The spring constants are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M2 and M1.
Answer:
Given:
For moving coil meter M1
Resistance of wire, R1 = 10Ω
Number of turns, N1 = 30
Area of cross-section, A1 = 3.6 × 10-3 m2
Magnetic field strength, B1 = 0.25 T
For moving coil meter M2
Resistance of wire, R2 = 14Ω
Number of turns, N2 = 42
Area of cross-section, A2 = 1.8 × 10-3 m2
Magnetic field strength, B2 = 0.50 T
Spring constant, K1 = K2 = K
a) Current sensitivity is given by,
For M1,
…(1)
By putting the values in equation 1, we have
⇒
For M2
…(2)
By putting the values in equation 2, we have
⇒
Now finding the ration of I1 and I2
⇒
Hence, the ratio of current sensitivities is 1.4.
b) Voltage sensitivity is given by,
For M1,
⇒ …(3)
For M2
⇒ …(4)
By dividing equation 3 by 4, we get
⇒
Hence, the ratio of voltage sensitivity of M1 and M2 is 1.
Question 11.
In a chamber, a uniform magnetic field of 6.5 G (1 G = 10–4 T) is maintained. An electron is shot into the field with a speed of 4.8 × 106 m s–1 normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. (e = 1.5 × 10–19 C, me = 9.1 × 10–31 kg)
Answer:
Given:
Magnetic field strength, B = 6.5 G = 6.5 × 10-4T
Initial velocity of electron = 4.8 × 106 ms-1
Angle between the initial velocity of electron and magnetic field, θ = 900
Force on the electron,
Fe = e × V × B × sinθ …(1)
Where,
e = charge on electron
V = velocity of electron
B = Magnetic field strength
θ = angle between direction of velocity and magnetic field
By putting the values in equation (1), we get
⇒ Fe = 1.6 × 10-19 C × 4.8 × 106 ms-1 × 6.5 × 10-4T × sin 90
⇒ Fe = 4.99 × 10-16N
This force serves as the centripetal force, which explains the circular trajectory of the electron.
Centripetal force Fc = mv2/r …(2)
By equating equation (1) and equation (2) we get,
⇒
⇒
r = 4.2 cm.
Hence the radius of the path of electron shot into the magnetic field is 4.2 cm.
Question 12.
In Exercise 4.11 obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.
Answer:
Given:
Magnetic field strength, B = 6.5 G = 6.5 × 10-4 T
Initial velocity of electron = 4.8 × 106 ms-1
Angle between the initial velocity of electron and magnetic field, θ = 900
We can relate the velocity of the electron to its angular frequency by the relation,
V = rω …(1)
Where,
V = velocity of electron
r = radius of path
ω = angular frequency
We understand that, magnetic force on the electron is equal to the centripetal force on it, hence we can write,
Fe = Fc
e × V × B = mV2/r …(2)
From equation (2) we can write,
⇒ eB = mV/r …(3)
Now, by putting value of V from equation (1) in equation (3)
⇒ e × B = m × ω …(4)
We know that, ω = 2πν
Putting in equation (4), we have
…(5)
Now, by putting the values in equation (5) we get,
⇒
⇒ v = 18.2 × 106Hz
Hence, the frequency of rotation is 18.2 × 106Hz.
Note: The frequency of rotation is independent of the initial velocity of the electron.
Question 13.
A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field lines make an angle of 60° with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.
Answer:
Given:
Number of turns in the coil, n = 30
Radius of coil, r = 8 cm
Current through the coil, I = 6.0 A
Strength of magnetic field = 1.0 T
Angle between the direction of field and normal to coil, θ = 60°
We can understand that the counter torque required to prevent the coil from rotating is equal to the torque being applied by the magnetic field.
Torque on the coil due to magnetic field is given by,
T = n × B × I × A × sinθ …(1)
Where,
n = number of turns
B = Strength of magnetic field
I = Current through the coil
A = Area of cross-section of coil
A = πr2 = 3.14 × (0.08 × 0.08) = 0.0201m2 …(2)
θ = Angle between normal to cross-section of coil and magnetic field
Now, by putting the values in equation (1) we get,
⇒ T = 30 × 6.0T × 1A × 0.0201m2 × sin60°
T = 3.133 Nm
Hence, the counter torque required to prevent the coil from rotating is 3.133 Nm.
Question 14.
Would your answer change, if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)
Answer:
From equation (1) we can understand that, torques depends on the total area of cross-section and has no relation with the geometry of cross-section. Hence, the answer will remain unaltered if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area.
Additional Exercises
Question 1.Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.
Answer:Here we have to find total magnetic field produced by the system so we will first find magnetic field due to each coil with direction and then add them in accordance with vector addition. Using the Right-hand thumb rule we can predict the direction of induced magnetic field in both the coils.
The orientation of both the coils is shown below in the figure.
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)
The direction of induced magnetic field in both the coil can be found with the help of Right Hand Thumb Rule.
As Shown in figure.
![](data:image/jpeg;base64,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)
So magnetic field in Coil X would be towards East, and in Coil Y would be towards West,
Explanation: if we curl our fingers in the Anticlockwise Sense in as in case of coil x our thumb will show the direction of the magnetic field which is towards East and if we curl our fingers in the clockwise Sense in as in case of coil Y our thumb will show the direction of the magnetic field which is towards West
The magnitude of magnetic field in a coil is given by the formula ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEgAAAAgCAMAAACGlM5CAAAAAXNSR0IArs4c6QAAAHtQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6Ojo6Oma2OpCQOpC2OpDbZgAAZgA6ZjoAZrbbZrb/kDoAkDo6kGYAkLbbkNv/tmYAtpA6ttv/tv/btv//25A627Zm27aQ29u22////7Zm/9uQ/9u2/9vb//+2///b9gC85wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABX0lEQVRIS9WV21KDMBCGsyBQxTYieEhVUAIm7/+E7iYtgkQhoTfuRYcZZj/+f09l7B9Ht4MDYzXEbz9N4JvUx5gkhn4o5zkyevYC3VYZghw5cq7yL7DMJJQGJBBYoc9zeIOYiF8vA1J8fxkQk9HNyFpfQES197eGpaEGibTt+cHUqaE6U9d0BRRR3i410M5Rd00ggPwIOT0rXjI7R4pnjOkj4O/qEHaWziCbp3E4CJcuSvr+jrCtV2jPWJuAvBTtbW5XQDLMp1H0+ZjMNmi10UERFTt9GedhMU/hsURGkRbLGQPc+RBWbKdr2zVdjRc43Jpn+52K7EAKmtpNcVqRq/tNlC3JuGCrVvT3b3wUuLL4mm7H+y68IuruiTU0dQSaHNwAf+aWEMgQN0RNhiTWKJlsljexoRKRop5GJzxqwzHWanD8Xa4lS+RIzKdDrXgcbE5x2n57qFuU5HNZ12j9AowNGni67SQNAAAAAElFTkSuQmCC)
Where, B is the magnetic field
I is the current in the coil
R is the radius of coil in metres
N is the number of turns
is the permittivity of free space = 4π × 10-7 TmA-1
For coil X
Current in the coil, Ix = 16A
Radius of the coil, Rx = 16cm = 0.16m
No. of turns of Coil, N �x = 20
So magnetic field due to coil X, Bx = ![](data:image/png;base64,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)
= 4π × 10-4 T
= 1.25
10-3 T (Towards East)
For coil Y
Current in the coil, Iy = 18A
Radius of the coil, Ry = 10cm = 0.10m
No. of turns of Coil, N �y = 25
So magnetic field due to coil Y, ![](data:image/png;base64,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)
= 9π × 10-4 T
= 2.82 × 10-3 T (Towards West)
So, the Resultant magnetic field of the system = By- Bx
(since fields are in opposite directions)
= 2.82 × 10-3 T- 1.25
10-3 T
= 1.57 × 10-3 T (Towards West)
So net magnetic field of the system is B = 1.57 × 10-3 T, Towards West direction
Question 2.A magnetic field of 100 G (1 G = 10–4 T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10–3 m2. The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns m–1. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.
Answer:Here, we have a particular value of No. of turns per unit Length and Current in the coil in order to obtain the given magnetic field.
The Required Magnetic field B = 100 G = 100 × 10–4= 10–2 T
Maximum Number of turns per unit length, n = 1000/m
Maximum Current flowing in the coil, I = 15 A
Permeability of free space, μ0 = 4π × 10–4TmA-1
We know magnetic field for a solenoid is given by
B = 𝜇 �0nI
Where,
B is the magnetic field
n is the Number of turns of the coil per unit length
I is the current in the coil
𝜇 �0 is the permittivity of free space
Explanation: here we can change the number of turns per unit length n (maximum 1000 turns per m) and current I (maximum 15A) since 𝜇ois a constant and we have to obtain a fixed value of magnetic field B = 10-2T, so we will alter values of n and I accordingly
Using the formula B = 𝜇 �0nI
We get, B/𝜇 �0 = nI
So, ![](data:image/png;base64,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)
= 7957.74 A/m ≈ 8000 A/m
If we take number of turns of coil N = 400,
If we take length of the coil L = 50 cm = 0.5m,
No. of turns per unit length, n = N/L
= 400/0.5 = 800/m
(less than 1000/m)
If we take current I = 10 A
(less than 15 A),
We get nI = 8000 A/m
Area of Coil A = 10-3 m2 = πr2, where r is radius of coil
We get ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ r = 0.017m
The values of N, L and I are within the proposed limits, Though there can be other values as well.
Question 3.For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by,
![](data:image/png;base64,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)
(a) Show that this reduces to the familiar result for field at the centre of the coil.
(b) Consider two parallel co-axial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by,
, approximately.
[Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.]
Answer:We know for a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by,
![](data:image/png;base64,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)
𝜇 �0 is the permittivity of free space
As can be seen in the figure.
![](data:image/jpeg;base64,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)
(a) To find the magnitude of magnetic field B at the centre of a circular coil.
Distance from centre, x = 0 m (as we are finding magnetic field at the centre of coil)
No. of turns of coil N = 1
Putting these values in equation
,
we get,
![](data:image/png;base64,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)
Or ![](data:image/png;base64,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)
Or ![](data:image/png;base64,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)
This is same as the known result for magnetic field of a current carrying loop at the centre.
(b) The situation has been represented in the figure, suppose two circular loops of equal Radius R carry equal current I in same direction, and are also separated by a distance R,
Now suppose a point at a distance d from midpoint of separation of the coils,so distance from one coil, ![](data:image/png;base64,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)
And distance from second coil,
x1
![](data:image/jpeg;base64,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)
Magnetic field due to 1st coil is given by ![](data:image/png;base64,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)
Magnetic field due to 2nd coil is given by ![](data:image/png;base64,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)
Net magnetic field due to both the coils is given by B = B1 B2
Explanation: Using Right hand thumb rule if curl our fingers in the direction of current the thumb shows the direction of the magnetic field,we find that magnetic field due to both coil is in same direction so their magnitude can be simply added to give net magnetic field
So we get,
![](data:image/png;base64,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)
Putting the values of x1 and x2 we get
![](data:image/png;base64,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)
i.e.
![](data:image/png;base64,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)
i.e. ![](data:image/png;base64,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)
Expanding equations of second order we get
![](data:image/png;base64,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)
i.e.
![](data:image/png;base64,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)
Since d is very small compared to R so neglecting
and taking terms of R2 common from both the terms we get
![](data:image/png;base64,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)
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)
Explanation: we have used the binomial expansions
and
![](data:image/png;base64,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)
Where x = 4d/5R and we have neglected second terms onwards because d<<R
So d2/R2 ≈ 0
![](data:image/png;base64,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)
i.e. ![](data:image/png;base64,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)
So ![](data:image/png;base64,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)
Solving and putting value of
= 0.72
We get
![](data:image/png;base64,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)
Hence proved the required result
Question 4.A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound.
If the current in the wire is 11 A, what is the magnetic field
(a) outside the toroid,
(b) inside the core of the toroid, and
(c) in the empty space surrounded by the toroid.
Answer:The Toroid is same as a solenoid but is bound in a circular region as compared to straight cylindrical region in a solenoid the length of a toroid is given by L = 2πR, (Perimeter of a Circle)
where R is mean radius of cross section of toroid
= 25.5 cm = 0.255 m
here Total number of turns of toroid N = 3500,
no. of turns per unit length n = N/L =
= 2475.74/m
the current flowing in Toroid I = 11 A
The toroid has been shown in the following figure
![](data:image/png;base64,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)
(a) Since Toroid is same as a solenoid so magnetic field outside the toroid = 0 T same as in case of solenoid.
Explanation: if we apply Ampere Circuital Law
to find magnetic field B at small element dl due to a current carrying conductor with current I flowing through it and
is permittivity of free space, outside the solenoid or toroid, where there is no conductor/wire/current carrying loop, the current I = 0 so we get
So Integrating over length l we get Bl = 0 so magnetic field B = 0 i.e. at all places where there is no current carrying loop magnetic field B = 0
(b) The magnetic field in the inner core of toroid is given by
B = 𝜇onI
Where n is no. of turns per unit length,
I is the current flowing in Toroid,
𝜇o is the permittivity of free space =
TmA-1
So putting all values, B =
=
T
i.e. Magnetic field inside core is 0.03 T.
(c) Again it’s the same case as of exterior of a solenoid as explained above so magnetic field is Zero, here also in the empty space between the toroid.
Question 5.Answer the following questions:
A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
Answer:When a charged particle enters a magnetic field it experiences a force known as Magnetic Lorentz Force which is given by:
![](data:image/png;base64,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)
Where
is the force on the Charged particle having charge q,moving with a velocity
in a magnetic Field ![](data:image/png;base64,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)
Note:
,
and
are vector quantities, and charge q is a scalar quantity, and
is the cross product or vector product of
and
,so resultant is perpendicular to plane containing
and![](data:image/png;base64,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)
if we evaluate the formula we get,
![](data:image/png;base64,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)
Where,
and
are magnitude of velocity and magnetic field respectively, θ is the angle between Velocity of particle and magnetic field and ŵ is a unit vector perpendicular to plane containing
and ![](data:image/png;base64,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)
When angle between Velocity of particle and magnetic field
is either
or
i.e. particle is either moving parallel or antiparallel to the field we can see force on the particle,
F = 0 N, since sinθ = 0 when θ is either 00 or 1800,
The particle came out of the magnetic field un-deflected, and with constant velocity i.e. it did not experience any force so we can say that particle was moving in same direction as that of magnetic field i.e. from East Towards West or in opposite direction from West towards East and magnitude of velocity can be any value.
The following figure depicts both the situations
![](data:image/jpeg;base64,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Question 6.Answer the following questions:
A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
Answer:When a charged particle enters a magnetic field it experiences a force known as Magnetic Lorentz Force which is given by
![](data:image/png;base64,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)
→ ![](data:image/png;base64,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)
Now, due to magnetic lorentz force, the particle accelerates so the velocity of particle changes, Magnetic field changes is both magnitude and direction so the Magnitude of Force on particle also keeps on changing, hence the velocity of particle also changes.
