Class 12th Physics Part I CBSE Solution
Exercises- What is the force between two small charged spheres having charges of 2 × 10-7 C and 3 ×…
- The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of…
- Check that the ratio is dimensionless. Look up a Table of Physical Constants and determine…
- Explain the meaning of the statement ‘electric charge of a body is quantised’.…
- Why can one ignore quantisation of electric charge when dealing with macroscopic i.e.…
- When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon…
- Four-point charges qA = 2 μC, qB = -5 μC, qC = 2 μC, and qD = -5 μC are located at the…
- An electrostatic field line is a continuous curve. That is, a field line cannot have…
- Explain why two field lines never cross each other at any point?
- Two point charges qA = 3 μC and qB = -3 μC are located 20 cm apart in vacuum. (a) What is…
- A system has two charges qA = 2.5 × 10-7C and qB = -2.5 × 10-7 C located at points A: (0,…
- An electric dipole with dipole moment 4 × 10-9 C m is aligned at 30° with the direction of…
- A polythene piece rubbed with wool is found to have a negative charge of 3 × 10-7 C. (a)…
- Two insulated charged copper spheres A and B have their centres separated by a distance of…
- What is the force of repulsion if each sphere is charged double the above amount, and the…
- Suppose the spheres A and B in Exercise 1.12 have identical sizes. A third sphere of the…
- Figure 1.33 shows tracks of three charged particles in a uniform electrostatic field. Give…
- Consider a uniform electric field E = 3 × 10^3 î N/C. (a) What is the flux of this field…
- What is the net flux of the uniform electric field of Exercise 1.15 through a cube of side…
- Careful measurement of the electric field at the surface of a black box indicates that the…
- A point charge + 10 μC is a distance 5 cm directly above the centre of a square of side 10…
- A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What…
- A point charge causes an electric flux of -1.0 × 10^3 Nm^2 /C to pass through a spherical…
- A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm…
- A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of…
- An infinite line charge produces a field of 9 × 10^4 N/C at a distance of 2 cm. Calculate…
- Two large, thin metal plates are parallel and close to each other. On their inner faces,…
Additional Exercises- An oil drop of 12 excess electrons is held stationary under a constant electric field of…
- Which among the curves shown in Fig. 1.35 cannot possibly represent electrostatic field…
- In a certain region of space, electric field is along the z-direction throughout. The…
- A conductor A with a cavity as shown in Fig. 1.36(a) is given a charge Q. Show that…
- A hollow charged conductor has a tiny hole cut into its surface. Show that the electric…
- Obtain the formula for the electric field due to a long thin wire of uniform linear charge…
- It is now believed that protons and neutrons (which constitute nuclei of ordinary matter)…
- Consider an arbitrary electrostatic field configuration. A small test charge is placed…
- A particle of mass m and charge (-q) enters the region between the two charged plates…
- Suppose that the particle in Exercise in 1.33 is an electron projected with velocity vx=…
- What is the force between two small charged spheres having charges of 2 × 10-7 C and 3 ×…
- The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of…
- Check that the ratio is dimensionless. Look up a Table of Physical Constants and determine…
- Explain the meaning of the statement ‘electric charge of a body is quantised’.…
- Why can one ignore quantisation of electric charge when dealing with macroscopic i.e.…
- When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon…
- Four-point charges qA = 2 μC, qB = -5 μC, qC = 2 μC, and qD = -5 μC are located at the…
- An electrostatic field line is a continuous curve. That is, a field line cannot have…
- Explain why two field lines never cross each other at any point?
- Two point charges qA = 3 μC and qB = -3 μC are located 20 cm apart in vacuum. (a) What is…
- A system has two charges qA = 2.5 × 10-7C and qB = -2.5 × 10-7 C located at points A: (0,…
- An electric dipole with dipole moment 4 × 10-9 C m is aligned at 30° with the direction of…
- A polythene piece rubbed with wool is found to have a negative charge of 3 × 10-7 C. (a)…
- Two insulated charged copper spheres A and B have their centres separated by a distance of…
- What is the force of repulsion if each sphere is charged double the above amount, and the…
- Suppose the spheres A and B in Exercise 1.12 have identical sizes. A third sphere of the…
- Figure 1.33 shows tracks of three charged particles in a uniform electrostatic field. Give…
- Consider a uniform electric field E = 3 × 10^3 î N/C. (a) What is the flux of this field…
- What is the net flux of the uniform electric field of Exercise 1.15 through a cube of side…
- Careful measurement of the electric field at the surface of a black box indicates that the…
- A point charge + 10 μC is a distance 5 cm directly above the centre of a square of side 10…
- A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What…
- A point charge causes an electric flux of -1.0 × 10^3 Nm^2 /C to pass through a spherical…
- A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm…
- A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of…
- An infinite line charge produces a field of 9 × 10^4 N/C at a distance of 2 cm. Calculate…
- Two large, thin metal plates are parallel and close to each other. On their inner faces,…
- An oil drop of 12 excess electrons is held stationary under a constant electric field of…
- Which among the curves shown in Fig. 1.35 cannot possibly represent electrostatic field…
- In a certain region of space, electric field is along the z-direction throughout. The…
- A conductor A with a cavity as shown in Fig. 1.36(a) is given a charge Q. Show that…
- A hollow charged conductor has a tiny hole cut into its surface. Show that the electric…
- Obtain the formula for the electric field due to a long thin wire of uniform linear charge…
- It is now believed that protons and neutrons (which constitute nuclei of ordinary matter)…
- Consider an arbitrary electrostatic field configuration. A small test charge is placed…
- A particle of mass m and charge (-q) enters the region between the two charged plates…
- Suppose that the particle in Exercise in 1.33 is an electron projected with velocity vx=…
Exercises
Question 1.What is the force between two small charged spheres having charges of 2 × 10–7 C and 3 × 10–7C placed 30 cm apart in air?
Answer:The coulomb attraction formula used to find the force, F is given as,
…(1)
Where, q1 and q2 are the charges.
r is the distance between the charges.
is a constant and its value is 9x109 N m2 C-2
ϵ0 is the permittivity of free space. Its value is 8.85 x 10-12 (F/m)
Now, the diagram is:
![](data:image/png;base64,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)
Since, both the charges are positive, thus, the nature of force will be repulsive. F12 is the force on charge q2 caused by charge q1 andF21 is the force on charge 1 due to charge 2 .
Now, Given:
Charge on the first sphere, q1 = 2 × 10–7 C
Charge on the second sphere, q2 = 3 × 10–7 C
Distance between the spheres, r(in m) =30/100=0.3 m
Putting the values in equation (1), we get,
![](data:image/png;base64,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)
F = 6 × 10-3 N
Hence, the force between the given charged particles will be 6 × 10-3 N. Since the nature of the charges is the same i.e. they are both positive. Hence, the force will be repulsive.
Question 2.The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of charge –0.8 μC in air is 0.2 N.
(a) What is the distance between the two spheres? (b) What is the force on the second sphere due to the first?
Answer:(a) The electrostatic force, F = 0.2 N
Charge on this present sphere, q1 = 0.4 μC = 0.4 × 10-6 C
Charge on the other sphere, q2 = –0.8 μC = -0.8 × 10-6 C
The electrostatic force between the spheres can be given by the equation,
…(1)
Where, q1 and q2 are the charges.
r is the distance between the charges.
is a constant and its value is 9x109 N m2 C-2
ϵ0 is the permittivity of free space. Its value is 8.85 x 10-12 (F/m)
Therefore, from equation (1),
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ r2 = 144 x 10-4 m2
Taking square root both the sides,
⇒ r = ![](data:image/png;base64,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)
r = 0.12 m
Hence, the distance between the two spheres is 0.12 m.
(b) Since the nature of the charges on the spheres is opposite, the force between them will be attractive in nature. The spheres will attract each other with the same amount of force.
Therefore, the force on the second sphere due to the first sphere will be 0.2 N.
Question 3.Check that the ratio
is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?
Answer:The given ratio is ![](data:image/png;base64,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)
It is the ratio of electric force i.e.
to gravitational force i.e.
between a proton and an electron with the distance between them as constant.
This is because
Here, G = Gravitational constant. (Unit = Nm2kg-2 )
me and mp are the mass of electron and proton respectively. (Unit = Kg)
e = Electric charge (Unit = Coulomb)
K is a constant = ![](data:image/png;base64,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)
is the permittivity of space. Its units are Nm2 C-2.