Note: Acceleration is Rate of Change of Velocity, so if a particle experiences force, it accelerates and hence its velocity changes. Velocity is a vector quantity so it depends on direction, so velocity of a particle changes if its magnitude or speed changes, direction remain the same, or velocity changes when direction of particle changes and magnitude of velocity or speed remains same, or velocity changes when both speed and direction changes.
In this Case force on the particle is always perpendicular to its velocity, which only changes the direction of the particle and its speed remains same, i.e. velocity of particle changes due to change in direction of particle and magnitude of velocity or speed same as it entered.
Following Figure depict the direction of force on particle at any instant
![](data:image/jpeg;base64,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Question 7.Answer the following questions:
An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.
Answer:If the Charged particle have to go undeflected then there should be no force experienced by it, or resultant of all the forces on the particle is zero. Here, the charged particle is experiencing Magnetic Lorentz force and electrostatic force due to electric field
We know Magnetic Lorentz Force is given by
![](data:image/png;base64,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)
Direction of the Magnetic force is perpendicular to plane containing V and B. and for a positively charged particle can be found out with help of Fleming’s left hand thumb rule.
Electrostatic force is given by
F = qE
Where F is the force experienced by particle having charge q and moving in an electric field E, direction of force is same as that of Electric field for a positively charged particle and is exactly reversed in case of negatively charged particle.
So both the forces on particle should be equal in magnitude and opposite in direction.
Since Electric Field is from North to South, and particle is an electron i.e. negatively charged so force on it should be towards North so force due to magnetic field should be towards south .As shown in figure
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Using the Fleming left hand rule we will decide the direction of magnetic field
Flemings rule : If the stretch our forefinger middle finger and thumb mutually perpendicular to each other then if forefinger depicts the direction of magnetic field, middle finger depicts the direction of the current(Direction of Velocity of Positive Charge) then, Thumb depicts the direction of Force.
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)
Applying the rule
Since Electron is negatively charged and moving from West to east so direction of current is from east to west, depicted by middle finger, force should be towards both depicted by our thumb, so we find our forefinger depicting magnetic field is in a direction vertically downwards in the plane
Now equating magnitude of both the forces
![](data:image/png;base64,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)
Here θ = 90° because Velocity of particle is perpendicular to Magnetic field,
So,
sinθ = 1
i.e. ![](data:image/png;base64,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)
or magnitude of magnetic field is given by
, in a direction vertically downwards.
Question 8.An electron emitted by a heated cathode and accelerated through a potential difference of 2.0 kV, enters a region with uniform magnetic field of 0.15 T. Determine the trajectory of the electron if the field
(a) is transverse to its initial velocity,
(b) makes an angle of 30° with the initial velocity.
Answer:When an charged particle having charge q is accelerated by a potential difference V volts it gain kinetic energy given by
K = Vq, which imparts it with velocity
We know kinetic energy of a Particle with mass m kg and velocity v is given by
![](data:image/png;base64,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)
Equating both equations
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGIAAAAqCAMAAAB/cH49AAAAAXNSR0IArs4c6QAAAJBQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6Ojo6OjpmOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZjqQZpCQZpDbZrbbZrb/kDoAkGYAkGY6kLbbkNv/tmYAtmY6ttu2ttv/tv//25A625Bm27Zm27aQ29uQ29u22////7Zm/9uQ/9u2//+2///b1prlzQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABvUlEQVRYR+1Wa1cCIRBltIdblmvawy2jB2kJLv//3zUzoLakLrvFOZ2T8wFNYO7MvRdIiH8d8/Fj2v6XI+i+JoUwFy8qMQTWf4CIFPFA1B8iqpP2dNuHDACObvd3/DECuIwkpd2ycjgVs8S9YmXmDOksABDJ4keKS0cNiAHJvdjiZNGOj327Zk4KDRMcy5zGXw7lxS7zHgExTYY8cN8MTANM3jK0Dg/E+OnCZES7RgRNyRxFkkgz2YDWNIPAXf1HoaA/FYpVpXRUcZmjsV0ymiiHJIjk2QqEpGUcO+1nMkxD1eGA3yidcDKvg2Y1JS9z10ptF2tYoCQegnE8mKt4E9Qa8xQNUXVFAEHpNMn7NVT3+YrE3gYRT9SqC9JBhkSY7JxRbcHeai73hiPn/5vr8IytTaQ6U7EcN4Xgmrzc7jBDVWz+zZ9s+4TH4r1e7sAt6Ew8CH4gHuquoghHCTvHM3rc+sGIgZBwJ5Z5XbGBqzZ/6i1Mhosl+UI1FW2VBa+cyK2Nrbezq50TsjVRsVgxmsXm2r7OFt/N/7OM4W53EyQN2UvwDldvTn5ZUlLF/7tYfgFShb/iU0KkKr1t3k+dDyZhYOT2bgAAAABJRU5ErkJggg==)
We get velocity of the particle as
![](data:image/png;base64,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)
Here Potential difference of the particle, V = 2.0 kV
= 2000 V
Particle is electron, charge of electron
q = 1.6 × 10 -19 C
mass of electron
m = 9.1 × 10-31 Kg
so velocity of the particle,
m/s
Solving we get
Velocity of particle,
v =
m/s
(a) Now here the particle enters the magnetic field orthogonally so it will experience Lorentz magnetic force is given by :
![](data:image/png;base64,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)
Where
is the force on the Charged particle having charge q, moving with a velocity
in a magnetic Field ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Where,
and
are magnitude of velocity and magnetic field respectively, θ is the angle between Velocity of particle and magnetic field and ŵ is a unit vector perpendicular to plane containing
and ![](data:image/png;base64,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)
Here,
since particle entered orthogonally now force on particle will be perpendicular to both magnetic field and its velocity at every instant, since magnetic field and velocity are in one plane and force is in a plane perpendicular to them, this force does not change the magnitude of velocity or speed it only changed it the direction of particle and force always act tangentially to the velocity of the particle causing it to move in a circular trajectory
As shown in the figure
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwkHBgoJCAkLCwoMDxkQDw4ODx4WFxIZJCAmJSMgIyIoLTkwKCo2KyIjMkQyNjs9QEBAJjBGS0U+Sjk/QD3/2wBDAQsLCw8NDx0QEB09KSMpPT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT3/wAARCAEZAWwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2aiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAopGztOOuK4E6H463kjWYsZOPn7f981tSpKpe8kvUTdjv6K8U8D6l408TXOqRR60zGzkCHzGA6lumB7V1v9m+ObP/SP7QiufK+byd2d/t0H865nNqVrNndSwkakFN1Yryd7/kd9RXn8mveN4Ymkk0mIIgLMdmcD/vqsqT4i6/Coaa3gjU8AvAyj9TRGTl8MW/kzR5bNb1If+BI9VorzGx+KN6m/7ZaQzg42+WdmP55rQT4lXMiB49CndD0ZWJH57aJTUNJpr1TEsrxEvgtJd1Jf5nfUVwX/AAsi7/6AFz+Z/wDiatp8S9NjiQX1reW85GWj8vOPoTjNT7aHcJZXi19i/o0/yOyorjv+Fn6H/du/+/Y/xp8XxM0KSVEJuUDEDc0YwvueaftYdyf7Nxf/AD7f3F/Q/GOn65eS2sW+GdCcJLgb8dcVv15v4lHhq9U32j6nb2upRt5gZMgSH8uDWx4U8c2+p28dtqUiwXwIQFuBL7j0NRCrryyZ0YnL26ftqEWl1TWq/wA0dhRRWMl3fReJTaXM0P2WSMyQgR4Y4/hznqK2bsebCm53t0VzZoqpm5Op4WaP7ME+aPZ82exzn+lPkliuopoobkBwCCYnG5P8KL6C5NixRWVod2f7GSW8uNxVmUySsBnnAya0ftEPk+d5sfldd+4bfzoTTVxzpuEnHtoSUVTur9YoYnt/LnMjhVxIAPc59qX+1LIXEsDXMSyRYDhnAwTRdC9nNq9i3RUH221wp+0w4Y4B3jmnyzxQJvmkSNem52AFO5PK+xJRWPq92DPZWqXoto7gsWlRwGwBkYJ9a1Yk8uJF3s+BjcxyT7mkne5cqbjFSfUfRRRTMwooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooA8k+CX/IU8Uf8AXwv/AKE9et15J8Ev+Qp4o/6+F/8AQnr1ugAqKe2hukCXEMcqA5CyKGGfxqWihOwHO6h4F0PUDM7WghmlH+siJUqfUDp+lc8fBniLRJVfQdUMkYZgsTttCqfUHIJ/CvQ6K6YYurBWvddnqS4JnA2vxEurC7Nt4k017Zv78angY7g9c+1dZbSaRrsYuYVtLsfd3lFYj25+tWL/AE201S3MN7BHMh6BhnBxjI9DXD6l4Au9Kke+8M3ssTqCfJLckcfKD36d60th6+nwP8P+AClOGqZ239kad/z4Wv8A35X/AAo/sjTv+fC1/wC/K/4Vy+g+P0ln+w6/CbG8BVVLKQGyO/8AdP6c12dc1WhKk7TRoq03tJnPt4F8PEljp6cnJ+dv8a4m50mx1fxaml6DbQwRW7bpJw5YPggn8umPrXqk0SzwvFIMo6lWAPY8VleHvDdr4cgmitiXMjlt7gbgOy57gVyzpJtJLQ9PDZjOlGUpzblsk27evyNisfxHA/2SK9gVjPZyCVdoySv8Q/LNbFFayV0edSn7OakZkonl0W4lgU/aJ4yyjoRkcCsHQZdJtolne+f7QsXzxyIEaMjht20DP45rsaTaPQflUuGtzaGIUYSg1v2/LZnHWl3YvBZSTtHLYIzrLuBKq55G4GkZYIClw0ROim6LYAymCOG2/wB3NdltGMYGKMDGMcVPszX64r3Sf3/8DfzOS1KXQl09WtDCsZuFYMqnaG77fTtnFWFOkf25eC+jti1yY2hMkYO8FRyDj1rpdo9B+VNkDeW3lhPMA+Xd0zT5CfrSty6/f6eXkc7pOmW3nf2fLaRH+z5CyMYwQVb7v4/4VPqz2sGrxPqqxmxaIqhkXcivnuOmcdK09Pt54IWN3IklxIxZ2QYHsB7CrRAPUZp8miJniP3jk9fn97XzOLjbTre609L0QiLzJWjWZd2EP3e3TPSu0GMDHSjaD2FLThHlViK9f2tnbbz87hRRRVHOFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAHknwS/5Cnij/r4X/wBCevW68k+CX/IU8Uf9fC/+hPXrdABRRVPULeadAYJCpTnaO5ppXZMm0rpXLlFUbHUBOPLm+SZeoPem6he7f9GgG6Z+OO1Pkd7E+1jy8xoUVXsoHt7ZUkbc3UnNWKT3LTursyPEPhuz8RWRhuF2SDmOZR8yH+v0riY9Q1r4f34tLoPeaTu3CTBPyn0PY57GvTaiubaG8t5ILmNZIpBtZGHBFdFHEuC5Jq8e3+QnG+qGWF/b6lZx3VnKskMgyrCrFeX6ja6r8PL8T6dI8ukyybijcgH+63p7Gu/0TW7TXtPS6s3yDw6H7yN6Gith+RKpB3i+v+YKV9GaNc7rChdetll1O5tYJY2LBZwi5HTGa6Kue1didet3k0y5uoIo2DFYQ65PTGTXFU2R2YT436P+tRLy0tpPD14VvJb6NfmV5JN+1h6EVoDVbWws7VbmRg7xKQFRnPTqcA4qhc3BbR7mO10i7iVzhYxEAST1O3PA4qjNaF9RivbrSrye3lgVAseVkhZexUMMg0r2enl+p0qmqitUel31V9l8jobrWbGzSNppxiQZXYpckeuADxVa48S2FvPboZGdJ0MiyIjMMD6Cqpaaw1NL6PTp3tp4BH5cSDzIiDkAr6GnyyzQXdnfJp1wIRG6eTEg3rkggle3SnzMyjQp6XV/mt+xaj8S6XIQFuuS23BRgQffI4+pp8ev6dLK8SznegLYKMMgdccc/hWXAJb+bU4zYXdu10MpLLEAMADgnNORri6Nlv0+4haxBZyyDBwuMJzzn8KSnL+v66FPD0l3+9dvTvoaEHiHTbmWKOG53NLwvyMAT6ZxgH2rTrkUNwuiQRvpl75i3PmOojGeuc9a61W3KGwRkZweoqoSbWphiaUab93z6pi0UUVZzBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUjHCk4zgVx/hD4i2XijUrzTpYXsb+CRglvNwzoD1/wB4dxQByvwS/wCQp4o/6+F/9CevW68j+CjKmpeKWYhVWdSSTwBl6ueJvijPe6jBo3gRBfX8jkPNsyi4OMDPB+vTFAHqFFUtGa+bRrNtVVVvzCv2gLjAfHzYxx1qe6837M/kf6zHy0ITdlczNVEUlwiQgm4J52/1pdMZLe7eK4Uicnhj3qxpti1vulmwZW/HH41altoppEkdfnQ5BFauaS5TnjTk37TZ9iRtwRtoBbHAPrWfbX8sU5gvgFYn5W7VpVWvraK4gPmkLtGQ/pURa2ZrUUt4vYnZ1RSzEBRySaoW13Nd37GPP2ZeuRWZ50koSKaZvI3Y3V0EEccUSrEAExxjvVuPItTOE3VemiQlzbQ3ltJb3EayRSDaysOCK86ltbv4cay13bobjR7khX4+ZPQE+ozx616VUN3axXtrLbzorxyKVZWGRV0K/s7xlrF7o2krjbC/t9Ss47q0lWSGQZVh/nrVivN9GuLjwF4jGj3pSSxvH3RzZAIzxuPp6GvR+tLEUfZS913i9mEXcWiiisCgooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACuA+IPw+bWmXW9Bb7LrlsQ6sh2+djtn+96H8DXf0UAfLnhTR9c8T6vd6LZXv2dpSZ7oO5UMVOCTjqfmPFfQXhXwTpPhG0RLC3U3OwLLcsPnk78+nJ6CrNj4T0XTdam1aysI4b6YFXkQkZBxnjOB0HatigAooooAKKKYZUEojLgORkLnmgLj6yLw3F7efZlUiJTyex981r0yWVIU3SMFXpk1UXZmdSPMrN2RE1lC1t5Gz5B09frWeBNpEoJJkt26+1a4YFQwPBGc1xfh3xnN4l8a63oz2kSWNgpVXyWZ2DbSSemD1FNStoxSpp6x0Z2UciTRh42BU9CKfUcMEdvHsiXauc4qSofkaK9tTn/ABloC67ocqJGGuohvhYLlsj+EfXpVDwBrz39i+m3a7LmyAUA53MnTJz3HSofF3xR0fwrObRQ99f4U+RCeBn1bnBxzivNxceKTrdl4wmh/s23uX3COIkCUdwQf7wzyfrSnOVlrornZhlGpGVHkvKVrPz/AMrHvtFQWV3Ff2cNzAwaOVQykHIqemcrTi7MKKKKBBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAVzk3jjTItQnsfI1GS4tziRI7KRseh4HQ10dcT5+rp491pNIt7KXMMBc3MrJj5TjGAaOth9GzqtM1OHVrT7RbrMihipWaMxsCPUHmrlcu99rV3dW+lrNb2F8YDPPKsfmgc4CqDjI96zo9Z8RXEtnDHdWiStcSWk2YcqSvPmA564x8vT3ov/Xzt+Yv6/X8juaK461uPEupTXtvbanZxy6cwjYtbZFw2M88/IO3Gai1DX9fuNdksNLt3/wBEWMTtFGkis7DJBLMCo46gGgDtqoX2necTNCSs45Bz1q3bmUwIbhUWXHzhDkA+1OkkWJC7kBR1Jqk2noRKKkveKFrqilSl18kq8HI61B+91ebulsh/OmGJ9WuWkRRHGowGI5NS2d99kxa3S7SpwGHTFa2trHc5lJyspv3fzLl9LDZ6ZPJNIkUMcR3O5wFGO5rzX4DQSx6BqcrxusctyDG5HD4GDg9+a6b4o6lFp3w+1NpVZhcR+Qu3szcAn2ryvwp4r8SN4RtPD3hGwme5VpTPc7AQu4kgKx4U4OcnvWB2HsXiXxvonhWI/wBpXiCfHy26fNIeCRwOgOOp4rzu41jxr8S7gpoUUuk6I23Ez/IWHIJ3dW7jC+grc0D4RWn2gan4quJNV1GXDyLIf3YbByD/AHuo9OleiQwx20KQwoscUahVRRgADsKAOP8ACHww0XwvDDNJCl5qSgF7iUZAYHOUB+7j168Vv+JNHTW9EntCB5m3dEcDIYdMZ6Z6fjWrRQVGThJSjujgvhtrLGOfRrk/vICWj5J4zhh6YB/nXe14/wCKLWfw34we4tR5SOwnh8vKjHdc+vXP1r1TStQj1XTLe9hIKTIG47HuPwOanl9nL2fzXp/Wh346Kqxji4LSW67SW/37lyiiiqPOCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArBg8Kpb+IZtXTU9Q82cjzIjIvlsB0XG3OB9a3qKOtw6WMrV9Bi1WWGdbm5s7mEELPbMFfaeqnIII4FUZ/BsEjWrQalqFsbYlh5Mije56u2VOSa6OigDBvPCcNxqT39rqF/YXEqBJmtpFAlx0LAgjPuKZdeDrWW+S8s72+sLkRCF5LaQAyqOm7IOSPWtue7htmRZXwWPFSg5GR0p2aEmm7EdvD9nt0i3vJsGN7nLN7mor6zN4iKJNgU5PGc1PLKsMTSPwqjJpIJ0uIhJGSVPTIppte8KSjL3WEECW8QjjHyim3NrHdRlJByeh7ipqKV3e4+VWt0OY1nwwPEmlSaLqhmFoWDrLEwBBHTr2rhYPhB4h8OI1z4c8S7boH5YyhjVs8HPJHT2r2Gihu7uKEeVWPIhN8VvDnyvFb6x53IYDf5eO3G3Gc+/SvVrJ5pLG3e6TZO0amRR/C2OR+dT0UigooooA4P4q2m7S7O+8zAglKbMddw6/pUHgbU30W/bRNRYL54WW3PJBLAHGfpj8c10/jO1N54Tv40h86QR7kULk5B6j9a4Oe0e+8D6Zq9rM0l5p+UlZWJZV3EgZ7Y6/Stq8ebDRqLeLt8nqd+XzUpywtR+7P8JdH+h6xRWb4f1ZNb0a3vFwGdcOAMAMOo/OtKsE7q6OOpCVOThLdBRRRTICiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAgubSK6QiRecYDdxWfDdS6a/kXILR/wADD0rVd1jQs5AUdSaySz6vcbV+W3jPJ7mtIarXYwq6NOPxCsZdWn2rlLZDyfWtSKJIYwkYwo6CsrdNpErAKZLduR7VqQzpcRCSM5U/pRPbTYKNru/xDndY0LuQFHUmmwzJPGHjbcp70skaSoUkUMp6g1lyRy6VP5sWWt2PzL6VMUnp1LnNxd+hr1DHdRSzPEjZdPvDHSqNxqZnRY7MMZH9uVqzY2K2iEk7pW+81NxstRKpzStHYtE4GT0FRw3MVwGMThtpwakIDAgjIPBrLurN7KQXNmMAfeQelKKT0HOUo6paGrUJuohciAt+8IzjFUn1lDBmJSZjwFIp9hYsjG4uCWmbnn+GnyWV5C9pzNKGpZvQWsLhVBLGJgAO/FcT8MooZvD9/ZXKqzGciWF+uMAcj8672vP/AAB/yNXiE9/MP/obV0UdaFRej/EttqSaG6PO/g/xlLpEgA0+8fdExBOCfugHv6GvQq5Px/oTanpS3dqjNd2p3LsHzMvcf1/CtHwnrI1vQYZmP79P3coxjDD29K86HuycPuPWxaWIoxxS32l69H80bdFczpnit9T8W3WmwRK9pEhxMufvDrn+X4V01aRkpbHBWoTotRmrNq/3hRRRVGQUUUUAFFQ3MkkUReMK2OoPp7U9JFkjDqeCM07dRX1sPoqvbzyTSyhlVUQ4HqanzQ1YE0xaKTNFIYtFN3qWK55HUUkbl13FSvPQ0CuPooqosty8siKIfkOMnNNK4N2LdFRI8gKrIg3HOSvQVIecgHmlYE7i0VBau7LIJG3FXIzjFIjOLx0L7k27gMdOadhc2lyxRRRSKCiiigAooooAKKKKACioLsziA/ZgDJ79hUNhfi5XZJ8sy9R61XK7XIc0pcrLFzbrcwmJyQp9KLe2jtYgkY47k9TSXNzHaxF5D9B3NQabLcTxvJP90n5OMcUWfL5Cbjz26lxlDKVYAg9Qaz4rGa0vA1uR5DH5lJ6Vo0UlJoqUFKzCs3UL0k/ZbcB5H4PtWlVO202K3maXJdicjd2pxaWrJqKT0iUWsZtPCXEJ3so+cYrQs76O8BAG1x1U1aqjcWGbqO4gO1ww3gcZFVzKXxEcjp6w27F6qd/fraptXDSt0Hp9auVTOmxNeG4cliTnaemamNr6mlTmtaJRGmTrCLhT/pAO7aP89at2WpLct5ci7Jcd+9X6p39gLpd6fLMvRvWq5lLSRn7N09Yfd3Llee+Am2+J/ETYzhycf8Dau6tmmS1zd7VZc5Oe3rXEfD1TJ4g165QFreSUhJR91vmJ4P0Irooq1Gr6L8zS92mPPxOwSP7EuuD/AHv/AK1cxpPiGTR/Ec93Y2LpFdkqtq5I5PTHqc/zr2KoLixtbt43uLeKV4zlGdASv0rzJUpuz5vwPbo5hhqalFUdJKz95s5D4c2U6jU765BjknnKPEVI2sCSf/Qv0rt6KK1hHljY8/FYh4iq6jVrhRRRVHOFFFFAEU7qkYLMFGR1NQR5jka3H3W+ZD7d6tMqt95QfqKXA9KadkS43dyjvBW7EbrkH17YpII4JJt4REAX7pYHPv1q1LCGQ+Wqgnrx19qi8hpXXfDHGFOcqck+1WmZuLuVl8lbfzFZQwk4O7oM07CyXUhlmVCrfKCOcexq/wCVHjGxcfSlMaNjKKcdMilzh7Ip7Lf7TIZdmSAQWOM1ErR+VGpYGHzCGweB6ZrRaNG+8qn6igRoAQEXB6jFHMN0yO3WJQwhbK5zgHIFVkCS3k485lORgI+M8VeVVUYUAD2FII0ByEUH1xSTKcLpIqOqRXUIDDeFI5PJ44qK0CEiSSYCTPzLjDZ960Cik5Kgn1xQY0JyUXPrinzaEunrczzJGVOXBjM3z4Pb39qlgMKXzCJhgoMAHjr2q2I0AICKAevFARFxhVGOmBRzIOR3uOoooqDUKKKKACiiigAooooAKzNVt0QC5R/LlB7fxVosdqE4zgZxWRbxS6ld+dcIREvRTx+FaQ7mNbVcttWRWp+23iC8cnCjap/irdAwMDpVW8sEu1BB2OvRgKq2t3JaTfZbvp/A5py99XX3Ew/dO0uvU1aKSoLi9htnRJWwX6e3vWaTexu2krssUUgIIyDkGmTzLbxNI+dq+lIG7K5JRUcE63EKypna3TNSUAndXQUUUUDCiiigCrqUiR6ZdNIyooibJY4A4rk/hXG6eHJyyMqtcEqSMAjA6Vo/EC8itPB94soY+eBEuBn5jzz+VWvB1nLYeFLCCYqXEe75TkYYkj9DXXH3cK/N/kR9o26KKK5CwooooAKKKKACiiigBryJEu52Cj1NUkmSOSd0cFcArubjNTXWVkik2llUnIAzj8Krs675yIpAJFGPkPNXFaGU3qW/tMSjDyIGABPNO+0RFwnmLuPQZqojo08WY34TbkoeDTYkWORlmSUtuJGMlTRyoXOy61xEkgRpFDHsTTDeQiRkLgMvrUKFYjJHNEzFmyCFyDThIIZpN6P82CMLmiyHzslS4XyBJI6AHuDxS/aYdqnzFw3Q561UiOwRSFH2oWBG05GfakkGAT5bbXkDABSeKOVXF7R2L0cqSgmNgwHpUBZ1vSDKRGF3EYGKIWH2yXCsAQMEqQKRpAL4na+AmM7TjNCWpTd18yZbmF2CrIpJ6AHrSm4iWTYXUP6VRDAWyfu3DeZk4Q+tSbsT/ug+C2WVk4+uaOVE+0ZYjuFaNpHdNoPUGoYXRr12jclCmfvZGc1EDwWEbkLLuI2kZFEuZZJfKjcF48AlcZp2E5MuxzRykiNwxHXFQ3G/7RGqzMitnIAFNtPLyMJLvx/GDx+NF3sa4iDxs6jOflJFJKzKcrwuRTM5SVGct5ZBVwcdfpV1544yFd1UnoCaguQkVtsSM4Y8BVzUM7PI0nlo4BwcFfvD+lO1ybuF/wCu5ca5hQkNIoI6gmlaaNEDs4CnoarCRWu9xR8CPAJQ1AFJjgZll2LkMFBBGaXKU6jNJWDqGUgg9xTqit9nl/u1YD/aGCalqWaJ3QUVSvL82kyKYmMZ+8/+FW0dZEDoQVPQihppXEpptpDqintorlQsyBgOlRX14LOLPBc/dU96mt5GlgR3XazDJHpRZpXFeMnyj1AVQB0AwKiuLaO5jKyKORwe4qamSypDGXkOFHehXvoU0ra7GVFcy6XJ5FwC8X8LD0pQsurz7mylsh4HrSLv1e4JY7beM9O5oP2jSZG2KZLdufpW35nHr1+D+vwNUBIYsABUUfkK82v/AI2abFrbadpem3GpfvBHHJC4AlY8YUY556etejwzR3cG5MMrDBB/ka+fb7wSz/Fa90WxuVs7t3NzZPENscX8YB7jC8DHesGdis1odc3jz4i7jt8HYXPGYJP8avaBb/EyTXbO41e4t1015A80IMeVQ87cYzx9axLbx74u8BSpaeL9PkvLQYUXI5boej9GJ9znivSPDnjTRfFMIbTLxGlx80D/ACyDgE/KeSBnqOKBm9RRRQBwXxFme9vdK0iBvN86XdLbryxGRg/luruoYUt4I4YhtjjUKo9ABgV5/oDv4n+IN1qcsZ+z2I8uLkAoc4Gcdf4q9DrsxXuRhS7K79WRHW7CiiiuMsKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAoopksqQxl5DhR1NAN2H0VSstQN5K4EZVFHBq7TaadmTGSkroKKKQkDqQPrSKFoqOSeKJdzyKB65qFtRtVUnzlOOwppNkuUVuy1RWedatscbyew21F/bLHgWr5PvVezl2Idamupq0Vlfa9S/59R+X/16PL1ST596pu52+lHJ5i9t2TNKSNZYykgBU9QayHabSJdqMHhY5ANJdW89tELia5YvkfKM4zU1hbG7kN3dZYk/KpHFWkoq7d0Zyk5ySSsw0+3+1yG7uGDtn5V9K1ayZrSexkaazP7vqyVdtb1LqAug+dRynfNTNX1WxdJqPuvf8yzUVxbpcxGOTO0+hqpa6iXmMNynlSZ+Uf0q/wBKlpxZopRmhkECW8YSMYUfrTyAwIIyD1FVLe++03skceDEq8NjqalvBOYCLbAk9T6UNO+oKS5bx2K0VhJbXm+3cCFvvIa4n4leGdUu9d0TXdDtHvLmylHmW6ME3KDuyWyPTFdxYX/n/uphtmXgg96nurqO0iLyHnsO5py5m7MmDgo3WwklvFfWflXkCOsi/PG4DDkcj9TXnXiT4MWNzI154auH0y8GSIwT5ZPGAMcr0Pr1r0DTHuJInkuCSGPyA+lXalqzsXGXMrnjVv488X+BLpbTxfYSXtmGwLpeW27j824cH2BweldXq/xA06/8FG+0ifdJdDygjY3xE9dwzxxnn6V2txbw3UJiuYo5Yj1SRQwP4GvH7Tw1per+M57LQrVbWwz+8aIlhtXqwz0yeKcJxptTkr26d2dWGwzxEmr2SV2+yPQvAukSaP4ahSfImmJmcEDK57Z7/wD166OmRRiGFI1ztRQoz7U+nUm6k3N9TnStoFFFFQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAEFxeQ2uPNbBboAM1i3V6bucGRW8hTwi962bqyiuwPMBDDow7VS+yX1r/qJFkToFPYVrTcV6nNWU27dBqahLt/0Oz/dj27/hTvO1Of5o41iA4we/50iapLCMXNuwA4LAYyauwX9vcEBJBu9DxTd10FG0tOb9Cn9n1Kf5ZZhGByCv/wBalGkzScXFyzJ6D1/GtSio9o+hp7GPXUzo9FgVsszuPQ1Kul2qsCIuR6k1copOcn1KVKC6EQtoQQRFGCP9kVLRRU3LSS2CiiigY140kXDqGHoRmlAAAAGAKWigAqounxx3fnxsyHuo6GrdFNNoTinuVL6yS7jzkLIv3WrJN5PMotpJQFLYL+31q1qFzLcXH2OAEc4bHf8A+tVs6ZAbTyMe+7vn1rVPlS5jlnF1JPk+fmTW1tHaxBIx9T61NWfYRXNtO0Mzb49uVParzEqpIGSB0rOS1OiD93axnatDEqiff5cw6EdWqpaEXF6n21mJCjYG6GprW3mvrvz7pCEXorcVfu7GO7UBvlYdGHUVpzKPus5+RzfOl8u5Ypayba5ksJvs10cofuPT9e1y10LTWubh+TxEg5Lt2AFQ4O9jppy59Fv2MPx94kbSrJbC0eRLy5GQyj7q5wefU9KueDfDY0HTA1wiG9m+aR15IHZc1yvg3SbrxFrj63qpldYmDo54V3HYewr02udJSlzdOh62Kl9WorCx3esvXovl+YUUUVqeWFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFACFQwwwBHvVY6fbmZZQm11bdle5q1RTTa2E4p7oKKKKQwooooAKKKKACiiigAqs19Al0IGbDn8h7VZqreWMd3GeAsnUMBTja+pM+a3ulqoLq7jtIw8mcE4wOtZ8OpSWeYLtGLL0Yd/SltraS/m+03X3P4Eq+S2stjJ1ebSG/wCRpptYB1A+YZzjmn0gGBgdKWszcQjIIyRnuKbGnlrguz+7Hmn0UBYKKKzNd1+z0Cwe5u35HCRg/M57AVUYub5YrUL2H61eWVjp8s980WyNSyq5xuPoK8ie5vvGPiCBZjh5WCRxj7sSeg/DvVzVorzV7NvEOvyPFA7bLW3UcsCDjGeg9+9dl8P/AA7/AGXpov7gH7TdKDtZceWvYfj1/KtcQ1Sj7CDvJ/E+y7L16nfgoRoxeMqLbSPm+/yOl07T7fSrGK0tE2QxDCjOfqatUUVglY4ZScm5S3YUUUUCCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACobq6S1iLyH6DuamqC5tIrsKJc/KcjBxTVr6kyvb3dzOgtn1NmuLhsIchFHaiO4n0xvKnUvCDw/oK1lVUUKoAUdAKSWJJoykgyp6ir576PYy9jZXT1FR1kQOhBU8ginVRsrOa0mZRIGgPQHrV6oaSehrBtrVWCiua13x1pOihkEwubgD/VxHOOOMnpiuaLeK/G2Qo/s7T2yDnK5HGQe7eo6CumnhJyXNP3Y92DkuhueIfHkGnz/YtJj+3ahv2GNQcA/h1PsKzdG8Gy6hN/bniqZjIx80wPwoUdN3oB6V0mh+EdL0LbJbw+ZcjrPJy2SOcelYvjrXJ2dNB0ou95PgSqi/wHtn3/lRUxUKEGqK+fV/5G+FwssTVUP+GS7mfb2//CceL5Lg7X0ixIQKSQG9MD3/AJCvRFVUQKoAVRgAdhWZ4d0SLQNIjtIizH7zs3UsetatcNONld7s6MbiFVmoU/gjov8AP1YUUUVocQUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAEVxdQ2kLS3EqRRqCSzHAwKwbzx94fs4RIL5Z8nG2Ebj9fpVzX/Dlr4ijto7x5BHBL5m1DjfxjB9qhsvBehWExlh0+MsV2/vMuPyOa6KfsFG87t9kS+boYE3xHnvJWg0XSJ52k4glcHDH3H596gfQ/FnieWOXU7oafbnJEUZIKEcdB6+5rv4YY7eJYoI0jjXhUQYA/CpK0+sxh/Cgl5vVi5b7s5vR/AmjaPKZUhNxLnIac7tvGDgdK6MAAYAwBUN7eQafaSXN1II4YxlmNN0++h1OwhvLYkwzLuUkYOPpXNUqyqS993ZoqbUeZLTYg1zV4dE0ua8mK5RfkQtje3YCuV8C6XNf30/iS/2mS4LeSvOUyeSPbtiq2qsfHPi2LToGkSwscmV9v8WecfXpz6V6DHGkUaxxqFRRhVUYAFcy/eSv0R6lR/U8P7NfHPfyXRfMdRRRWx5QUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAGT4psV1Dw1fQM5QeUXyBn7vzf0rhrfxS0fw+t7C3KrfSP9mjVHO7b/AHvbrivSriBLq2lgkzslQo2DzgjFeM6N4autc1G4gsCqx277XkdvujOB+OB+lc1a6kuXroe/lKpToyVZ2UGpeXY63TdR0jwJpQinZZ9UkGZ1gbcc56E9Bj0+tdJ4X12bXtPae4sntXVsDOdrg8gqT14qlongPTNJZZpgby6B3eZL0B9QK6YAKAFAAHAA7VdOMlvouxxY2vh6l+ROUm9ZPT7l29RaKKK2PNCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKihtYLcsYIY4y5yxRAM/XFS0UDu9gooooEFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAH//Z)
Now the required centripetal force for circular motion is provided by the magnetic force we know centripetal force is given by
,
Where F is the centripetal force,
m is the mass of the particle,
moving in a circular region of radius r,
with velocity v
Magnitude of magnetic force on particle moving with velocity v in a magnetic field B orthogonally is
F = qvB(sinθ)
here
at every instant so
F = qvB
Equating both equations
![](data:image/png;base64,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)
We get radius trajectory of the particle,
![](data:image/png;base64,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)
The particle is electron, thus, charge of electron is:
q = 1.6 × 10 -19 C
mass of electron
Kg
Velocity of particle,
v =
m/s
Magnitude of magnetic field
B = 0.15 T
so ![](data:image/png;base64,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)
= 100.47
m
= 1.00 mm
So trajectory is a circle of radius 1.00 mm normal to plane of magnetic field
(b) when the particle enters the magnetic field, with its velocity at some angle with it, and not exactly orthogonal, particle follows a helical path, since there is force on the component of velocity which is perpendicular to the magnetic field, and No force is experience due to the component of velocity parallel to magnetic field, which keeps moving the particle forward so path is helical instead of circular. Velocity makes angle of 30 degree with the magnetic field, consider magnetic field along x axis
so particle moving in x-y plane initially making an angle 30o with x axis, so using the Fleming left hand rule we find out the force is Toward positive Z axis,
as shown in figure
![](data:image/jpeg;base64,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Explanation: It can be visualised as particle moving in circular path, at the same time moving forward, like an spiral, if there would have been no horizontal component of velocity it would have moved in a circular path.
Now particle tends to move in circular path in y-z plane due to Y component of velocity perpendicular to the field,and move forward along x axis due to x component of velocity,
Now angle made by velocity with x-axis,
θ = 30°
So x component of velocity,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUYAAAAXCAYAAAB3cuYWAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABC1SURBVHhe7Vw9bBtHFn6zcK/Ux/K4PERhqwCiXJsheUB0hVWwoa4QpepIAWZlhTJppVIQkalEpojY0DimiAKEZFyfKANmuggyRPJK9VF67d73ZnbJJcU/yaQtn3cBwwB3d/bNm5lvvvfeN3qQyWTIvVwPuB5wPeB6oOeBB64zXA+4HnA94Hqg3wMuMLozwvXAHTyQTkfN/IpOydOBl+M1ynia4g5Nuq/cIw+4wHiPBsM15UPzQI7aZoLK2axQQBkjSoXoqtz80Dri2jvgARcY5zAl5CLZjFGyqOhEACyiVAjJBTSHz30wTUYXLs1qpADg+PD9kM2WBQWJx1T5v75PFf8OBefct/Tnl4YWOhMHrQYlddIy2az5wUyAD8hQFxhnPFjdEMtfA5sIkbdTp009TDpxiDXjj92xObaxU6/S/l6SLOxm9KZcaXrQ4jbqAP89NHAaAHNqKObEJqWjC+aKnqTBKHOXApSL3NHoGb8WXVow9/cqtFhqDAXqG5sb+rhTSlBzCPDZbHFN+m++bPHXn4pkYqNN+oSGwulHCYrwt9Gp74v1vSI17EmG+XtwdIjNQmhZx2bBz+a31sV2oUHsrEDggJ4eJSmMTcV+Lr10aTyMFEVDPhCnKtpxgXHGC46ZQ/IUAFDqMcRCLW4Ww3u00G6Y94Et1Td1CheJ4rU2ZZplkY4umQzeYCBUMwtmcwKzxUQyVwQeZibcRj8BFl3m5PBnvGaSp9nPDtH/WXv8Vu3JvsawUe3ya3GqeYkGoay7uRGHyg25ueXxTlg/H+4fHnOwxcy82WL6c2NTIxGvfkHFIq/i9+vLWzl+hg/z/I0UA/RttUUnYV2jTv06vx4R274zotaJkU6nJehJUHzoE9vmt3RhnJD+X4zjeoT+7ntDvxiH8jlQ/est7VI8vjDoBKDaqW9e+/75nXCBcYYDJiOqYyAO2EUEC65st60vgisV6bxNdE9IowQ1D0CRTcyWmyKVC5jFZJGO64WxNkpQBKr6Aar8fnlODCmdBoCtHNNqo0DDgFoB3Oj7w4ZVMtn9FpifSanqCoHUDr/sza3tYME7cTOJfg/6x2aLim3Ply3Srz/R9yYYzReCZoGLaQbalZ8E+zhMN8Ny+NiAj8XqSYFCosewZrxk7tZc/CltR3Ttz4xMJWjRx8vG9umpeIM1xnu2FCFiHLdPl+nbiwTpbH+5aaafbhjbYIc/1w8pgk6bnRadxVepAAZ+hbbS6VWKR47pwcLLXbNbWYtjhywksEPmqRcKYVc1h0/Ou/Vodm/dqAxOsJ8XxmbMET4CruK1RpfVDN4PDAmfeEHmY3tghV0OD/a9I3OIXupQfgVUxO/rzyd6feRHt89anXsBjE1PRmQGeJLXxxYOBr/9YyXBSuzSKUA1aIHq7EZzsCWdFrGZhFfAYhv9LFbZEcaEBrjfIm+bLV+JIHYmhMOkL8jIauglNzewSZ+TTYawYGBP8bjenxIZwxZ5ExFMzbk1sOdUa5Ni2HzYy5x3DqJ6zXnXwd+GgjqznxWfMONVCmu9MDod/dzIx56L4fNxEph54ePvbR8bYTAoO2cJH4OdRsTZxi9U1ACaCoAmXunoJ8bWekIgcrUurLHqCRXDsJlZ3MB9ucaOEhRyhrYA5Pz6nthGnKw+GpBr7OgwpAAuS9oz+g3oh3/W1T6HV7FpfBkiKuA35tJyHPEbj2P3kuP4PRV+rpNCRqzN4jE9bn1hJPQ0M0Y6CyzSg0QDEMuyAw4bAIp2nqiB8A9z796CIneUE+DpRtucxn4778VMxxk+2g4bdn8wfLoRYjEQgtYnz1poBiMy8sIiDxAVQRl5Yd7HywaDVXSjOYr41I8BDVjkYx+aTe+cYxteWUQOM22q6q8CxeKcZDFqjLG5YXGAeNwIs7G7UbRg26Iq0aPYYrbpEWY7J/OtZ3ubVAWrDF55RGnhpaknsbgCcXNhJ0XBjP3bHq2NSrd0alR5tUy5oxAlC4ALoIMMFQGWSTqgFkJ+Xc5Hn5yP5tj5qMYIPtbSjZZBaIN93GokDN0KLxkUiwBFINqtQPGhLyE++wXrASEuEtnXW76IsBGVQXHwPofAYd85Vbuhbee6F/6iTwJ92vLR9u8XQ9cYs9r8/p7YA35VwfBtZqvC6GeCAp/CL0NqnvBRywgbWLfaYfX4+uHfNJE0yVA5xn/RA56A0bWAmUxWqNpJdGd1p3WGiLA0NIy569Rfutw1rQ10QhPI0bWHJ8UHX5zW/vo+igHYnUohL3HEw+Gjh0/9NFWeRt53MCG+ny7lzAomdS98ahNvTAFUELqFhhSegUpDXeo+nYYJS6u7w+7uyoQWmOT0npuHr0Z9XW0KzGrGRwY2eC5Sns4RadiFm1FVdwaDs9OiKXnoLYs71sLtbnw6mGO7xOG1AsW2rPLPOXTtc5ja3JyXqkzL0vTEgfXv9Apb3sgaBThMW0vRlcW81W/JkemWTu3f9Gp5jY4wTrxK1Rc7dP7KpMBBmHxgUplM2UynckYlZopp5Q9OcPTBx62Sz/gmFiEGxVYBuVjQL7vwPqmT9f0EnS7n6AfQP8nayk3tL8+eEf32XJK7+iWijY0qNRACMwNFH7T0Uc74EWDaDW2xht7ANcvfRlSfsujTkwPjx/V+dGNGuwXwFrsWp4w/Ju9fJ1nI93X6FOPYRWu2s+nRHj3L0CPr9d9ePFfFF3tQKtUOKxCwE/Gu/BK7lxd5k2k+Nt0zMoSb8gTibZL0k+xX/ekHNKfFvfuYdVeOxTYQAmezTbEa51wcnsNuv1NKYfDLQq0N3sGX1CgNsJke05zOT/zUvHw1aIFtG3aiG4WSfh9ZTAqcsdJC0QUlPA5jubobC4cptgg2bL/gjdBaoELnYEMesKaGTD9wceeMN7xbFaCczFFnCscV8P8T6ZO/L1YfPTcUM3wmlteOLABUYW02+1r7x0bAKKJEHQjEjaVoioTXq2WCWWbXU0+2PnDU0TR83DpkJcWkULz3CRV6C7HMID0k9FZAxvf1/oSNVwdfEPR7uyOTg9lMU/tyY9kobqNPP6JPRykAlFd79Chrvnje6xPWogRdhhPMQWM9si18xTdO5jl1/4c9qIovciInKVmpYsKnTUKcXURMP+8q21tZ7nx5bvbfDIGbnqBo1/xmDFKBsM6FlriJHJjFrG+yCmWmxTTXBoB3Zg64W0NOaVHmShViJl7MuhO9inu5eSV24mSGrbnDTNpmUijOyOac7NvefCd+5949YEUD8YH88buw81dVRDgAXTzt0UX55deeoNau+43Y86Kw5qOxNKKY8i5Mvf03FIMrcGVSJi+YFAS1Vs1vQI6DMFuuMaN6ckhh0S/Fsb+FOaidVDcMDUWVr/NPKALiMjohqhipueEbCuB2mxIY5a4sq27nWMJYxkhaxldBhkcmm27ffX5jXuHh/OwfDmhlsKBgMEOlHWZL0ERtrsqEPNux5MeYOPJQTk9NyxDm6SunPSx7SLLe8i3DUl0lUOXcGXlZ7Pu2eda+vG7bR/ssteGw2so53m0mjn6rO4Yj+hNYfPeb2yTtYvm1R5Pz8atPjFgoIXg+IjeI4sR04VlfrhI+5lDa95CVL4mu9GXWfu61p4Aq8LifSWKNaY/Qp6MdxQYjW1/KPo3sklR+iC4gMgte+sw0qPhGtPHrYJ4x8Cm+N0bx1JPryGpNmI7ziyif5igFXJy1+mCu4eFY+ycVP6z7DtYjB45L+fjPBjSZi0M+sWSJmbtsyQGECiT687UojyEARXV/XGFjYObN1Vf4VpQLAC9ZmN1jf1KK00IxYAh7HAcYsiIYWOsWK3gD3OPQ2tmO5cvbAEsfKFo+LzRQ3kXxRUeRoW0VQWa9aOUYYsT6pDl24WnK8HdWNklJzQjtIhczVpBP5PmIwitr97Sv4mSEzlqiZZrGNKFwHyiiHX6n0KheE/J3vi2d84xTgmNvjdnMr98HFjOs1FD0QJFHKK0hddpYYyb5da8EqnRnwXiIfOIP/7EkNujT0w3TiKBPFyiW6CJKKM5Q5fEF2DNylbaYu32OEN2kDYyPra2Q4yiKZOcvlYSH12L/c8PGqguMKn+GkAgJ4ADyTc7ja1EsmBiqJqd8cgFFkQSS71LOM3DiYVaT4S7tjLO/V6AJ02WtbbL+Tp3c2KcWdgAMkMWYkxTLR1Se1cqLqYKNY5M4TdJ+PSJlN0pLJ5Gz6y9vYofiqDgm9+ty4aqTLzjzAZ9OEk7fpd93eccutuScOj3pDyyLReR0uG9Dqr+hVI4CRcWQbVDiucFi6Xitp2jg90+TsW6FtetL3hwSXrveNdb0YaDIL/A4F0wLHN/6NNEZQUF147LHsLiXl8xUybA4rwzC4JwL0zhfLtjhdbdh8q0bv03SLr7i+YiCFI5ymG2AaAy0CfPRh7Bz0smYYaBonQbRCkbVkOBIsjI9kXwyQ4uuQUuYiIiNasvYDac1oN51fWtftJ4cwiihmU83rrcjSbH+XRjzg+1lWU5ENGTBRsiCjbxOt+kbu0+oOuPgijC5T8hdmiZd4wnxKrlOB+ETI8lVdCnwRgV6+YCeWO1wNlKO43aECl/nqRVKouKuQHXwubHAyDdDQEbWY+wMTF4OHaV8Z29RCpc7+YosMNy3JPgo+7lv5SvkBnPIDWICsbpp9+Ul5VAcsE+isLSijT7yfa4ocyGZq639ffQhFxugit2GfMYuBqiijVy4bSxcDvlk1g4arBw0a9Pm8KZZbG/5jKzA8/xTBsp0jF05x9ofebEOsAH5iTw5ojKS5i5XmyGBunKccAmlahQ/g9bTal/5Mkc1PlI3re4QTOLc3y8hsw1TPs6ZBLF2NK2kM9O4xD7mV0E53dIJKBsDATO+ViKPNUb9Y5iUTatx7gf/Sd9UG5D6EnR8rGU0C7pDIwxw8I/4jU8M2cA1qF3sfRfzcZnnIxY7kcHCZns+eiHpAciNN7GDqrb/QGmXBwotXNwotHIG7bdFCjIWL1kMb0yL5T+QG8wjNxhBPZnt4bmBNZb0Kg1jljxaqxrv3Zf2VlWhxxKQYxOlx4FlqkSsPknfQ47Ez8gKOSRGRwBtSHQqQMptfEeNT5UuHO3wb9yHwxaeBfj6NDxptXVxmOx+b1R3+k6+MDgoBctNh0rgWKuY+kqFeBIFPTj18E7lEpOmoSy7j7Sf3y5DQxZEB+3qKaQSfY3K3KHjPqvYnH3kIgLLM4L8r/vmVe8PCVi/SSkQ8iOZ3ocmG/8OnxgbplsyBAYHljMNCsEZHPv6BrsH/aj6H0T/e17CU1JYPe0l2wAtH1VdlXaMuT/sO7Io5MHYYWCclslnB+QXN8YQ9t+m0isXJgvKnfMJ0jBeMtP8Jm0aol109itbfq1NMx9H+ZzfH+/jP8beH9Zu+Q/kBtFnW/rCcyPjEHrI3KFDGgMtD7143hNqs8SHHmF8+F/3A3/iGUdFmp+5MY797divSsnQI1SvbYOov62pgHHypPXLo21F5OLmlfyebIP7hOuBj8MDw7WLH0ff33cvpz4rnYZeLU9pajRSMt+ir+BAfQlHteZ8cP59O8j9vuuB9+EBlWN9RoPaxfdhy8f4zamAkc9zroT5jKyPElC1y2O1Rej4Yr2jWh+j89w+ux6YmwesP4AwTLs4t2+6DXc9MBUw9nJzTU5o4k/EIPcka9+3z7u4vnc94Hpgsgc4X/4M4tirF1n1l2Lc6516YCpgfKcWuR9zPeB6wPXAe/bA/wBBiafN3P8VfQAAAABJRU5ErkJggg==)