Let us substitute the units into the ratio in order to deduce the dimensions,
![](data:image/png;base64,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)
All the units get cancelled, and we see that the given ratio is dimensionless i.e. M0 L0 T0
Let us now calculate the value of the given ratio,
G = 6.67 × 1011 Nm2 Kg-2
e = 1.6 × 1019 C
me = 9.1 × 10-31 kg
mp = 1.66 × 10-27 kg
On substituting these values into the ratio, we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Note:
![](data:image/png;base64,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)
This implies that the electric force between a proton and an electron is 1039 times greater than the gravitational force.
Question 4.Explain the meaning of the statement ‘electric charge of a body is quantised’.
Answer:Electric charge of a body is quantised.
This statement means that charge on a body can take only integral values i.e. (1, 2, 3, 4, …. N) number of electrons can be transferred from one body to another. The charges cannot be transferred in fractions. It can only be an integral multiple of the charge of one electron.
Therefore, as a result, a body will possess a charge that is an integral multiple of the electric charge of an electron.
Question 5.Why can one ignore quantisation of electric charge when dealing with macroscopic i.e. large-scale charges?
Answer:When considered on a macroscopic level or a large scale, we tend to ignore the quantisation of electric charges. This is because on a large scale, the charges that we deal with are extremely huge when compared to the magnitude of an individual charge. Hence, we can say that the quantisation of electric charge is not useful on a macroscopic scale. It is therefore ignored and considered to be of continuous nature.
Question 6.When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.
Answer:i. When two bodies are rubbed against each other, this process results in the production of charges on the bodies involved.
ii. The charges on each body will be of equal magnitude but of opposite nature. This happens because charges are always created in pairs.
This phenomenon of charging bodies by rubbing them against each other is termed as charging by friction. However, the net charge of the system – of both the bodies – is zero.
iii. This is because equal amounts of charge of opposite nature cancel each other out.
iv. When a glass rod is rubbed with a silk cloth, then opposite charges appear on both the bodies. This is in accordance with the law of conservation of energy. (Net charge of isolated system remains constant) This phenomenon is also observed when other pairs of bodies are also rubbed with each other.
Question 7.Four-point charges qA = 2 μC, qB = –5 μC, qC = 2 μC, and qD = –5 μC are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 μC placed at the centre of the square?
Answer:Consider a square of side 10 cm. Four charges are placed in its corners. Let O be the center of the square.
The diagram is:
![](data:image/png;base64,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)
AB = BC = CD = DA = 10 cm
Diagonal of a square = √2 × Side of a square
Therefore,
AC = BD = 10√2 cm
AO = OC = DO = OB = (10√2)/2 cm = 5√2cm
i. A charge of magnitude 1μC is placed at O, the center of the square.
ii. The force experienced at center due to side charge at B is same in magnitude but in a direction opposite to the direction to the force at center due to charge at D.
iii. The force experienced at center due to side charge at A is same in magnitude but in a direction opposite to the direction to the force at center due to charge at C .
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)
Force on the 1 u C in the center is = Fa + Fb + Fc + Fd = Fa + (- Fa) + Fc + ( - Fd) = 0
Therefore, we can conclude that the resultant force by the four charges kept in the corners on the charge that is kept in the center will be zero.
Question 8.An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
Answer:An electric field line always points in the direction that a positive test charge would accelerate in if placed upon that line. A charge will experience a continuous force when placed in an electrostatic field. Therefore, an electrostatic field line will be a continuous curve. The field lines do not have any sudden breaks as the test charge or any charge will move continuously and does not jump from any point to another.
Question 9.Explain why two field lines never cross each other at any point?
Answer:An electric field line represents the direction in which a positive test charge would accelerate in if placed on the line. If two field lines intersect, then this will imply that the electric field intensity points to two directions at the same point. This is not possible.
Hence, two electric field lines will never cross each other.
Question 10.Two point charges qA = 3 μC and qB = –3 μC are located 20 cm apart in vacuum.
(a) What is the electric field at the midpoint O of the line AB joining the two charges?
(b) If a negative test charge of magnitude 1.5 × 10–9 C is placed at this point, what is the force experienced by the test charge?
Answer:(a) The diagram is shown as below:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUAAAAA8CAIAAACYZfTzAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOwwAADsIB3nSZJQAAB35JREFUeF7tXb1uG0cQPqZKKeQJXJAuBBUpA7kQ1ZlyQzVu3VFdyMZQY1gnwYUEN2Q6qgnSuhDU2EwnsrDhBxBUmCzyBEGeQMzs7d3x/nicJXnUzvFbEAZ13Nub/Xa+m9nZnXVlOp06KEAACMhE4CeZYkNqIAAEFAIgMPQACAhGAAQWPHgQHQiAwNABICAYARBY8OBBdCAAAkMHgIBgBEBgwYMH0YEACAwd2CIEBieVdHnRm8iFAASWO3aQfGkEWl9oA9N0Ou7uUxPfOjW5HAaBl1YC3Cgegeqr14rBxOGHsdDOgMBCBw5iAwGFgBQCT3ovgsmLXHcHKmcZApPPn74pkfa7bxuWicYVRwiBA6Q9d+fTZ8FBB+7AoF6RCFwfeeag1tH8ff2qWuTTimxbBoEHHzXSuoDBuRoRcVY8LYXHkobLD2JNp19aSqE6tcrJoEiaFde2CAIPbq89BFpdL2pIgH8UCndxA6lbVsskyqxEFVSpp1j9LBqwRlMxmMr1rUyVkkDgkL/NdhA1lAp3ofpIpvfIe9O1vvSDKV2j79kY5/oIhrhQ8J+qcQEEnvG34YRxfzA4pTHhPKPVjEZkAhsDtyWLY4FyiQ1jWU/gSe+D7z97agkGz3vVT37c65/2d2uxOrVdvdbp3P9A8M9Hxg9iVSqey0ITjq9toWEs2wk8Cz/HA4fkFH6QvAOuQI9r73lcF6vP9wp8mqymG31vB1aihBMOWZ3xpLWcwCF/w6hMsP8Nweh52pY0tKFpFqieEHkRAnYTeMbfyLSu2n6nI4dYToqObmhok9sCxw/+ElzSNC/SjdL+ns5nENzVLJfClms6gKonKbEy9wdbJH8SOfTW/CRcAVb73fGTSGXVQ/OJapWoTGEqOFZW8Ns3JTqtAwdhGT2xS10oU29N+kJWl1ldFiNAYOawyqlGy8H+FkEtM5lesTHWNaHOZ69+oCAOl4jAo5EzjAz42cGaRh/NiEfAbgIHXpIPs9kLVw6Bz0eqg8N/nPoz9aXuOAegqHhqbaADpuw1M8JJf4fupogNd2FK3x2lrL7Cb0ICgQ//UrzNLMMzByzeAAkkP6JQAmvrGfItNKYsBnq1MwzupNcbt9u8BMfNLyMljiXK3aJLRrdyPpe9yg6fO0RvFCAwB4Hl2EuNsW9U0f3Z1vO3/kpAsNVXaXsk0Un9GWq8t42z9S69B6zKZS/JaUjgZKoaddMgD8u7++g+sp4x7jpzU7loTkv8XFjIOIPDAUrRFc6FyG1VBeaqjK7GR6bRzw4QJvezZrSo+Rvbt85/blgzg8CapJmWUe+XjydTqi2OLBIPThLuPglRbX+lk8V2MwWvD7n9IQ7rGfIWF03dKADpK1sLjxEnCSXT+iGwQUJJll3NQp/B8wWDZmiB1ZrERhyGbKP6b89xK873jD357tDZYgrn+HtsV3Br2c3reMr3jBmtYF6oFuGVfeMGsXjPzqtlRuDNOQzzolY5fRluMYNXVwS0kI+A8hVjJcbRMEmC9r15WTfM7OvVT8M0I3Cij0U5DEsxseLWMw7t3o5L+bq3HRhk91IjY+qGhPUvLi7M3mxh9vXig9u8qivntQcEjsSG9TYe7yAWvySnuEU7DEvZ0qnjGgUqylQ5X8nK1FPTvlxeXoYc5r/I6JbHx8fRaLRoMjw4YZjaWXpYPDFMMzgjK5aWkdjn+wQEjiRK6j3x0b3vSY++aIdhCf/Z7D1Ztto5erZIBcsGRaI/p6enS/fw4ODg7Oxswe3xA/EGJ/pQo9jqUHgWSvxsRsdp9Ilrif8XQs21a50HttArudBOQQ6D3mulio5ahZ8/Ouri37XYxayYFrv/pamYXv8wXREpDRSJjpj6z3S7+6frsHIfGt66b3i+R5hJEotitVqOPsX2yKGvsaJXYdRSalBqnT2jIJgRgZ/eYSirkq2rX1EPc11tSm/n7u7OtAvv37yv8Bicim3RCKRC0M3gHJB+n74lF46TTZhFsI0InDxBtyiHYZaH8EubZrazz+9dNRQvx7GLv/knyMzstul4oX6ZESBP+Pj4mN9DIvwSRpvf/nprZhBYvxGyNpg8vcOQ13kQeL2qUaLWbm5uDg8P6yoDJq+Q10zsrdcXVLMKmPUmM6jd2Q4/FyMHCbWPcpj6nabENA0mCxxY3bAGsffujVXIQhjbELi6uqKgdOe/X91Y3qkSU3G77riuS+baNrHz5TF0oTfWOcLRyKK6zzYmGh4kFAGKSN/e3v58+XJnZ4e6QP/qL81ms+7WyfaKYy8Jb6sF1jqSTCScY4GRVCiUUhB7ZQTWS+CVxUk3QFkKtM95XiErTbZXmttTAExocksRsJ7ANC76rJwEjYm69MG5OVuqt+i2j4AEAmOwgAAQmIOArUEsDBgQAAIMBEBgBkioAgRsRQAEtnVkIBcQYCAAAjNAQhUgYCsCILCtIwO5gAADARCYARKqAAFbEQCBbR0ZyAUEGAiAwAyQUAUI2IoACGzryEAuIMBAAARmgIQqQMBWBEBgW0cGcgEBBgIgMAMkVAECtiIAAts6MpALCDAQAIEZIKEKELAVgf8B1rvuIARnMhIAAAAASUVORK5CYII=)
AB = 20 cm
∵ O is the midpoint of the line AB.