m/s
So y component of velocity,
![](data:image/png;base64,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)
m/s
For the radius of the path we will again use the equation
![](data:image/png;base64,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)
where, q is charge of Particle which is electron so
C
m is mass of particle, i.e. mass of electron
Kg
Component of Velocity of particle undergoing circular motion,
vy =
m/s
Magnitude of magnetic field
B = 0.15 T
Putting values in equation ![](data:image/png;base64,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)
m
= 0.5mm
So radius of the helical path followed by electron is 0.5 mm and is moving along magnetic field with speed
m/s.
Question 9.A magnetic field set up using Helmholtz coils (described in Exercise 4.16) is uniform in a small region and has a magnitude of 0.75 T. In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of (single species) charged particles all accelerated through 15 kV enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is 9.0 × 105 V m–1, make a simple guess as to what the beam contains. Why is the answer not unique?
Answer:Now here the charged particle is two forces, magnetic Lorentz force due to magnetic field and Electrostatic force and electrostatic force due to electric field, now for particle to go undeflected, the direction of both the forces should be exactly opposite to each other, and magnitude should be equal. direction of force is same as that of Electric field for a positively charged particle and is exactly reversed in case of negatively charged particle and direction of magnetic force is given by Flemings left hand rule.
The situation is depicted in the figue.
![](data:image/png;base64,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)
Electrostatic force is given by
![](data:image/png;base64,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)
Where F is the force experienced by particle having charge q and moving in an electric field E Magnitude of magnetic force on particle moving with velocity v in a magnetic field B, velocity makes angle
with the Field
![](data:image/png;base64,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)
here
,since velocity is perpendicular to magnetic field
so ![](data:image/png;base64,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)
So Equating both we get
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFEAAAAXCAMAAABEUFN1AAAAAXNSR0IArs4c6QAAAHhQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOma2OpDbZgAAZgA6ZjoAZjo6ZjqQZpCQZrbbZrb/kDoAkGYAkLbbkNv/tmYAtmY6tpA6ttv/tv//25A627Zm29uQ2////7Zm/7aQ/9uQ/9u2/9vb//+2///biHbJRwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABIklEQVRIS+2U25KCMAxACSgK6HpDRYUVROn//6FJ2kJxFGtnd2YfNg+OrZ5jbuh5//HnOyBSkLFxSFXBflyacDOb4vESuRg9hsURSNGGSPmYORkl3MxCfK2/AOItapTRpmbFUK2Tso4gyLURvXWUoIuax5ffvbRf2FtGpCE2rgpyCd+24xyL5DtppLn0jJkaFoC/N+wdU9B9kWg4PFHleMREdY6VRY4GQ9k2c7RyjiLDH3g02nSxx4QlJ9FNZtj4vGqDoR7yckijSAP1TvXRcnskzQzWuFrSVhvbU/g777qgT+WGc0vfRMfgZIEGoTacD+KA63hGjX4Ke1N9rm4ZShVXR48aRmsN2CT2KB9mft5YyWZ8FINM5fAf5sJ8lPEvfvkOCxYZA0ttK2UAAAAASUVORK5CYII=)
so we get
velocity of the particle, ![](data:image/png;base64,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)
now the particle is accelerated through a potential difference When an charged particle having charge q is accelerated by a potential difference V volts it gain kinetic energy given by
K = Vq, which imparts it with velocity
We know kinetic energy of a Particle with mass m and velocity v is given by
![](data:image/png;base64,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)
Equating both equations
![](data:image/png;base64,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)
We get velocity of the particle as
![](data:image/png;base64,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)
So Equating both the values of velocity v we get
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH8AAABBCAMAAADPE4v8AAAAAXNSR0IArs4c6QAAAJxQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6Ojo6OjpmOjqQOma2OpCQOpDbZgAAZgA6ZgBmZjoAZjo6ZjqQZpCQZrbbZrb/kDoAkDo6kGYAkLbbkNv/tmYAtmY6tpA6tpBmttu2ttv/tv//25A625Bm27Zm27aQ29uQ2//b2////7Zm/7aQ/9uQ/9u2/9vb//+2///bZ/fvqwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACzUlEQVRoQ+1Y63bTMAy2OzYWKGWBAWvYaq5hwEJG/P7vhi5p02Q0ljwzn8OZfqTntKo+62J9Uox5lMcI6CLQ2JDo7Gm1m1PtP9Lq12dp7Wmt5cZ3mf13a23E0upnxvfvN2n9UVrLjd+9yut/9/qrMmJp1XPjty9ujPHfz6093hhfWbvgjyNxWFCbJOoiE76zF+a2REgH8HCe6gS+lUpXIoX8KqLwG0RyaKBGBxryois1tnxFFBbXSAb6I2j2paHot5CU1WX4JD2+NFxjvQHfIShHnjihLc6wEoT415E0vqO/lvNXQwFwT3B4Es7HvHAB3hPfV8yD6DXVRFdyECT4gB07xvT0u8shJoC+U+KHgnTo975q3en2wtVHn6klPih+TbmmDLTFc0olR0SW//j7x/TXPoOn51TsSr5eXJnbN4L64zsrqZS7SWB8xw2UK5DqHg/yAa7/j3D9bfsvdU6thOg3ziv5KUL0lxu/6ZMi90inSfR3WHA5CzcgHeRIO4CvtQyd+OlNW8inB2q16YTpi+lTJLFt+5BxpC8zWun6uw2J/NsF1eHP28IzIX2F7vT+2emogRcAgUDu/ZvnB41PybdfyP14EJuPmW77DccfaPPdW0VJxw2Ncxlxqo6VHl9x+aBc/oPtt+ffxUqR9m0CNVf1YNJp/vAfYybgEP2KeihPal0Z0crH+MB262+FXRl6iGWLH7EBTOivLZYb2AOXV7SGSIXwf18ei0lnMHwHH8geW7hqmuQCPPkiPe+e3oR+adoaHkKD5L/nzV0pE6q4B35c/SXE95V86thFaUJ/D+e//0QXbIJP21ZffzgYyIT7j4p3rpfnNNeO6RcGR7seHjJ0elsF8uRCqM9qbUEvOv7pcD17IHrdlBEf+3VW+oUAZMWHAPzMOn7U9mXWl89dKd/TVHdLqtzYiJFBalygp3vNLDCoVUm8/Wrhk+v/AVB8RLDYffAfAAAAAElFTkSuQmCC)
Solving we get
![](data:image/png;base64,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)
Here we are given,
Electric field E = 9.0 × 105 V m–1
Magnetic Field B = 0.75 T
The Potential difference V = 15 kV = 15000 V
Putting all the values we get
![](data:image/png;base64,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)
⇒ q/m = 4.8
107 C/Kg
This is the charge to mass ratio of Deuterium ions Dor deuterons, which is a stable isotope of Hydrogen having one proton and one neutron in its nucleus.
So charge on Deuterium ion = e (since 1 charge)
=
C
Mass of Deuterium ion,
m =
Kg
so charge to mass ratio,
≈ 4.8 × 107 C/Kg
the answer is not unique because only the ratio of charge to mass is determined. There can Other possible species whose charge to mass ratio is same as this value examples are
He, Li, etc.
Question 10.A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires.
(a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?
(b) What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before? (Ignore the mass of the wires.) g = 9.8 m s–2.
Answer:Given:
Length of rod = 0.45 m
Mass of rod = 60 gm
Current = 5.0 A
Acceleration due to gravity, g = 9.8 m/s2
![](data:image/jpeg;base64,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)
(a) Let magnetic field in conductor so that tension is zero = B
Tension will be zero if the force due to magnetic field and the weight is balanced.
We know that,
B × I × l = m × g …(1)
Where,
B = magnetic field
I = current through the conductor
l = length of conductor
m = mass of conductor
g = acceleration due to gravity
From equation (1) we have,
![](data:image/png;base64,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)
Now plugging the values of m, g, I and l in equation (1)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIoAAAAjCAMAAAB8SmJwAAAAAXNSR0IArs4c6QAAAMlQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmZmOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZjqQZmaQZma2ZpC2ZpDbZra2ZrbbZrb/kDoAkDo6kDpmkGYAkGY6kGaQkLbbkLb/kNv/tmYAtmY6tmZmtpA6tpBmttuQttu2ttv/tv//25A625Bm27Zm29uQ29u229vb29v/2/+22////7Zm/9uQ/9u2/9vb//+2///bco4B3gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAC8ElEQVRYR+1XDZPSMBBNigftiXr16oF6nlD8pPVUruCptJj8/x/l202/QC0fqXOM485kBtrs5uXtZvsixH87Ugb0RMqTm6MApy5manBuByWRrk2AzJNkY8RQT/dlRb+RzhWvvhieLYWImqBkg3zyaiAlzf6zZc8bX//OMXGX2elUCB0/Zt9kE0rMW3xGL1UwEpmH/zo8F6ugKQHp5TIzO9zZVDDmwCUEQInA8IKY7hDFajjGAFghUnoQYTJ5EX+p7H70nHfX0nkv5vAoF1cB3PesFfUEiyCoDs+GfaI8cfX88psKrkTq8PrA8RJoyIi+VQjadOgvVwQnwZyIhpudjkWy5+LrhBVQMs//ekurJFJ2l9g2oFDeGIFXLIGXj/hgUK34BBxzebg6dF7sXR1rWIoEMSQTNPOAKO0X1VxjhTmiiWowAjMEvIQixO3AMeQdYpT7qMtlS5Rz8JgqwP1+UZ5EqhOqF2MrkJJ2PnkbUOLeogv/zQTpkM+2QwQ2G0FROJ+jivKUqi2SPYphDvkHSpM5QQB8D3PhRlWNykIbcckD4wGe/NpfVUCVdW3TrLKHWHoO9i2NiUblWURKTmboNFaNlzdRQLGIpGMkqLmd7sQXQ/nx+hi+jKZuu7M6bnTQ3PLGtdOmrCcxK5qa4BYr4f2lH1WtWJTttk3s+t6UrQ75a5bbXSbI7jDvuutt80yLi/b9SG8Le8D7vPFTi/4HjHm9S4MakaYDpP16yReYKhmMJywsK4+WcSeFEtCvPpNEI6spW0gZI4PJ9OQ+QTlcoDRjLwOnfin8a8q2lMEUJRmFJZS6wm2JHaLbZyqmRlGTVcq20J6cQV8zFONRKdyWkFAYrgBzryq4L5VtDQquWzocvSU5Qx51WdkaGHMPwTAde52V4p5i2GA5bq5ErUPRkynvkW8VIjZnqa5scxlsckcJKjwKKHHPWvblhwJyCTIXHRIooFZ503Vlm8tgA+WL17khgQWPmsK1ugi1ltvjDvQT69poEcGpVbkAAAAASUVORK5CYII=)
⇒ B = 0.26 T
So, a magnetic field of 0.26 Tesla has to be set up normal to the conductor in order to get zero tension in the supporting wire. Using Fleming’s left hand rule we find that the magnetic field applies a force in upward direction on the conductor which balances its weight.
(b) Let total tension in wire if the direction of current is reversed = P
According to question, the magnetic field is kept the same. Using Fleming’s left hand rule we find that Force due to magnetic field on the conductor acts downwards.
Writing the balancing equations:
P = B × I × l m × g …(2)
Where,
P = tension
B = magnetic field
I = current through the conductor
l = length of conductor
m = mass of conductor
g = acceleration due to gravity
Now, putting the values in equation (2) we get,
⇒ P = 0.26T × 5A × 0.45A 0.06Kg × 9.8ms-2
⇒ P = 1.17 N
The tension in wire is 1.17 N.
Question 11.The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? Is the force attractive or repulsive?
Answer:Given:
Current through the wire, I = 300 A
Length of wire, L1 = 70 cm
Length of wire, L2 = 70 cm
Distance between the wires, d = 1.5 cm
![](data:image/jpeg;base64,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)
We understand that current carrying conductors create magnetic fields which in turn applies force on nearby current carrying conductor(s).
We know that,
…(1)
Where,
F = force applied
�0 = permeability of free space
I = current through the conductors
d = separation between the conductors
Now, putting the values of F, �0, I and d in equation (1)
⇒ ![](data:image/png;base64,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)
⇒ F = 1.2 Nm-1
Hence, the force applied on the wires is 1.2 N per metre. The force is repulsive in nature because the current is carried in the opposite direction.
Question 12.A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,
(a) the wire intersects the axis,
(b) the wire is turned from N-S to northeast-northwest direction,
(c) the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?
Answer:Given:
Magnetic field strength, B = 1.5 T
Radius of cylinder, r = 10 cm
Current in wire travelling north to south, I = 7A
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(a) Let the force on wire = F1
If the wire intersects the axis of the magnetic field, then we observe that length of wire will be equal to the diameter of the cylinder.
L1 = 2 × r = 20 cm
We know that,
F = B × I × L1 × sinθ …(1)
Where,
F = Force on wire
B = magnetic field strength
I = current through the wire
L1 = length of wire
θ = angle between direction of field and direction of current
Since, the field is along east to west and current flows along north south, direction so, θ = 90°.
By putting the values of B, I and L1 in equation 1.
⇒ F = 1.5T × 7A × 0.2m × sin90°
⇒ F = 2.1 N
So, force on wire is 2.1 N and it acts in vertically downward direction.
(b) Let the force on wire = F2
If the wire is turned towards Northeast-Northwest direction.
We observe that wire has been turned 45°, i.e. θ = 45°
L2 = L1/sinθ.
L2 = 2 × L1
F2 = B × I × L2 × sinθ
F2 = B × I × L2
F2 = 2.1 N
Hence the force is 2.1 N and it acts vertically downwards.
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(c) Let, the force on wire = F3
The wire has been lowered 6 cm,
⇒ x = ( r2-p2)0.5
⇒ x = ( 100-36)0.5
⇒ x = 8
So length of wire in the magnetic field region = 16 cm
(By using the geometry)
We know that,
F = B × I × L1 × sinθ …(1)
Now, putting the values in B, T and I in equation 1.
⇒ F = 7T × 0.16A × 1.5T
⇒ F = 1.68 N
The direction of the force will be vertically downward, the direction of force is given by screw rule.
Question 13.A uniform magnetic field of 3000 G is established along the positive z-direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A. What is the torque on the loop in the different cases shown in Fig. 4.28? What is the force on each case? Which case corresponds to stable equilibrium?
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)
Answer:Given:
Magnetic field strength, B = 3000G
B = 3000 × 10-4T
B = 0.3 T
Length of rectangular loop = 10 cm
Width of loop = 5 cm
Current in loop = 12 A
We know that,
Torque, T = IA × B …(1)
Where, I = current through loop
A = area of cross-section
B = magnetic field strength
Note: We take vector normal to the cross-section for A.
For each of the case we plug in the variables in equation (1).
(a) T = 12A × (50 × 10-4) î m2 × 0.3
T
= -1.8 × 10-2 ĵ Nm (∵ î ×
= -ĵ )
Force on the loop is Zero as the angle between area of cross section and magnetic field is Zero.
(b) This case is similar to A, hence the results will also be same. There is no change in any vectors.
(c) T = IA × B
We observe that A is perpendicular to x-z plane and B is along z axis.
⇒ T = -12A × (50 × 10-4)m2 ĵ × 0.3T ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAYCAYAAAAlBadpAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACgSURBVDjLY2hsbGQgFzMMI8319bGSxgwMdxkYjO/G1tdLkqQ5x0222Di6wQdEy7rlFBOtuT7Pw9DYLS8Fxs9zM07xyKs3HMQB1tGRxuMhw7CHwThqIUma4RoZGP6TrBmGo4wZFg685oZoYx+wN3B4Ba9mUDi4yxnPwpXKcGoGJVEjBtlTuBIIVs3RxgyBDPLyufIMDGXmsfVqIyU/D3PNABVtE0TNIIc1AAAAAElFTkSuQmCC)
⇒ T = -1.8 × 10-2 î Nm (∵ ĵ ×
= -î )
(d) Magnitude of torque,
|T| = IA × B
⇒ |T| = 12 × (50 × 10-4)m2 × 0.3T
⇒ |T| = 1.8 × 10-2 Nm
This torque is makes 240° with the positive x direction. The force again is Zero.
(e) T = IA × B
= 12 × (50 × 10-4) m2 × 0.3
T
= 0
Since cross section and magnetic field are in same direction net torque is zero. Net force is also Zero.
(f) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGwAAAAfCAYAAAAC0CiiAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAVvSURBVGje7VlLb9tGEB4mvQSIkR6bVCtfgiLHkCv9A5WhajlGDgwjEjwVIARBYOvIBg9GQPmmoHV77yEPnxr9g6TJpUDRAr23qF/nOsk/iGp3d0lJNLUr0tbDkqPDAIZJkbPzzXzzzRA2NzdhbrNjH92BWwCXAI6lCw/YrB1UB7gMAJ9EzXH0T7/EeEs1qsug65enN6FASg3YrB40ar5vX1cAdojvH+ImAfxH4tGGnPnEaTavTmdCOcI4z9xBh7Fm07l6J5d7rFmrxfNOKAzwjzjO0AbFfMqL80wd9KJbL8614syLjmNS3tBqXfrYBUnvDxqQGKemsIkcjgayanxVymvWt60Wa8oxP5KDrOukZwzovzS7iyS7SZ8ujTMxeL0rZuS6+P09XnU1GYH0jvHnSU49Irgcxf5H7kHvNdeXxw4WAaiMF7cAaS/tun+zpqHV0Mfj0K82tv2lpOeYCmyTvrA9KMn8un1TQfD7olpdGwdoNCk0BC9j/kd7WDuTyfyGC0Zdd7xrKQDDf9CgxJrjPmS019EGuGppxSxk/x43YPREFRWtI2x+F31/4Cu8B8B7Wr1xO+k5Dc++IQMc0CQrVDeUNEFFamV9XPTYqGu3if+kOPC+7fvXowlD3y1JRHgg+U/d8z8XAtaw8RK2G0scNdMHmOj+UdujsnwXJLwbPVSSXzyrqWiNBYEggNTaWioVJ8GuXH50d1ziQsvA6zhgHbMwPGMVKJvb4goj6EarKykwvPtHaR6pCjJi7CPNfSiQxakAa3rOwp0s/sm2818zes+obxyvuZD0fldDD9PeO2rAGhYuBZTZfz3NvJA6k0deXYI+eRq//DJeRtj6vlM1NBC47C8nVllIu6J7mfgZ0OeY4hRcTwKM+hwCtjcTgIUHesNz+DR+UYFhEsHS6XOsamgglH6qEbxjT3RvlTyL9TkOKKz3Fkjv5bBDEmBMEZPfMj+x+fRUc9hZAOPLboEJMjDpvWn92qgWFISKP3fu6TV7+cD2vBvD0Fboww4qnBQnDKwyNgGyhyJB1Hu2fFByXRRdTVVU7ARqnf/7kQMWyu4PaQxptdVBdEQy7PkwflGxERVGbNZC8IpmbxpBYWJ4Pmh8oX2cgobLFZOCRsEKqFwM1knA+mR9sJoiCvGeU7/Fm8emkhK7TXcIwJhoQcqLaAZT8wx5hT07oxFB4S0MA1inarMAh7LhrdBnk3Hnr6RRQ1S9Ddf9zFLz39DnMUWrGD/GWejCAhY27jZ3wSrRZUDyTJYGsJNzYbplQqJK7FJ3/xgynT1sSEr0iJTXEHohyvTOnIPU6vqwgFFh4zmFXBakQwnQ24Lj5ZJWdkmAhcP7L7yknc4eFkjwPUZbZxAdTGwQKS+sYDL0Bys3sfjoKlWJr1SjYBGR8Jaux3zyXLoBSgItCTCmbmXYDgCznqUGzOusdFLw/agtqIKBCm2fByit8AcK+gFbjVJywIj4MDZWeCuo7jtiAYta3bl3C0vSbt6qGd3fsWQYXGmMAYKxpX8w7iYBpVjpKJ7UwjKnlFUxsBUMcITvmQOT+9ocVAF6F+8zFJDegeSDQE0FAaebcLp7pP9n/gq2856jX3ughBlMzsb7ks6qlMhr0fqN7icpWKTH9LFEzcobkoR39erGF7xtfb//ka/Ohroc9C+pTRfe8YQcpHz+7acxZUdED+MYnqkEj/cZHuVSOopswnvXcuYTXuVwv6rH7q1S4FHxlagVUD9ElB6OFH3XuT7yWgVCv9KqPfMX5/MyRi80U10vM8n3eq6eodWT5rPNpG2qAWPrJHXxPqGGLa/ZvDKZyvaukCrYWlTd+9MYj6kHbG5zwOaAzW0O2NzmgM0Bm9s52P/5IXew9e7c/wAAAABJRU5ErkJggg==)
= 12 × (50 × 10-4)
× 0.3 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAYCAYAAAAlBadpAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACgSURBVDjLY2hsbGQgFzMMI8319bGSxgwMdxkYjO/G1tdLkqQ5x0222Di6wQdEy7rlFBOtuT7Pw9DYLS8Fxs9zM07xyKs3HMQB1tGRxuMhw7CHwThqIUma4RoZGP6TrBmGo4wZFg685oZoYx+wN3B4Ba9mUDi4yxnPwpXKcGoGJVEjBtlTuBIIVs2RxgwaDLKyZrIMDNbGsQ3CIyU/D3PNAMbaEouyCvAgAAAAAElFTkSuQmCC)
= 0
Hence the torque and forces are zero.
Stable equilibrium:
In case E, the angle between A and B is zero. If we displace the wire, it will come back in this position, hence it is the stable equilibrium condition.
Unstable equilibrium:
In case F, the angle between A and B is 180°. If the wire is displaced, it will not come back in this position so we can conclude that it is the case for unstable equilibrium.
Question 14.A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil. If the current in the coil is 5.0 A, what is the
(a) total torque on the coil,
(b) total force on the coil,
(c) average force on each electron in the coil due to the magnetic field?
(The coil is made of copper wire of cross-sectional area 10–5 m2, and the free electron density in copper is given to be about 1029 m–3.)
Answer:Given:
Number of turns, N = 20
Radius of coil, r = 10cm
Magnetic field strength = 0.10 T
Current in the coil = 5 A
![](data:image/png;base64,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)
a) The torque on the coil is zero because the magnetic field is uniform along the coil.
b) The total force on the coil is Zero due to uniform magnetic field.
c) Let average force on each electron in the coil due to magnetic field = F
Cross-sectional area of the wire, A = 10-5 m2
Free electron density or number of free electron per metre cube of copper, D = 1029
Charge in each electron = 1.6 × 1019 C
We know that,
…(1)
Where,
F = force due to magnetic field
B = Magnetic field strength
e = charge on electron
Vd = drift velocity of electron
Vd = I/ (NeA) …(2)
Where, I = current through the coil
N = Density of free electron
A = cross sectional area.
Putting values in equation (2)
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Vd = 3.125 × 1043 ms-1
F = B × e × Vd …(3)
By putting the values of B, e and Vd in equation 3, we get,
⇒ ![](data:image/png;base64,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)
⇒ F = 5 × 10-25 N
Hence, average force on each electron is 5 × 10-25 N.
Question 15.A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of 6.0 A in the wire. What value of current (with appropriate sense of circulation) in the windings of the solenoid can support the weight of the wire? g = 9.8 m s–2.
Answer:Given:
Length of solenoid, L1 = 60 cm
Radius of solenoid, r = 4 cm
Number of layers, n1 = 3
Number of turns, N = 300
Total number of turns,n = N × n1 = 900
Length of wire, L2 = 2 cm
Mass of wire, m = 2.5 gm
Current flowing through the wire, I2 = 6 A
Acceleration due to gravity, g = 9.8 ms-2
Intuitively, this problem can be broken down into three parts. In first part we will establish the magnetic field inside the solenoid and in second part we introduce a current carrying conductor in the magnetic field. Then we can evaluate the force on the wire. In the final part we try to find the balancing force and finally the current.
Part (1)
We know that magnetic field inside a solenoid is given by,
…(1)
Where,
B = Magnetic field strength
n = total number of turns
I1 = current through the coil
L1 = length of the coil
�0 is the permeability of free space.
�0 = 4 × π × 10-7 TmA-1
Part (2)
We know that, when a current carrying conductor is placed in a magnetic field, it experiences a force given by,
F = B × I2 × L2 …(2)
Now putting the value of B from equation 1 into equation 2.
…(3)
Where, I2 = current through the conductor
L2 = length of wire
Part (3)
Since, the wire is suspended inside the solenoid, the upward force on it must be equal to its weight.
By equating the weight (m × g) of the body with force in equation (3), we get
m × g =
…(4)
⇒ I1 = ![](data:image/png;base64,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)
⇒ I1 = ![](data:image/png;base64,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)
Note: It can be noted that in SI base units Tesla(T) = Kgs-2A-1
⇒ I1 = 108A
Hence the current flowing through the solenoid is 108A.
for the suspension of the wire.
Question 16.A galvanometer coil has a resistance of 12
and the metre shows full scale deflection for a current of 3 mA. How will you convert the metre into a voltmeter of range 0 to 18 V?