∴ AO = OB = 10 cm = 0.1m
Let the Net electric field at the point O = E
The electric field at a point caused by charge q, is given as,
…(1)
Where, q is the charge,
r is the distance between the charge and the point at which the field is being calculated
is a constant and its value is 9x109 N m2 C-2
ϵ0 is the permittivity of free space. Its value is 8.85 x 10-12 (F/m)
∴ The electric field at the point O caused by qA = 3 μC
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALMAAAAxCAMAAACmsmgSAAAAAXNSR0IArs4c6QAAALFQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmZmZmaQZpC2ZpDbZrbbZrb/kDoAkDo6kDpmkGY6kLbbkLb/kNv/tmYAtmY6tpA6tpBmttu2ttv/tv//25A625Bm27Zm27aQ29u229vb29v/2////7Zm/7aQ/9uQ/9u2/9vb//+2///b/dj7/gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAEAElEQVRoQ+1Z61rbMAyNOy7ZBrRQ2t0gG6zpNsgKW0Oy+P0fbJJ8iR07bRJIRr/hH6UX2T45lmTpEAQv4/9jYDUfr3frqfnydMcQB0FyOCzHfPWWsf1Fg03v5sKKXzF2cmNM4NF4fmT4xt2MsVGfvhKProM8Gm0Fnc/Yq1uCHB2s8wjeF1NG4zILJ7/uI811wk7X/Nv2FRvQVGMS414Juyx/Lt4RtiCXf+lDNr5JBOYU0aTWhHP4JjmQLp2FuCL/vJWF7phpZizgiMGjffxUTCf2qhIz2RZTw4V5NFlzzXPSJ8MaUX41Nt2TTt9GRaYCM/0Ivypa6UTAgSeSZo5u0/dAt6wEDOC6nx1W05eJWSD3Dftp+gN/F1a44RFzMT0vzBBSZxYjWzFb/lyZOoBv4I5ZaGEm33CItmPQfkgDdtx7DPIIN7dSl47BisdKzJQX7QkW0eLM+sx1HK+T3IooGV/O8cskhkFWH4KYWEYXQb93Sn4VlomKCMs/CIIz+Zc+cDRje59kZtt0M/MlmO593Lmqqb8cN/jKkI9kjTL41t03FEHyEBrlTffFBpopy5J4BzEPxNDTbEM8rwZuax4JXQRhDeZYBih0OX0X320eg3hO2/Csn+MfvcFLssRbX2e1YaF/WxNzelSpAJ+zb0AvB7mOf/kx3YmUJ/whwzslnQTUPz/3oe5uzAvLRZAO1B7AoX4/adqlJqo5vscu12I0wzrRVBw28f3YXp5HJM5V1SSlMtlbZ0fkssX5dbCyk24CnYEZkZsgZ+HjErZobEo1SeylVabq1tlrdT2U72gCxd+yEZZi+r6RHZLj05OUD9pqUqkyOXRpfQmJ1QMcG2CkzNPeu4THZ7QbnqwYsFI+h9vywrH16knqOB01SXSLgOLyZwiuSy84FL0r251bZIv0ZE2Yl4vsza3IOfAK8gv3LOLTk8QUj5okO9wsPF6A/Hd8Hci4kb6UdIZcgBpImAGpxhzXSUKIrKonydmiiTVbWY0ZnomkB/l0IglDMg7STjcIPTPsmuC6CnMxrZUqAFTV4RpiJuACI1IiZN9OmMHbdDtmYMbv/NndxSzpVEpjeZHZPFcwt/Ber2nVNwp160NcjlALMKPb0ZPkbKH+mkc0BGa8N+n4dGJPDtd2DlUxaCoVCrOjJtVjfoKiQsYz7gGx8oBZEvLcn9/ItwxywbRXT1JeqtUkVQXLZUkUkzFIcbIpXJq6DPg0JQ48XJCp0Bkgl7Ljr5hTrErLryepoh11clSTCLNWmbCKgP+vqBcjPzfF18rOweyf3bYW0/dgKzANjR3f8M+z3Gf70naEbLdvaQGJtMkOsq5rtris65oZd7AqZr6qw12oS/3cAc7LlM4M/AWtJYF+rOc0uQAAAABJRU5ErkJggg==)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUAAAAAxCAMAAACcR4BIAAAAAXNSR0IArs4c6QAAALRQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmY6OmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmY6ZmaQZpC2ZpDbZrbbZrb/kDoAkDo6kDpmkGY6kLaQkLbbkNvbkNv/tmYAtmY6tpA6tpBmttu2ttv/tv//25A625Bm27Zm27aQ29u229vb2////7Zm/7aQ/9uQ/9u2//+2///bPPY4CAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAFhUlEQVRoQ+1ae0PbNhC3UqDeoBu0IXQv6o1RQrfOCyyZbX3/77W700nWy7HSmjgD648EopP000/30OOybCoTAy+SgWohZr+kzfxxIcTFFtG++rRRUqRWV+frFLk9yDTz66zKP6SM1FzeZqvZXadoX33KGEky8v7todCXZZtXf2XZ8l0ScBCqvukmEPvoq08dZ6tc+XqQbjo7eQBLO/7cUf1wpRiQN0K8ASGccV0oRM1coILJQogulSxbqnGYmW9JVn0cgFx9C+i2r4Jq6SM1/cni/OrUGlgBGY7TcnabySUqVljqhVAVsjhZ1wX+XQrx/YJpAQaRymbexd+qdYGleLuWn4BwaEQF21j1HRNaArq62OIIuF2I1IxT5Rf/PPKagzQDGYzAZo5sqE+/VOefS0XgBqewYUVrLlkjmssf8SdZdBBYtvxVOVItf3V0yapHDO/VItb8Tf8ssVlpa3hUrAMpdUFwyxN2gxrIYASqiIAaRniFOFmDkhlGmEDS0GZOpltrBQRoH7GdJnAD7f7OIfDSBxAOHxvuqYwokV1PGI6RwWYeRG7HPrrEIkgVSbK4WEujgTEgX0Wm0j1NYLaEidoapWCp6mZObB1d6wFhbTfiXStf5Wd3oC5ntxnCVDakCJRk/m6x61kI+udVskTrm3PHQxOYUCxAaroA8xYXrIAxIF/FHyjdK6DsEyiemYTt2W1YhmWLQGTcEE7aXOWwIv5Oh7jvLTDA4+K1K4g0e6EnJgZGai11gNQMnQakF6ktgPH1+HdlnVCq/DvbhHoJBJ/iE0gsum4xETcE9AjRD7mnvlGx0Qhk2kwQcZ2Eaxjehkq5Z3GtgwhrYITARMuJEwjRyw1xvQSGBq5VJhHITiqIwi1rzfsf7PV2XbMXqolAcOoLVrduAsm39hayzYgKkldoS1xsK9K2cRKQXqShP9e6BRsNZ/kYFm0k9DamdSi0n8Hgq81fK19w2lNK5G1jPBg6OlhOUBbYzB04IkY6oNY9jrQdSQPZmaNtDR5yE6TwlGZbDKsm+rDQM/MOeqkJpIlyEPGUVRaza4hV2/SQ+3fWD5rhycfWypiYZURxpLb6KiADEgibj1vuDpzLDDRQsM+RNzlsRI7w8gW3Av45DAVR97S6VSD9of1wIcp7qD36eUssrn9SlRV/0z81QtDLq36JifUgtaEwkAEJnLqaGBiMAbwYMSf1wXp9SR0pD/xv2o3nSyImda58aF4mXRmndvrM5aoz66jd3jo881kPOT26qzP7EDDh1RNfYQ8Jfry+9IUrxoyWQRVF4gTCXR+XlGPVeDMbYeRypn0emfBmFw00rL6wP5xl8gjkuu4riRHW+PCG7DLhVvs2p+412mTCHasYBBG4Zcannt/+7HwtOzx9GBGRs41RZkune3iyoSetqezAgD7KYZi9v1NpBAdV5B9vUiGV/JS0vwwalym8VurOGBiJVVlQlopOc9AodFKBN4NT3FvsLYPGpwSf1g7tXKLul600BwJtkgr8KZjEmb1k0Hij1xRA7sfaMkfTB7RLcdIcsjapIDALnU7Qm0EzvEHR1TK+VqQ8xw4/fDzLQBuEneZAY6vnDD+xweRu9WfQPMEMxu4ylj7AV/9WmgOj5PcgN7GBbB1N3s2gGXtiexs/kj7AG1ZFoP1EZQj0ExtwH+Zl0OxtAqMPFL5+JxJovcsvT9ZBBs3oE9sXgJBAVjRtwu0u39VAl8B9wT24cSLpA/rMyUGkfTmeCAyXL5Y+oAkMkge6CXyxZ9Fo+oB+gDfJA/rCjdMfgsSGeN7swRnbUwCKpw/oNFGd5kAEmqSCMLFhjBPIU7AxWJ+7Xm6YxObBEPzPO+KzcOosJgUMmOLbmDQGK7qNmYrDwBfcB04MTgw8Swb+Awpowc4mDL/PAAAAAElFTkSuQmCC)
The direction of EA will be along OB.