Answer:Given:
Resistance of the galvanometer coil, G = 12Ω
Current for full scale deflection = 3mA
![](data:image/jpeg;base64,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)
For converting a galvanometer into a Voltmeter we can connect a resistance in series with the galvanometer. A minimum value of current should be allowed to flow through the voltmeter.
Required range of the voltmeter = 0 to 18 V
V = 18
Let the resistance needed = Rs
…(1)
By plugging the values of V, G and Is in equation 1, we get,
⇒![](data:image/png;base64,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)
⇒ Rs = 5988 Ω
For converting the galvanometer into a voltmeter of range 0-18 we can add a resistance of 5988Ω, is series with the galvanometer.
Question 17.A galvanometer coil has a resistance of 15
and the metre shows full scale deflection for a current of 4 mA. How will you convert the metre into an ammeter of range 0 to 6 A?
Answer:Given:
![](data:image/jpeg;base64,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Resistance of galvanometer coil, G = 15 Ω
Current for full scale deflection, Ig = 4mA
Upper limit of ammeter I = 6A
A galvanometer can detect only small currents and their direction. Thus, to measure large currents it is converted into an ammeter. A galvanometer can be converted into an ammeter by connecting a low resistance called shunt resistance in parallel to the galvanometer
Let shunt resistance = S
We know that value of shunt is given by:
…(1)
By plugging the values of Ig, I and G into Equation (1), we get,
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAAhCAMAAAA27N8rAAAAAXNSR0IArs4c6QAAAK5QTFRFAAAA///b//+22///tv//tv/b/9u2/9uQ29vb29u2ttv/29uQttu2kNv//7Zm27aQ27ZmkLbbZrb/Zrbb25BmZra225A6ZpDbZpC2OpDbtmZmOpC2tmY6kGaQtmYAkGY6Oma2OmaQOmZmkDpmkDo6ZjqQAGa2kDoAAGaQZjpmZjo6OjqQZjoAOjo6OjoAADqQADpmZgBmADo6ZgA6ZgAAOgA6OgAAAABmAAA6AAAAG5eDLAAAAAF0Uk5TAEDm2GYAAAH3SURBVHja7ZZbc5swEIWPJGrSC8TFLSktdUgvJqV2nLQusP//j3VWQg52MEbjhpl0si/74GWPdLSWPuA5hoTcLI6V+CUR1Zly6isuqb5oZW4TcQpXlddRnuplxKwUIKw8nJeJk2C8UP6f4D5DfLthQfH1zSYyJSln+Z038u7L0gian1hQ5ImbcZH+xGYgnuXcLcwwbzyVRQRZBHaBe4LTOnAS/B2AO9uMMBNaMDWGNYrviwg7gkSUASER3b7CKYLyhyfy2Wel54Gi7XQk2BFsjjqsvMnx2eq1lJdOtFZxAoh8cWiHfMh5oj2It8s6Hlw/X5thsZk7RZjogUnN8fD5yUZRzK8VD1ZgdlgHkJsKwPSG6NdsiKBcUs2FNgOvy+pFroeetwrgY7CdUm1AApESV/slF8QExPVbiHytxrokjPn+zxEFx9tcM0qUjayYUv1hR3JONtwuhsExKejWO1ZE/yaabufl6AfZfl4e11J55+0LPvpjreB6q54U0xXtj+kTpZgTytt+FFfqMMVY2hkIPQPuwfST8b5FMV3U0wM9jv8ea0yLYjqe6D7ocbzor4qVtrRNMQ8hpBd6XMIvs7OX/JxZipEbc0FE3YLd0ONKUTE/3G2KOWxpJ/S4WZop/nCHYrqopwd6HN+VJRFrtimmi3p6oOf/j79V/mBorWdcJAAAAABJRU5ErkJggg==)
⇒ S = 10mΩ
For converting the galvanometer into an ammeter of range 0-6 we can add a shunt of resistance 10mΩ.
Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.
Answer:
Here we have to find total magnetic field produced by the system so we will first find magnetic field due to each coil with direction and then add them in accordance with vector addition. Using the Right-hand thumb rule we can predict the direction of induced magnetic field in both the coils.
The orientation of both the coils is shown below in the figure.
The direction of induced magnetic field in both the coil can be found with the help of Right Hand Thumb Rule.
As Shown in figure.
So magnetic field in Coil X would be towards East, and in Coil Y would be towards West,
Explanation: if we curl our fingers in the Anticlockwise Sense in as in case of coil x our thumb will show the direction of the magnetic field which is towards East and if we curl our fingers in the clockwise Sense in as in case of coil Y our thumb will show the direction of the magnetic field which is towards West
The magnitude of magnetic field in a coil is given by the formula
Where, B is the magnetic field
I is the current in the coil
R is the radius of coil in metres
N is the number of turns
is the permittivity of free space = 4π × 10-7 TmA-1
For coil X
Current in the coil, Ix = 16A
Radius of the coil, Rx = 16cm = 0.16m
No. of turns of Coil, N �x = 20
So magnetic field due to coil X, Bx =
= 4π × 10-4 T
= 1.2510-3 T (Towards East)
For coil Y
Current in the coil, Iy = 18A
Radius of the coil, Ry = 10cm = 0.10m
No. of turns of Coil, N �y = 25
So magnetic field due to coil Y,
= 9π × 10-4 T
= 2.82 × 10-3 T (Towards West)
So, the Resultant magnetic field of the system = By- Bx
(since fields are in opposite directions)
= 2.82 × 10-3 T- 1.2510-3 T
= 1.57 × 10-3 T (Towards West)
So net magnetic field of the system is B = 1.57 × 10-3 T, Towards West direction
Question 2.
A magnetic field of 100 G (1 G = 10–4 T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10–3 m2. The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns m–1. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.
Answer:
Here, we have a particular value of No. of turns per unit Length and Current in the coil in order to obtain the given magnetic field.
The Required Magnetic field B = 100 G = 100 × 10–4= 10–2 T
Maximum Number of turns per unit length, n = 1000/m
Maximum Current flowing in the coil, I = 15 A
Permeability of free space, μ0 = 4π × 10–4TmA-1
We know magnetic field for a solenoid is given by
B = 𝜇 �0nI
Where,
B is the magnetic field
n is the Number of turns of the coil per unit length
I is the current in the coil
𝜇 �0 is the permittivity of free space
Explanation: here we can change the number of turns per unit length n (maximum 1000 turns per m) and current I (maximum 15A) since 𝜇ois a constant and we have to obtain a fixed value of magnetic field B = 10-2T, so we will alter values of n and I accordingly
Using the formula B = 𝜇 �0nI
We get, B/𝜇 �0 = nI
So,
= 7957.74 A/m ≈ 8000 A/m
If we take number of turns of coil N = 400,
If we take length of the coil L = 50 cm = 0.5m,
No. of turns per unit length, n = N/L= 400/0.5 = 800/m
(less than 1000/m)
If we take current I = 10 A
(less than 15 A),
We get nI = 8000 A/m
Area of Coil A = 10-3 m2 = πr2, where r is radius of coil
We get
⇒
⇒ r = 0.017m
The values of N, L and I are within the proposed limits, Though there can be other values as well.
Question 3.
For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by,
(a) Show that this reduces to the familiar result for field at the centre of the coil.
(b) Consider two parallel co-axial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by,, approximately.
[Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.]
Answer:
We know for a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by,
𝜇 �0 is the permittivity of free space
As can be seen in the figure.
(a) To find the magnitude of magnetic field B at the centre of a circular coil.
Distance from centre, x = 0 m (as we are finding magnetic field at the centre of coil)
No. of turns of coil N = 1
Putting these values in equation ,
we get,
Or
Or
This is same as the known result for magnetic field of a current carrying loop at the centre.
(b) The situation has been represented in the figure, suppose two circular loops of equal Radius R carry equal current I in same direction, and are also separated by a distance R,
Now suppose a point at a distance d from midpoint of separation of the coils,so distance from one coil,
And distance from second coil, x1
Magnetic field due to 1st coil is given by
Magnetic field due to 2nd coil is given by
Net magnetic field due to both the coils is given by B = B1 B2
Explanation: Using Right hand thumb rule if curl our fingers in the direction of current the thumb shows the direction of the magnetic field,we find that magnetic field due to both coil is in same direction so their magnitude can be simply added to give net magnetic field
So we get,
Putting the values of x1 and x2 we get
i.e.
i.e.
Expanding equations of second order we get
i.e.
Since d is very small compared to R so neglecting and taking terms of R2 common from both the terms we get
Explanation: we have used the binomial expansions
and
Where x = 4d/5R and we have neglected second terms onwards because d<<R
So d2/R2 ≈ 0
i.e.
So
Solving and putting value of = 0.72
We get
Hence proved the required result
Question 4.
A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound.
If the current in the wire is 11 A, what is the magnetic field
(a) outside the toroid,
(b) inside the core of the toroid, and
(c) in the empty space surrounded by the toroid.
Answer:
The Toroid is same as a solenoid but is bound in a circular region as compared to straight cylindrical region in a solenoid the length of a toroid is given by L = 2πR, (Perimeter of a Circle)
where R is mean radius of cross section of toroid
= 25.5 cm = 0.255 m
here Total number of turns of toroid N = 3500,
no. of turns per unit length n = N/L = = 2475.74/m
the current flowing in Toroid I = 11 A
The toroid has been shown in the following figure
(a) Since Toroid is same as a solenoid so magnetic field outside the toroid = 0 T same as in case of solenoid.
Explanation: if we apply Ampere Circuital Lawto find magnetic field B at small element dl due to a current carrying conductor with current I flowing through it and
is permittivity of free space, outside the solenoid or toroid, where there is no conductor/wire/current carrying loop, the current I = 0 so we get
So Integrating over length l we get Bl = 0 so magnetic field B = 0 i.e. at all places where there is no current carrying loop magnetic field B = 0
(b) The magnetic field in the inner core of toroid is given by
B = 𝜇onI
Where n is no. of turns per unit length,
I is the current flowing in Toroid,
𝜇o is the permittivity of free space = TmA-1
So putting all values, B = =
T
i.e. Magnetic field inside core is 0.03 T.
(c) Again it’s the same case as of exterior of a solenoid as explained above so magnetic field is Zero, here also in the empty space between the toroid.
Question 5.
Answer the following questions:
A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
Answer:
When a charged particle enters a magnetic field it experiences a force known as Magnetic Lorentz Force which is given by:
Where is the force on the Charged particle having charge q,moving with a velocity
in a magnetic Field
Note:,
and
are vector quantities, and charge q is a scalar quantity, and
is the cross product or vector product of
and
,so resultant is perpendicular to plane containing
and
if we evaluate the formula we get,
Where, and
are magnitude of velocity and magnetic field respectively, θ is the angle between Velocity of particle and magnetic field and ŵ is a unit vector perpendicular to plane containing
and
When angle between Velocity of particle and magnetic field is either
or
i.e. particle is either moving parallel or antiparallel to the field we can see force on the particle,
F = 0 N, since sinθ = 0 when θ is either 00 or 1800,
The particle came out of the magnetic field un-deflected, and with constant velocity i.e. it did not experience any force so we can say that particle was moving in same direction as that of magnetic field i.e. from East Towards West or in opposite direction from West towards East and magnitude of velocity can be any value.
The following figure depicts both the situations
Question 6.
Answer the following questions:
A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
Answer:
When a charged particle enters a magnetic field it experiences a force known as Magnetic Lorentz Force which is given by
→
Now, due to magnetic lorentz force, the particle accelerates so the velocity of particle changes, Magnetic field changes is both magnitude and direction so the Magnitude of Force on particle also keeps on changing, hence the velocity of particle also changes.
Note: Acceleration is Rate of Change of Velocity, so if a particle experiences force, it accelerates and hence its velocity changes. Velocity is a vector quantity so it depends on direction, so velocity of a particle changes if its magnitude or speed changes, direction remain the same, or velocity changes when direction of particle changes and magnitude of velocity or speed remains same, or velocity changes when both speed and direction changes.
In this Case force on the particle is always perpendicular to its velocity, which only changes the direction of the particle and its speed remains same, i.e. velocity of particle changes due to change in direction of particle and magnitude of velocity or speed same as it entered.
Following Figure depict the direction of force on particle at any instant
Question 7.
Answer the following questions:
An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.
Answer:
If the Charged particle have to go undeflected then there should be no force experienced by it, or resultant of all the forces on the particle is zero. Here, the charged particle is experiencing Magnetic Lorentz force and electrostatic force due to electric field
We know Magnetic Lorentz Force is given by
Direction of the Magnetic force is perpendicular to plane containing V and B. and for a positively charged particle can be found out with help of Fleming’s left hand thumb rule.
Electrostatic force is given by
F = qE
Where F is the force experienced by particle having charge q and moving in an electric field E, direction of force is same as that of Electric field for a positively charged particle and is exactly reversed in case of negatively charged particle.
So both the forces on particle should be equal in magnitude and opposite in direction.
Since Electric Field is from North to South, and particle is an electron i.e. negatively charged so force on it should be towards North so force due to magnetic field should be towards south .As shown in figure
Using the Fleming left hand rule we will decide the direction of magnetic field
Flemings rule : If the stretch our forefinger middle finger and thumb mutually perpendicular to each other then if forefinger depicts the direction of magnetic field, middle finger depicts the direction of the current(Direction of Velocity of Positive Charge) then, Thumb depicts the direction of Force.
Applying the rule
Since Electron is negatively charged and moving from West to east so direction of current is from east to west, depicted by middle finger, force should be towards both depicted by our thumb, so we find our forefinger depicting magnetic field is in a direction vertically downwards in the plane
Now equating magnitude of both the forces
Here θ = 90° because Velocity of particle is perpendicular to Magnetic field,
So,sinθ = 1
i.e.
or magnitude of magnetic field is given by
, in a direction vertically downwards.
Question 8.
An electron emitted by a heated cathode and accelerated through a potential difference of 2.0 kV, enters a region with uniform magnetic field of 0.15 T. Determine the trajectory of the electron if the field
(a) is transverse to its initial velocity,
(b) makes an angle of 30° with the initial velocity.