Also, the electric field at O caused by qB = –3 μC
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALMAAAAxCAMAAACmsmgSAAAAAXNSR0IArs4c6QAAAKtQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmZmZmaQZpC2ZpDbZrbbZrb/kDoAkDo6kGY6kLbbkLb/kNv/tmYAtmY6tpA6tpBmttv/tv//25A625Bm27Zm27aQ29u229vb29v/2////7Zm/7aQ/9uQ/9u2/9vb//+2///bSOKEIwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAEEklEQVRoQ+1Za3faMAyNWR/Z1hZaCnu1GV3TrctoN9Jk8f//ZZNkObEThzwgcDhrPlCgsnQtS7J08bzX53/1wHI+Xh3W3uXD5YEh9rzodMc+lsv3QhzfN1t9mishuRDi4tGQl8F4fmbExtNMiNGgsRKO7rw0GDWBTmfizU+CHJys0gDeZ1NBz23iT34/B7mvI3G5kt8bFTY7qV4iRGORuM0lsg+EzUv5L31Ixo+RwhwjmtiQ97Jr+CY64ZBOfFQovzY5YRPMtDZUeNTZB8f4IZtObLWMmUSzqRHCMpisZO7naFAP55DSxdiOT/CZhYokFWYMDcSs3UonAgE8YTdLDJvBH4xLO2MA1/PstFy+TMwKueuxd7M18KHKHXj0MT75tnNkIKqY9orZsflYXJnfNmKuRk6RDbuIDbSW+CZmio2Ko+0ctPZo7jccPgdlgNat2kXBCp4sRSxjprJoydvnpo5s0Fon8TpJzZTi/KocPxcxTLL6FMTCMrrxBr5T0oVfVCqqXJ+UgxP+Sx8kSomjL1zZ1t3M8gFEjz4fXNe0tRq3T0VQibg72SeKjrZVerz4RV/TUcEexLkhCQ8Q8x681d8k+Xm564GmP14qlpSENZirHdBmxra0mvwcd/Fz3snt6Q36mfEmeDmJY7Nh35Jbtq6mGGRiaPxSc86BManSHW/dfh+FRa1DzF5YNzP00T3UGnWnJHCnIObk+gDqtL67oYmMMRCudtVCyR8XbefTSE/FzzjfWodH8VzQIesPdtMpXgZEy5V5JM0v2caTMzr97PrOW9qTC8VzToesh5z4m009aqIpeCRlLeeXysaTt5qVKd6RTAc/Z9OPbTE7mSSyhSYtHqnglyoOy10ZWbOjqs/t6LzwiqzhyaoHNKVz4AtuKtacTJIusBUeSc2JkFm3v3wIXXrBR7t3aYdzh8IUX6wI88N98g5qDfWxQK2tPOlQoqdY819qiYNH4tk28c/vgfc7v/M4bziWot6QkQckzIA0x1xf2B1MEq9W46s5xOaYYU/EOfDuPGIvY4Ac9yrGtGewGqFejTmb1pIU2IaVbqqWmAm4woguUYRvL8xUx3m1gRm/cdM+VczsTs0xFh2a7ecS5g7R6xQtx0Y25f1DXo6QBSgeB5PEqxXtax7RLjDTfY/Hl7da0enKrqEuJkljrvBI9Zi7dMs1B8L5jDYgV17w5oc69/cP+puTXK10Mkk6SnMeSRNNrJboMM5BypN16dI2ZCCmqXDg4QJBhcEAtVScf6PfFijJ+XEzSbpFQIYcrwTCnPNLeFXALyv6BetTfhG2RdhBroLZvZbvwdaKW7YUrfVZgpXYcKuxwqfZ0qBupkLaxgL3dc1wUYL7unbCPaSymavrqCrq0z/3gPO6pLcH/gFc437aKsSH7gAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
The direction of EB will be along OB.
Note: Both the field are acting in the same direction along OB, this is because the charges are of opposite nature, ∴ the force will be attractive.
Hence, we can sum them up to find the resultant electric field.
Enet = EA + EB
⇒ Enet = 2EA
![](data:image/png;base64,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)
∴ Enet = 5.4 × 102 N/C(along OB)
(b) The diagram is:
![](data:image/png;base64,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)
q = 1.5 × 10–9 C
The force that is experienced by q when placed at O, F.
FO = q × ENet
Where E is the Electric field at the point O.
∴ F = 1.5 × 10–9 C x 5.4 × 102 N/C
⇒ F = 8.1 x 10-7 N
The negative test charge will be repelled by the force placed at B and attracted by the force placed at A. Therefore, this force will be in the direction of OA.
Question 11.A system has two charges qA = 2.5 × 10–7C and qB = –2.5 × 10–7 C located at points A: (0, 0, –15 cm) and B: (0,0, + 15 cm), respectively. What are the total charge and electric dipole moment of the system?
Answer:
![](data:image/png;base64,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)
The charge at point A, qA = 2.5 × 10–7C
The charge at point B, qB = –2.5 × 10–7 C
∴ the total charge of the system, Qnet = qA + qB
Qnet = 2.5 × 10–7C + (–2.5 × 10–7 C)
Qnet = 0
The distance between these two charges = Distance between point A and B, d = 15 + 15
d = 30 cm = 0.3 m
The electric dipole moment can be defined as the measure of the separation of positive as well as negative charges within a specific system. It tells us about the given system’s overall polarity.
The electric dipole moment of the system, p = qA x d = qb x d
p = 2.5 × 10–7C x 0.3
∴ p = 7.5 x 10-8 C-m along the positive z-axis
Hence, the electric dipole moment of this system is 7.5 x 10-8 C-m along the positive z axis.
Question 12.An electric dipole with dipole moment 4 × 10–9 C m is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 104 NC–1. Calculate the magnitude of the torque acting on the dipole.
Answer:The electric dipole moment can be defined as the measure of the separation of positive as well as negative charges within a specific system. It tells us about the given system’s overall polarity.
Electric dipole moment, p = 4 × 10–9 C-m
Angle between p and uniform electric field,
= 30![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAXBAMAAAA1qkh7AAAAAXNSR0IArs4c6QAAADBQTFRFAAAAAAAAADpmADqQOgAAOjqQOma2ZgBmkNv/ttv/tv//27Zm2////7Zm/9uQ//+2XNrvcwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAI0lEQVQYV2NgwAV4HTUZGL43bD7A8Izh+wIga+sBBrAYpQAAzlIJQrHIx3UAAAAASUVORK5CYII=)
Electric field, E = 5 × 104 NC–1
The torque acting on a dipole is given by:
τ = p × E
τ = p×E×sinθ(θ=30)
= 4 × 10–9 C m x 5 × 104 NC–1 x (0.5)
= 10-4 N m
The magnitude of torque acting on the given dipole is 10-4 N m.