Answer:
When an charged particle having charge q is accelerated by a potential difference V volts it gain kinetic energy given by
K = Vq, which imparts it with velocity
We know kinetic energy of a Particle with mass m kg and velocity v is given by
Equating both equations
We get velocity of the particle as
Here Potential difference of the particle, V = 2.0 kV
= 2000 V
Particle is electron, charge of electron
q = 1.6 × 10 -19 C
mass of electron
m = 9.1 × 10-31 Kg
so velocity of the particle,
m/s
Solving we get
Velocity of particle,
v = m/s
(a) Now here the particle enters the magnetic field orthogonally so it will experience Lorentz magnetic force is given by :
Where is the force on the Charged particle having charge q, moving with a velocity
in a magnetic Field
Where, and
are magnitude of velocity and magnetic field respectively, θ is the angle between Velocity of particle and magnetic field and ŵ is a unit vector perpendicular to plane containing
and
Here, since particle entered orthogonally now force on particle will be perpendicular to both magnetic field and its velocity at every instant, since magnetic field and velocity are in one plane and force is in a plane perpendicular to them, this force does not change the magnitude of velocity or speed it only changed it the direction of particle and force always act tangentially to the velocity of the particle causing it to move in a circular trajectory
As shown in the figure
Now the required centripetal force for circular motion is provided by the magnetic force we know centripetal force is given by
,
Where F is the centripetal force,
m is the mass of the particle,
moving in a circular region of radius r,
with velocity v
Magnitude of magnetic force on particle moving with velocity v in a magnetic field B orthogonally is
F = qvB(sinθ)
here at every instant so
F = qvB
Equating both equations
We get radius trajectory of the particle,
The particle is electron, thus, charge of electron is:
q = 1.6 × 10 -19 C
mass of electron
Kg
Velocity of particle,
v = m/s
Magnitude of magnetic field
B = 0.15 T
so
= 100.47 m
= 1.00 mm
So trajectory is a circle of radius 1.00 mm normal to plane of magnetic field
(b) when the particle enters the magnetic field, with its velocity at some angle with it, and not exactly orthogonal, particle follows a helical path, since there is force on the component of velocity which is perpendicular to the magnetic field, and No force is experience due to the component of velocity parallel to magnetic field, which keeps moving the particle forward so path is helical instead of circular. Velocity makes angle of 30 degree with the magnetic field, consider magnetic field along x axis
so particle moving in x-y plane initially making an angle 30o with x axis, so using the Fleming left hand rule we find out the force is Toward positive Z axis,
as shown in figure
Explanation: It can be visualised as particle moving in circular path, at the same time moving forward, like an spiral, if there would have been no horizontal component of velocity it would have moved in a circular path.
Now particle tends to move in circular path in y-z plane due to Y component of velocity perpendicular to the field,and move forward along x axis due to x component of velocity,
Now angle made by velocity with x-axis,
θ = 30°
So x component of velocity,
m/s
So y component of velocity,
m/s
For the radius of the path we will again use the equation
where, q is charge of Particle which is electron so
C
m is mass of particle, i.e. mass of electron
Kg
Component of Velocity of particle undergoing circular motion,
vy = m/s
Magnitude of magnetic field
B = 0.15 T
Putting values in equation
m
= 0.5mm
So radius of the helical path followed by electron is 0.5 mm and is moving along magnetic field with speed m/s.
Question 9.
A magnetic field set up using Helmholtz coils (described in Exercise 4.16) is uniform in a small region and has a magnitude of 0.75 T. In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of (single species) charged particles all accelerated through 15 kV enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is 9.0 × 105 V m–1, make a simple guess as to what the beam contains. Why is the answer not unique?
Answer:
Now here the charged particle is two forces, magnetic Lorentz force due to magnetic field and Electrostatic force and electrostatic force due to electric field, now for particle to go undeflected, the direction of both the forces should be exactly opposite to each other, and magnitude should be equal. direction of force is same as that of Electric field for a positively charged particle and is exactly reversed in case of negatively charged particle and direction of magnetic force is given by Flemings left hand rule.
The situation is depicted in the figue.
Electrostatic force is given by
Where F is the force experienced by particle having charge q and moving in an electric field E Magnitude of magnetic force on particle moving with velocity v in a magnetic field B, velocity makes angle with the Field
here ,since velocity is perpendicular to magnetic field
so
So Equating both we get
so we get
velocity of the particle,
now the particle is accelerated through a potential difference When an charged particle having charge q is accelerated by a potential difference V volts it gain kinetic energy given by
K = Vq, which imparts it with velocity
We know kinetic energy of a Particle with mass m and velocity v is given by
Equating both equations
We get velocity of the particle as
So Equating both the values of velocity v we get
Solving we get
Here we are given,
Electric field E = 9.0 × 105 V m–1
Magnetic Field B = 0.75 T
The Potential difference V = 15 kV = 15000 V
Putting all the values we get
⇒ q/m = 4.8 107 C/Kg
This is the charge to mass ratio of Deuterium ions Dor deuterons, which is a stable isotope of Hydrogen having one proton and one neutron in its nucleus.
So charge on Deuterium ion = e (since 1 charge)
= C
Mass of Deuterium ion,
m = Kg
so charge to mass ratio,
≈ 4.8 × 107 C/Kg
the answer is not unique because only the ratio of charge to mass is determined. There can Other possible species whose charge to mass ratio is same as this value examples are
He, Li, etc.
Question 10.
A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires.
(a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?
(b) What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before? (Ignore the mass of the wires.) g = 9.8 m s–2.
Answer:
Given:
Length of rod = 0.45 m
Mass of rod = 60 gm
Current = 5.0 A
Acceleration due to gravity, g = 9.8 m/s2
(a) Let magnetic field in conductor so that tension is zero = B
Tension will be zero if the force due to magnetic field and the weight is balanced.
We know that,
B × I × l = m × g …(1)
Where,
B = magnetic field
I = current through the conductor
l = length of conductor
m = mass of conductor
g = acceleration due to gravity
From equation (1) we have,
Now plugging the values of m, g, I and l in equation (1)
⇒
⇒ B = 0.26 T
So, a magnetic field of 0.26 Tesla has to be set up normal to the conductor in order to get zero tension in the supporting wire. Using Fleming’s left hand rule we find that the magnetic field applies a force in upward direction on the conductor which balances its weight.
(b) Let total tension in wire if the direction of current is reversed = P
According to question, the magnetic field is kept the same. Using Fleming’s left hand rule we find that Force due to magnetic field on the conductor acts downwards.
Writing the balancing equations:
P = B × I × l m × g …(2)
Where,
P = tension
B = magnetic field
I = current through the conductor
l = length of conductor
m = mass of conductor
g = acceleration due to gravity
Now, putting the values in equation (2) we get,
⇒ P = 0.26T × 5A × 0.45A 0.06Kg × 9.8ms-2
⇒ P = 1.17 N
The tension in wire is 1.17 N.
Question 11.
The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? Is the force attractive or repulsive?
Answer:
Given:
Current through the wire, I = 300 A
Length of wire, L1 = 70 cm
Length of wire, L2 = 70 cm
Distance between the wires, d = 1.5 cm
We understand that current carrying conductors create magnetic fields which in turn applies force on nearby current carrying conductor(s).
We know that,
…(1)
Where,
F = force applied
�0 = permeability of free space
I = current through the conductors
d = separation between the conductors
Now, putting the values of F, �0, I and d in equation (1)
⇒
⇒ F = 1.2 Nm-1
Hence, the force applied on the wires is 1.2 N per metre. The force is repulsive in nature because the current is carried in the opposite direction.
Question 12.
A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,
(a) the wire intersects the axis,
(b) the wire is turned from N-S to northeast-northwest direction,
(c) the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?
Answer:
Given:
Magnetic field strength, B = 1.5 T
Radius of cylinder, r = 10 cm
Current in wire travelling north to south, I = 7A
(a) Let the force on wire = F1
If the wire intersects the axis of the magnetic field, then we observe that length of wire will be equal to the diameter of the cylinder.
L1 = 2 × r = 20 cm
We know that,
F = B × I × L1 × sinθ …(1)
Where,
F = Force on wire
B = magnetic field strength
I = current through the wire
L1 = length of wire
θ = angle between direction of field and direction of current
Since, the field is along east to west and current flows along north south, direction so, θ = 90°.
By putting the values of B, I and L1 in equation 1.
⇒ F = 1.5T × 7A × 0.2m × sin90°
⇒ F = 2.1 N
So, force on wire is 2.1 N and it acts in vertically downward direction.
(b) Let the force on wire = F2
If the wire is turned towards Northeast-Northwest direction.
We observe that wire has been turned 45°, i.e. θ = 45°
L2 = L1/sinθ.
L2 = 2 × L1
F2 = B × I × L2 × sinθ
F2 = B × I × L2
F2 = 2.1 N
Hence the force is 2.1 N and it acts vertically downwards.
(c) Let, the force on wire = F3
The wire has been lowered 6 cm,
⇒ x = ( r2-p2)0.5
⇒ x = ( 100-36)0.5
⇒ x = 8
So length of wire in the magnetic field region = 16 cm
(By using the geometry)
We know that,
F = B × I × L1 × sinθ …(1)
Now, putting the values in B, T and I in equation 1.
⇒ F = 7T × 0.16A × 1.5T
⇒ F = 1.68 N
The direction of the force will be vertically downward, the direction of force is given by screw rule.
Question 13.
A uniform magnetic field of 3000 G is established along the positive z-direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A. What is the torque on the loop in the different cases shown in Fig. 4.28? What is the force on each case? Which case corresponds to stable equilibrium?
Answer:
Given:
Magnetic field strength, B = 3000G
B = 3000 × 10-4T
B = 0.3 T
Length of rectangular loop = 10 cm
Width of loop = 5 cm
Current in loop = 12 A
We know that,
Torque, T = IA × B …(1)
Where, I = current through loop
A = area of cross-section
B = magnetic field strength
Note: We take vector normal to the cross-section for A.
For each of the case we plug in the variables in equation (1).
(a) T = 12A × (50 × 10-4) î m2 × 0.3 T
= -1.8 × 10-2 ĵ Nm (∵ î ×
= -ĵ )
Force on the loop is Zero as the angle between area of cross section and magnetic field is Zero.
(b) This case is similar to A, hence the results will also be same. There is no change in any vectors.
(c) T = IA × B
We observe that A is perpendicular to x-z plane and B is along z axis.
⇒ T = -12A × (50 × 10-4)m2 ĵ × 0.3T
⇒ T = -1.8 × 10-2 î Nm (∵ ĵ × = -î )
(d) Magnitude of torque,
|T| = IA × B
⇒ |T| = 12 × (50 × 10-4)m2 × 0.3T
⇒ |T| = 1.8 × 10-2 Nm
This torque is makes 240° with the positive x direction. The force again is Zero.
(e) T = IA × B
= 12 × (50 × 10-4) m2 × 0.3
T
= 0
Since cross section and magnetic field are in same direction net torque is zero. Net force is also Zero.
(f)
= 12 × (50 × 10-4)
× 0.3
= 0
Hence the torque and forces are zero.
Stable equilibrium:
In case E, the angle between A and B is zero. If we displace the wire, it will come back in this position, hence it is the stable equilibrium condition.
Unstable equilibrium:
In case F, the angle between A and B is 180°. If the wire is displaced, it will not come back in this position so we can conclude that it is the case for unstable equilibrium.
Question 14.
A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil. If the current in the coil is 5.0 A, what is the
(a) total torque on the coil,
(b) total force on the coil,
(c) average force on each electron in the coil due to the magnetic field?
(The coil is made of copper wire of cross-sectional area 10–5 m2, and the free electron density in copper is given to be about 1029 m–3.)
Answer:
Given:
Number of turns, N = 20
Radius of coil, r = 10cm
Magnetic field strength = 0.10 T
Current in the coil = 5 A
a) The torque on the coil is zero because the magnetic field is uniform along the coil.
b) The total force on the coil is Zero due to uniform magnetic field.
c) Let average force on each electron in the coil due to magnetic field = F
Cross-sectional area of the wire, A = 10-5 m2
Free electron density or number of free electron per metre cube of copper, D = 1029
Charge in each electron = 1.6 × 1019 C
We know that,
…(1)
Where,
F = force due to magnetic field
B = Magnetic field strength
e = charge on electron
Vd = drift velocity of electron
Vd = I/ (NeA) …(2)
Where, I = current through the coil
N = Density of free electron
A = cross sectional area.
Putting values in equation (2)
⇒
⇒ Vd = 3.125 × 1043 ms-1
F = B × e × Vd …(3)
By putting the values of B, e and Vd in equation 3, we get,
⇒
⇒ F = 5 × 10-25 N
Hence, average force on each electron is 5 × 10-25 N.
Question 15.
A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of 6.0 A in the wire. What value of current (with appropriate sense of circulation) in the windings of the solenoid can support the weight of the wire? g = 9.8 m s–2.
Answer:
Given:
Length of solenoid, L1 = 60 cm
Radius of solenoid, r = 4 cm
Number of layers, n1 = 3
Number of turns, N = 300
Total number of turns,n = N × n1 = 900
Length of wire, L2 = 2 cm
Mass of wire, m = 2.5 gm
Current flowing through the wire, I2 = 6 A
Acceleration due to gravity, g = 9.8 ms-2
Intuitively, this problem can be broken down into three parts. In first part we will establish the magnetic field inside the solenoid and in second part we introduce a current carrying conductor in the magnetic field. Then we can evaluate the force on the wire. In the final part we try to find the balancing force and finally the current.
Part (1)
We know that magnetic field inside a solenoid is given by,
…(1)
Where,
B = Magnetic field strength
n = total number of turns
I1 = current through the coil
L1 = length of the coil
�0 is the permeability of free space.
�0 = 4 × π × 10-7 TmA-1
Part (2)
We know that, when a current carrying conductor is placed in a magnetic field, it experiences a force given by,
F = B × I2 × L2 …(2)
Now putting the value of B from equation 1 into equation 2.
…(3)
Where, I2 = current through the conductor
L2 = length of wire
Part (3)
Since, the wire is suspended inside the solenoid, the upward force on it must be equal to its weight.
By equating the weight (m × g) of the body with force in equation (3), we get
m × g = …(4)
⇒ I1 =
⇒ I1 =
Note: It can be noted that in SI base units Tesla(T) = Kgs-2A-1
⇒ I1 = 108A
Hence the current flowing through the solenoid is 108A.
for the suspension of the wire.
Question 16.
A galvanometer coil has a resistance of 12 and the metre shows full scale deflection for a current of 3 mA. How will you convert the metre into a voltmeter of range 0 to 18 V?
Answer:
Given:
Resistance of the galvanometer coil, G = 12Ω
Current for full scale deflection = 3mA
For converting a galvanometer into a Voltmeter we can connect a resistance in series with the galvanometer. A minimum value of current should be allowed to flow through the voltmeter.
Required range of the voltmeter = 0 to 18 V
V = 18
Let the resistance needed = Rs
…(1)
By plugging the values of V, G and Is in equation 1, we get,
⇒
⇒ Rs = 5988 Ω
For converting the galvanometer into a voltmeter of range 0-18 we can add a resistance of 5988Ω, is series with the galvanometer.
Question 17.
A galvanometer coil has a resistance of 15 and the metre shows full scale deflection for a current of 4 mA. How will you convert the metre into an ammeter of range 0 to 6 A?
Answer:
Given:
Resistance of galvanometer coil, G = 15 Ω
Current for full scale deflection, Ig = 4mA
Upper limit of ammeter I = 6A
A galvanometer can detect only small currents and their direction. Thus, to measure large currents it is converted into an ammeter. A galvanometer can be converted into an ammeter by connecting a low resistance called shunt resistance in parallel to the galvanometer
Let shunt resistance = S
We know that value of shunt is given by:
…(1)
By plugging the values of Ig, I and G into Equation (1), we get,
⇒
⇒ S = 10mΩ
For converting the galvanometer into an ammeter of range 0-6 we can add a shunt of resistance 10mΩ.