Question 13.A polythene piece rubbed with wool is found to have a negative charge of 3 × 10–7 C.
(a) Estimate the number of electrons transferred (from which to which?)
(b) Is there a transfer of mass from wool to polythene?
Answer:Given:
Charge on polythene piece = -3 × 107 C
(a) Number of electrons transferred from wool to plastic.
Explanation: We know that all materials are electrically neutral. As per the question, after rubbing the polythene piece is found to be negatively charged which suggests that negatively charged particles i.e. electrons were transferred from wool to plastic.
Let number of electrons transferred from wool to plastic be ‘n’
From quantization of charges we know that
q = n × e …(1)
Where, q is the total charge
e = charge of individual particle
n = number of charges (either positive or negative)
e = -1.6 × 10-19 C
From equation (1) we get,
q = n × e
⇒ n = q/e
⇒ ![](data:image/png;base64,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)
⇒ n = 1.87 × 1012
The number of electrons transferred is 1.8 × 1012
(b) Yes, mass is transferred because each electron has a mass of 9.1 × 10-31 Kg.
Mass transferred = n × me …(1)
Where, n = number of electrons
Me = mass of electron (9.1 × 10-31Kg)
Now, putting the values of Me and n in equation (1).
⇒ M = 1.87 × 1012 × 9.1 × 10-31Kg
⇒ M = 1.706 × 10-18 Kg
Hence, the mass transferred from wool to plastic is 1.7 × 10-18 Kg
Question 14.Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 × 10–7 C? The radii of A and B are negligible compared to the distance of separation.
Answer:Given:
Distance between centres of spheres, r = 50 cm = .5m
Charge on each sphere, q = 6.5 × 10-7 C
![](data:image/png;base64,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)
Mutual force of electrostatic repulsion
…(1)
Where, F= mutual force of attraction
q1 = charge on sphere 1
q2 = charge on sphere 2
r = distance between centres
![](data:image/png;base64,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)
Where, ε0 is the permittivity of the free space.
Now, putting the values of q1, q2 and r in equation (1).
![](data:image/png;base64,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)
⇒ F = 1.52 × 10-2 N
Hence the mutual force between two spheres is 1.52 × 10-2N. Since the sign is positive so the force is repulsive in nature.
Question 15.What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?
Answer:Force if charges on each sphere is doubled and the distance is halved.
Given:
Q1 = 2 × q
Q2 = 2 × q
R = 0.5 × r
Using Coulomb’s law, we get,
…(1)
![](data:image/png;base64,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)
Where, ε0 is the permittivity of the free space.
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ F = 0.243 N
The mutual force is 0.243N and it is repulsive in nature.![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAXCAMAAADjjeWOAAAAAXNSR0ICQMB9xQAAAANQTFRFAAAAp3o92gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAADUlEQVQoz2NgGAX0BAABcAABXnnoOAAAAABJRU5ErkJggg==)
The new force is found to be 16 times the force in case I.
Question 16.Suppose the spheres A and B in Exercise 1.12 have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between A and B?
Answer:Note: If a conducting uncharged material is brought in contact with a charged surface then the charges are shared uniformly between the two bodies.
Given: Charge on sphere 1, q1 = 6.5 × 10-7 C
Charge on sphere 2, q2 = 6.5 × 10-7 C
Charge on sphere 3, q3 = 0
![](data:image/png;base64,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)
Step 1: The uncharged sphere is brought in contact with sphere 1. Since sphere 1 has charge ‘q’, it gets distributed among sphere 1 and sphere 3.
Now, charge on sphere 1 = q/2
Charge on sphere 2 = q/2
At this point the sphere 3 which was initially uncharged has a charge “q/2”.
Step 2: Now sphere 3 is brought in contact with sphere 2 due to which 1/4 × q will flow from sphere 2 to sphere 3. Now sphere 2 and sphere 3 have “3/4 × q” charge.
Now, q1 = 1/2 × 6.5 × 10-7 C
⇒ 3.25 × 10-7 C
q2 = 3/4 × 6.5 × 10-7 C
⇒ 4.87 × 10-7 C
q3 = 3/4 × 6.5 × 10-7 C
⇒ 4.87 × 10-7 C
We know that,
…(1)
Where, F= mutual force of attraction
q1 = charge on sphere 1
q2 = charge on sphere 2
r = distance between centres
![](data:image/png;base64,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)
Where, ε0 is the permittivity of the free space.
Plugging the values of q1, q2 and r in equation (1), we get
⇒ ![](data:image/png;base64,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)
⇒ F = 5.703 × 10-3 N
The repulsive force between sphere 1 and sphere 2 is 5.703 × 10-3 N.
Question 17.Figure 1.33 shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?
![](data:image/png;base64,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)
Answer:1. Particles 1 and 2 are deflected towards the positively charged plate, hence it can be concluded that particles 1 and 2 are negatively charged.
2. Particle 3 is deflected towards the negatively charged plate hence it is positively charged.
The deflection of a particle is proportional to the charge to mass ratio (q: m) of the particle. We observe that particle 3 has maximum deflection, so it has the highest charge to mass ratio.
Explanation: Force on a particle in electric field
F = q × E …(1)
Where, q = charge on particle
E = magnitude of electric field
m × a = q × E …(2)
Where m = mass of particle
a = acceleration of particle
From equation (2)
⇒ ![](data:image/png;base64,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)
The electric field in the given case is constant, hence we can write
⇒
…(3)
From the equation (3) we can conclude that acceleration of a charge particle with charge q and mass m in uniform electric field is proportional to the charge to mass ratio of the particle.
Question 18.Consider a uniform electric field E = 3 × 103î N/C. (a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane? (b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?
Answer:Given:
Electric field E = 3 × 103
N/C
Side of square, s = 10 cm
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a) Flux of field through square whose plane is parallel to yz plane.
We understand that the normal to the plane is parallel to the direction of field.
So, θ = 0°
Φ = E . A
Φ = E × A × cos(θ) …(1)
Where, E = Electric field
A = Area through which we have to calculate flux
θ = Angle between normal to surface and the Electric field
A = s2
A = .01 m2
Plugging values, of E, A and θ in equation (1)
Φ = 3 × 103 NC-1 × 0.01m2 × cos0°
Φ = 30 Nm2C-1
b) If normal to its (square’s) plane makes 60° with the X axis.
θ = 60°
Φ = E × A × cos(θ)
Φ = 3 × 103 NC-1 × 0.01m2 × cos60°
Φ = 15 Nm2C-1
Question 19.What is the net flux of the uniform electric field of Exercise 1.15 through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?
Answer:Flux, Φ = q/ε0
Where, q = net charged enclosed
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
Since no charge is enclosed by the cube, i.e. q = 0, the net flux through the Cube is zero.
![](data:image/png;base64,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)
Note: The number of field lines entering the cube is equal to the number of field lines leaving the cube. Hence the net flux becomes zero.
Question 20.Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is 8.0 × 103 Nm2/C. (a) What is the net charge inside the box? (b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or Why not?
Answer:Given:
(a) Φ = 8.0 × 103 Nm2C-1
Let net charge inside the box = q
We know that,
Flux, Φ = q/ε0 ..(1)
Where, q = net charged enclosed
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
Plugging values of Φ and ε0 in equation (1) we get,
q = Φ × ε0
⇒ q = 8.0 × 103 Nm2C-1 × 8.85 × 10-12N-1C2m-2
⇒ q = 7.08 × 10-8 C
Hence, the net charge inside the box is 0.07 μC.
b) No, we cannot conclude that the body doesn’t have any charge. The flux is due to the Net charge of the body. There may still be equal amount of positive and negative charges. So, it is not necessary that if flux is zero then there will be no charges.
Question 21.A point charge + 10 μC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig. 1.34. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.)
![](data:image/png;base64,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)
Answer:Given:
q = + 10 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAXCAMAAAA8w5+RAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAA///b//+22///tv///9vb/9u2/9uQkNv//7Zm27aQtrbbZrbb25A6tpCQtpA6ZpDbZpC2OpDbOpC2tmY6tmYAOmaQkDo6AGa2kDoAZjo6ZjoAADqQADpmADo6ZgAAOgAAAABmAAA6AAAAKGIMOQAAAAF0Uk5TAEDm2GYAAACASURBVHjaxZDLDoJQDESnFrVFrwoqiqBe2v//RxYkPAILExfM8qTNTA6wStLK3QqesOBXprPJmO3jEwA9BFATIDQJEIabHlLZJDO4+db8G1x8x32hCOp5P8lzpC+TE1NpR3Tj1aJddtVbALpF90/GgNY8l6BD5whOBXTZHv5w3QIOEglD6K519QAAAABJRU5ErkJggg==)
s = 10 cm
Assume the charge to be enclosed by a cube, where the square is one of its sides.
Now, let us find the total flux through the imaginary cube.
We know that,
Flux, Φ = q/ε …(1)
Where, q = net charged enclosed
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
Now plugging the values of q and ε0 in equation (1)
![](data:image/png;base64,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)
⇒ Φ = 11.28 × 105 Nm-2C-1
We understand that flux through all the faces of cube will be equal;
Let flux through the square = Φa
Hence,
Φa = Φ/6
Explanation: The net flux will be distributed equally among all 6 faces of the cube. Hence, the square will have one sixth of the total flux.
Φa = 1.88 Nm-2C-1
The flux through the square is
.
Question 22.A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
Answer:Given:
Total charge inside the cube, q = 2.0 μC
Edge length of Cube, a = 9.0 cm
![](data:image/png;base64,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)
We know that,
Flux, Φ = q/ε0
Where, q = net charged enclosed
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
![](data:image/png;base64,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)
⇒ Φ = 2.26 × 105 Nm2C-1
The net electric flux through the cubic Gaussian surface is Φ = 2.26 × 105 Nm2C-1
NOTE: The flux through a Gaussian surface depends on the net charge enclosed by it. Geometry has no effect on the total flux.
Question 23.A point charge causes an electric flux of –1.0 × 103 Nm2/C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is the value of the point charge?
Answer:Given:
Φ = -1.0 × 103 Nm2C-1
r1 = 10.0 cm.
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)
a) Flux if the radius of the Gaussian surface is doubled.
If the radius is doubled then the flux would remain same i.e. -1.0 × 103 Nm2C-1.
The geometry of the Gaussian surface doesn’t affect the total flux through it. The net charge enclosed by Gaussian surface determines the net flux.
b) Let value of point charge enclosed by Gaussian surface = q
We know that,
Flux, Φ = q/ε0 …(1)
Where, q = net charged enclosed
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
Now plugging, the values Φ and ε0 in equation (1).
q = Φ × ε0
⇒ q = -1.0 × 103Nm2C-1 × 8.85 × 10-12N-1m-2C2
⇒ q = -8.85 × 10-9 C
The charge enclosed by the surface is -8.85 × 10-9 C.
Question 24.A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 × 103 N/C and points radially inward, what is the net charge on the sphere?
Answer:Given:
Radius of charged sphere, r = 10 cm
Electric field, 20 cm away from centre of sphere, E = 1.5 × 103 NC-1
We know that, electric field intensity at a point P, located at a distance R, due to net charge q is given by,
…(1)
Now plugging the values of q and R in equation (1)
q = 4 × π × ε0 × R2 × E
⇒ q = 4 × 3.14 × 8.85 × 10-12N-1m-2C-2 × (0.2m)2 × 1.5 × 103C
⇒ q = 6.67 × 10-9C
The net charge on the sphere is -6.67 × 10-9C. Since the electric field points radially inwards, we can infer that charges on sphere are negative.
Question 25.A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC/m2. (a) Find the charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere?
Answer:Given: radius of sphere, r = 1.2 m
Surface charge density, σ = 80.0 μC/m2
![](data:image/png;base64,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)
a) Let charge on sphere = q
We understand that,
Total charge, Q = Surface charge density × surface area.
Surface area of sphere, S = 4πr2
S = 18.08 m2
Q = 80 × 10-6Cm-2 × 18.08m-2
⇒ Q = 1.447 × 10-3C
b) Let total electric flux leaving the surface of sphere = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAXCAMAAADqZkX0AAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjpmOjqQOpDbZgAAZgBmZjpmZrb/kDoAkDo6kNv/tmYAtmY6tpA6tpBmttuQttv/tv//25A62////7Zm/9uQ//+2///buTYnrwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAaklEQVQoU6WNBw6AMAwDXVaBsvdom///khieQKQoVuKcgf8Vu5MQ2awxxr28OTsQbNKr9MkEXG7Ob10XQGzPYHvIoE7vEJuvZZy+qXtPm2r6F/0OJRHpXhNBjgyaIyvJemVsdby5CxP/1gMn3QXPwlu41gAAAABJRU5ErkJggg==)
We know that,
Flux, Φ = q/ε0 …(1)
Where, Q = net charged.
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
By, plugging the values of q and ε0 in equation (1), we get,
⇒ ![](data:image/png;base64,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)
⇒ Φ = 1.63 × 108 Nm2C-1
The total flux through the sphere is 1.63 × 108 Nm2C-1 .
Question 26.An infinite line charge produces a field of 9 × 104 N/C at a distance of 2 cm. Calculate the linear charge density.
Answer:Given:
E = 9 × 104 NC-1
d = 2 cm
Let the linear charge density = λ Coulomb/metre
![](data:image/jpeg;base64,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)
We know that, Electric field produced by a line charge with a linear charge density σ, at a distance d is given by,
…(1)
Where, λ = linear charge density.
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
d = distance
From equation (1) we have,
⇒ λ = E × 2 × π × ε0 × d
⇒ λ = 9 × 104 NC-1 × 2 × π × 8.85 × 10-12N-1 m-2C2 × 0.02m
⇒ λ = 10 ×10-8 Cm-1
The linear charge density is 10-7 Cm-1.
Question 27.Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0 × 10–22 C/m2. What is E: (a) in the outer region of the first plate, (b) in the outer region of the second plate, and (c) between the plates?
Answer:Given:
Surface charge density on plate A, σA = -17.0 × 10-22 Cm-2
Surface charge density on plate B, σB = 17.0 × 10-22 Cm-2
The arrangement of plates are as shonw:
![](data:image/jpeg;base64,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)
Let electric field in region 1 = E1
Region 2 = E2
Region 3 = E3
The electric field in region I and region III is zero because no charge is present in these regions.
E1 = 0
E3 = 0
We know that,
E2 = σ/ε0 ...(1)
Where, σ
Surface charge density
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
Now, plugging the Values in equation (1).
⇒ ![](data:image/png;base64,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)
⇒ E2 = 1.92 × 10-10 NC-1
The electric field in the region enclosed by the plates is found to be 1.92 × 10-10 NC-1.
The electric field in region II is 1.92 × 10-10 NC-1.
What is the force between two small charged spheres having charges of 2 × 10–7 C and 3 × 10–7C placed 30 cm apart in air?
Answer:
The coulomb attraction formula used to find the force, F is given as,
…(1)
Where, q1 and q2 are the charges.
r is the distance between the charges.
is a constant and its value is 9x109 N m2 C-2
ϵ0 is the permittivity of free space. Its value is 8.85 x 10-12 (F/m)
Now, the diagram is:
Since, both the charges are positive, thus, the nature of force will be repulsive. F12 is the force on charge q2 caused by charge q1 andF21 is the force on charge 1 due to charge 2 .
Now, Given:
Charge on the first sphere, q1 = 2 × 10–7 C
Charge on the second sphere, q2 = 3 × 10–7 C
Distance between the spheres, r(in m) =30/100=0.3 m
Putting the values in equation (1), we get,
F = 6 × 10-3 N
Hence, the force between the given charged particles will be 6 × 10-3 N. Since the nature of the charges is the same i.e. they are both positive. Hence, the force will be repulsive.
Question 2.
The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of charge –0.8 μC in air is 0.2 N.
(a) What is the distance between the two spheres? (b) What is the force on the second sphere due to the first?
Answer:
(a) The electrostatic force, F = 0.2 N
Charge on this present sphere, q1 = 0.4 μC = 0.4 × 10-6 C
Charge on the other sphere, q2 = –0.8 μC = -0.8 × 10-6 C
The electrostatic force between the spheres can be given by the equation,
…(1)
Where, q1 and q2 are the charges.
r is the distance between the charges.
is a constant and its value is 9x109 N m2 C-2
ϵ0 is the permittivity of free space. Its value is 8.85 x 10-12 (F/m)
Therefore, from equation (1),
⇒ r2 = 144 x 10-4 m2
Taking square root both the sides,
⇒ r =
r = 0.12 m
Hence, the distance between the two spheres is 0.12 m.
(b) Since the nature of the charges on the spheres is opposite, the force between them will be attractive in nature. The spheres will attract each other with the same amount of force.
Therefore, the force on the second sphere due to the first sphere will be 0.2 N.
Question 3.
Check that the ratio is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?
Answer:
The given ratio is
It is the ratio of electric force i.e.to gravitational force i.e.
between a proton and an electron with the distance between them as constant.
This is because
Here, G = Gravitational constant. (Unit = Nm2kg-2 )
me and mp are the mass of electron and proton respectively. (Unit = Kg)
e = Electric charge (Unit = Coulomb)
K is a constant =
is the permittivity of space. Its units are Nm2 C-2.
Let us substitute the units into the ratio in order to deduce the dimensions,
All the units get cancelled, and we see that the given ratio is dimensionless i.e. M0 L0 T0
Let us now calculate the value of the given ratio,
G = 6.67 × 1011 Nm2 Kg-2
e = 1.6 × 1019 C
me = 9.1 × 10-31 kg
mp = 1.66 × 10-27 kg
On substituting these values into the ratio, we get
Note:
This implies that the electric force between a proton and an electron is 1039 times greater than the gravitational force.
Question 4.
Explain the meaning of the statement ‘electric charge of a body is quantised’.
Answer:
Electric charge of a body is quantised.
This statement means that charge on a body can take only integral values i.e. (1, 2, 3, 4, …. N) number of electrons can be transferred from one body to another. The charges cannot be transferred in fractions. It can only be an integral multiple of the charge of one electron.
Therefore, as a result, a body will possess a charge that is an integral multiple of the electric charge of an electron.
Question 5.
Why can one ignore quantisation of electric charge when dealing with macroscopic i.e. large-scale charges?
Answer:
When considered on a macroscopic level or a large scale, we tend to ignore the quantisation of electric charges. This is because on a large scale, the charges that we deal with are extremely huge when compared to the magnitude of an individual charge. Hence, we can say that the quantisation of electric charge is not useful on a macroscopic scale. It is therefore ignored and considered to be of continuous nature.
Question 6.
When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.
Answer:
i. When two bodies are rubbed against each other, this process results in the production of charges on the bodies involved.
ii. The charges on each body will be of equal magnitude but of opposite nature. This happens because charges are always created in pairs.
This phenomenon of charging bodies by rubbing them against each other is termed as charging by friction. However, the net charge of the system – of both the bodies – is zero.
iii. This is because equal amounts of charge of opposite nature cancel each other out.
iv. When a glass rod is rubbed with a silk cloth, then opposite charges appear on both the bodies. This is in accordance with the law of conservation of energy. (Net charge of isolated system remains constant) This phenomenon is also observed when other pairs of bodies are also rubbed with each other.
Question 7.
Four-point charges qA = 2 μC, qB = –5 μC, qC = 2 μC, and qD = –5 μC are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 μC placed at the centre of the square?
Answer:
Consider a square of side 10 cm. Four charges are placed in its corners. Let O be the center of the square.
The diagram is:
AB = BC = CD = DA = 10 cm
Diagonal of a square = √2 × Side of a square
Therefore,
AC = BD = 10√2 cm
AO = OC = DO = OB = (10√2)/2 cm = 5√2cm
i. A charge of magnitude 1μC is placed at O, the center of the square.
ii. The force experienced at center due to side charge at B is same in magnitude but in a direction opposite to the direction to the force at center due to charge at D.
iii. The force experienced at center due to side charge at A is same in magnitude but in a direction opposite to the direction to the force at center due to charge at C .
Force on the 1 u C in the center is = Fa + Fb + Fc + Fd = Fa + (- Fa) + Fc + ( - Fd) = 0
Therefore, we can conclude that the resultant force by the four charges kept in the corners on the charge that is kept in the center will be zero.
Question 8.
An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
Answer:
An electric field line always points in the direction that a positive test charge would accelerate in if placed upon that line. A charge will experience a continuous force when placed in an electrostatic field. Therefore, an electrostatic field line will be a continuous curve. The field lines do not have any sudden breaks as the test charge or any charge will move continuously and does not jump from any point to another.
Question 9.
Explain why two field lines never cross each other at any point?
Answer:
An electric field line represents the direction in which a positive test charge would accelerate in if placed on the line. If two field lines intersect, then this will imply that the electric field intensity points to two directions at the same point. This is not possible.
Hence, two electric field lines will never cross each other.
Question 10.
Two point charges qA = 3 μC and qB = –3 μC are located 20 cm apart in vacuum.
(a) What is the electric field at the midpoint O of the line AB joining the two charges?
(b) If a negative test charge of magnitude 1.5 × 10–9 C is placed at this point, what is the force experienced by the test charge?
Answer:
(a) The diagram is shown as below:
AB = 20 cm
∵ O is the midpoint of the line AB.
∴ AO = OB = 10 cm = 0.1m
Let the Net electric field at the point O = E
The electric field at a point caused by charge q, is given as,
…(1)
Where, q is the charge,
r is the distance between the charge and the point at which the field is being calculated
is a constant and its value is 9x109 N m2 C-2
ϵ0 is the permittivity of free space. Its value is 8.85 x 10-12 (F/m)
∴ The electric field at the point O caused by qA = 3 μC
The direction of EA will be along OB.
Also, the electric field at O caused by qB = –3 μC
The direction of EB will be along OB.
Note: Both the field are acting in the same direction along OB, this is because the charges are of opposite nature, ∴ the force will be attractive.
Hence, we can sum them up to find the resultant electric field.
Enet = EA + EB
⇒ Enet = 2EA
∴ Enet = 5.4 × 102 N/C(along OB)
(b) The diagram is:
q = 1.5 × 10–9 C
The force that is experienced by q when placed at O, F.
FO = q × ENet
Where E is the Electric field at the point O.
∴ F = 1.5 × 10–9 C x 5.4 × 102 N/C
⇒ F = 8.1 x 10-7 N
The negative test charge will be repelled by the force placed at B and attracted by the force placed at A. Therefore, this force will be in the direction of OA.
Question 11.
A system has two charges qA = 2.5 × 10–7C and qB = –2.5 × 10–7 C located at points A: (0, 0, –15 cm) and B: (0,0, + 15 cm), respectively. What are the total charge and electric dipole moment of the system?
Answer:
The charge at point A, qA = 2.5 × 10–7C
The charge at point B, qB = –2.5 × 10–7 C
∴ the total charge of the system, Qnet = qA + qB
Qnet = 2.5 × 10–7C + (–2.5 × 10–7 C)
Qnet = 0
The distance between these two charges = Distance between point A and B, d = 15 + 15
d = 30 cm = 0.3 m
The electric dipole moment can be defined as the measure of the separation of positive as well as negative charges within a specific system. It tells us about the given system’s overall polarity.
The electric dipole moment of the system, p = qA x d = qb x d
p = 2.5 × 10–7C x 0.3
∴ p = 7.5 x 10-8 C-m along the positive z-axis
Hence, the electric dipole moment of this system is 7.5 x 10-8 C-m along the positive z axis.
Question 12.
An electric dipole with dipole moment 4 × 10–9 C m is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 104 NC–1. Calculate the magnitude of the torque acting on the dipole.
Answer:
The electric dipole moment can be defined as the measure of the separation of positive as well as negative charges within a specific system. It tells us about the given system’s overall polarity.
Electric dipole moment, p = 4 × 10–9 C-m
Angle between p and uniform electric field, = 30
Electric field, E = 5 × 104 NC–1
The torque acting on a dipole is given by:
τ = p × E
τ = p×E×sinθ(θ=30)
= 4 × 10–9 C m x 5 × 104 NC–1 x (0.5)
= 10-4 N m
The magnitude of torque acting on the given dipole is 10-4 N m.
Question 13.
A polythene piece rubbed with wool is found to have a negative charge of 3 × 10–7 C.
(a) Estimate the number of electrons transferred (from which to which?)
(b) Is there a transfer of mass from wool to polythene?
Answer:
Given:
Charge on polythene piece = -3 × 107 C
(a) Number of electrons transferred from wool to plastic.
Explanation: We know that all materials are electrically neutral. As per the question, after rubbing the polythene piece is found to be negatively charged which suggests that negatively charged particles i.e. electrons were transferred from wool to plastic.
Let number of electrons transferred from wool to plastic be ‘n’
From quantization of charges we know that
q = n × e …(1)
Where, q is the total charge
e = charge of individual particle
n = number of charges (either positive or negative)
e = -1.6 × 10-19 C
From equation (1) we get,
q = n × e
⇒ n = q/e
⇒
⇒ n = 1.87 × 1012
The number of electrons transferred is 1.8 × 1012
(b) Yes, mass is transferred because each electron has a mass of 9.1 × 10-31 Kg.
Mass transferred = n × me …(1)
Where, n = number of electrons
Me = mass of electron (9.1 × 10-31Kg)
Now, putting the values of Me and n in equation (1).
⇒ M = 1.87 × 1012 × 9.1 × 10-31Kg
⇒ M = 1.706 × 10-18 Kg
Hence, the mass transferred from wool to plastic is 1.7 × 10-18 Kg
Question 14.
Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 × 10–7 C? The radii of A and B are negligible compared to the distance of separation.
Answer:
Given:
Distance between centres of spheres, r = 50 cm = .5m
Charge on each sphere, q = 6.5 × 10-7 C
Mutual force of electrostatic repulsion
…(1)
Where, F= mutual force of attraction
q1 = charge on sphere 1
q2 = charge on sphere 2
r = distance between centres
Where, ε0 is the permittivity of the free space.
Now, putting the values of q1, q2 and r in equation (1).
⇒ F = 1.52 × 10-2 N
Hence the mutual force between two spheres is 1.52 × 10-2N. Since the sign is positive so the force is repulsive in nature.
Question 15.
What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?
Answer:
Force if charges on each sphere is doubled and the distance is halved.
Given:
Q1 = 2 × q
Q2 = 2 × q
R = 0.5 × r
Using Coulomb’s law, we get,
…(1)
Where, ε0 is the permittivity of the free space.
⇒
⇒
⇒ F = 0.243 N
The mutual force is 0.243N and it is repulsive in nature.
The new force is found to be 16 times the force in case I.
Question 16.
Suppose the spheres A and B in Exercise 1.12 have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between A and B?
Answer:
Note: If a conducting uncharged material is brought in contact with a charged surface then the charges are shared uniformly between the two bodies.
Given: Charge on sphere 1, q1 = 6.5 × 10-7 C
Charge on sphere 2, q2 = 6.5 × 10-7 C
Charge on sphere 3, q3 = 0
Step 1: The uncharged sphere is brought in contact with sphere 1. Since sphere 1 has charge ‘q’, it gets distributed among sphere 1 and sphere 3.
Now, charge on sphere 1 = q/2
Charge on sphere 2 = q/2
At this point the sphere 3 which was initially uncharged has a charge “q/2”.
Step 2: Now sphere 3 is brought in contact with sphere 2 due to which 1/4 × q will flow from sphere 2 to sphere 3. Now sphere 2 and sphere 3 have “3/4 × q” charge.
Now, q1 = 1/2 × 6.5 × 10-7 C
⇒ 3.25 × 10-7 C
q2 = 3/4 × 6.5 × 10-7 C
⇒ 4.87 × 10-7 C
q3 = 3/4 × 6.5 × 10-7 C
⇒ 4.87 × 10-7 C
We know that,
…(1)
Where, F= mutual force of attraction
q1 = charge on sphere 1
q2 = charge on sphere 2
r = distance between centres
Where, ε0 is the permittivity of the free space.
Plugging the values of q1, q2 and r in equation (1), we get
⇒
⇒ F = 5.703 × 10-3 N
The repulsive force between sphere 1 and sphere 2 is 5.703 × 10-3 N.
Question 17.
Figure 1.33 shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?
Answer:
1. Particles 1 and 2 are deflected towards the positively charged plate, hence it can be concluded that particles 1 and 2 are negatively charged.
2. Particle 3 is deflected towards the negatively charged plate hence it is positively charged.
The deflection of a particle is proportional to the charge to mass ratio (q: m) of the particle. We observe that particle 3 has maximum deflection, so it has the highest charge to mass ratio.
Explanation: Force on a particle in electric field
F = q × E …(1)
Where, q = charge on particle
E = magnitude of electric field
m × a = q × E …(2)
Where m = mass of particle
a = acceleration of particle
From equation (2)
⇒
The electric field in the given case is constant, hence we can write
⇒ …(3)
From the equation (3) we can conclude that acceleration of a charge particle with charge q and mass m in uniform electric field is proportional to the charge to mass ratio of the particle.
Question 18.
Consider a uniform electric field E = 3 × 103î N/C. (a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane? (b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?
Answer:
Given:
Electric field E = 3 × 103 N/C
Side of square, s = 10 cm
a) Flux of field through square whose plane is parallel to yz plane.
We understand that the normal to the plane is parallel to the direction of field.
So, θ = 0°
Φ = E . A
Φ = E × A × cos(θ) …(1)
Where, E = Electric field
A = Area through which we have to calculate flux
θ = Angle between normal to surface and the Electric field
A = s2
A = .01 m2
Plugging values, of E, A and θ in equation (1)
Φ = 3 × 103 NC-1 × 0.01m2 × cos0°
Φ = 30 Nm2C-1
b) If normal to its (square’s) plane makes 60° with the X axis.
θ = 60°
Φ = E × A × cos(θ)
Φ = 3 × 103 NC-1 × 0.01m2 × cos60°
Φ = 15 Nm2C-1
Question 19.
What is the net flux of the uniform electric field of Exercise 1.15 through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?
Answer:
Flux, Φ = q/ε0
Where, q = net charged enclosed
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
Since no charge is enclosed by the cube, i.e. q = 0, the net flux through the Cube is zero.
Note: The number of field lines entering the cube is equal to the number of field lines leaving the cube. Hence the net flux becomes zero.
Question 20.
Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is 8.0 × 103 Nm2/C. (a) What is the net charge inside the box? (b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or Why not?
Answer:
Given:
(a) Φ = 8.0 × 103 Nm2C-1
Let net charge inside the box = q
We know that,
Flux, Φ = q/ε0 ..(1)
Where, q = net charged enclosed
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
Plugging values of Φ and ε0 in equation (1) we get,
q = Φ × ε0
⇒ q = 8.0 × 103 Nm2C-1 × 8.85 × 10-12N-1C2m-2
⇒ q = 7.08 × 10-8 C
Hence, the net charge inside the box is 0.07 μC.
b) No, we cannot conclude that the body doesn’t have any charge. The flux is due to the Net charge of the body. There may still be equal amount of positive and negative charges. So, it is not necessary that if flux is zero then there will be no charges.
Question 21.
A point charge + 10 μC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig. 1.34. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.)
Answer:
Given:
q = + 10
s = 10 cm
Assume the charge to be enclosed by a cube, where the square is one of its sides.
Now, let us find the total flux through the imaginary cube.
We know that,
Flux, Φ = q/ε …(1)
Where, q = net charged enclosed
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
Now plugging the values of q and ε0 in equation (1)
⇒ Φ = 11.28 × 105 Nm-2C-1
We understand that flux through all the faces of cube will be equal;
Let flux through the square = Φa
Hence,
Φa = Φ/6
Explanation: The net flux will be distributed equally among all 6 faces of the cube. Hence, the square will have one sixth of the total flux.
Φa = 1.88 Nm-2C-1
The flux through the square is.
Question 22.
A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
Answer:
Given:
Total charge inside the cube, q = 2.0 μC
Edge length of Cube, a = 9.0 cm
We know that,
Flux, Φ = q/ε0
Where, q = net charged enclosed
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
⇒ Φ = 2.26 × 105 Nm2C-1
The net electric flux through the cubic Gaussian surface is Φ = 2.26 × 105 Nm2C-1
NOTE: The flux through a Gaussian surface depends on the net charge enclosed by it. Geometry has no effect on the total flux.
Question 23.
A point charge causes an electric flux of –1.0 × 103 Nm2/C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is the value of the point charge?
Answer:
Given:
Φ = -1.0 × 103 Nm2C-1
r1 = 10.0 cm.
a) Flux if the radius of the Gaussian surface is doubled.
If the radius is doubled then the flux would remain same i.e. -1.0 × 103 Nm2C-1.
The geometry of the Gaussian surface doesn’t affect the total flux through it. The net charge enclosed by Gaussian surface determines the net flux.
b) Let value of point charge enclosed by Gaussian surface = q
We know that,
Flux, Φ = q/ε0 …(1)
Where, q = net charged enclosed
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
Now plugging, the values Φ and ε0 in equation (1).
q = Φ × ε0
⇒ q = -1.0 × 103Nm2C-1 × 8.85 × 10-12N-1m-2C2
⇒ q = -8.85 × 10-9 C
The charge enclosed by the surface is -8.85 × 10-9 C.
Question 24.
A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 × 103 N/C and points radially inward, what is the net charge on the sphere?
Answer:
Given:
Radius of charged sphere, r = 10 cm
Electric field, 20 cm away from centre of sphere, E = 1.5 × 103 NC-1
We know that, electric field intensity at a point P, located at a distance R, due to net charge q is given by,
…(1)
Now plugging the values of q and R in equation (1)
q = 4 × π × ε0 × R2 × E
⇒ q = 4 × 3.14 × 8.85 × 10-12N-1m-2C-2 × (0.2m)2 × 1.5 × 103C
⇒ q = 6.67 × 10-9C
The net charge on the sphere is -6.67 × 10-9C. Since the electric field points radially inwards, we can infer that charges on sphere are negative.
Question 25.
A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC/m2. (a) Find the charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere?
Answer:
Given: radius of sphere, r = 1.2 m
Surface charge density, σ = 80.0 μC/m2
a) Let charge on sphere = q
We understand that,
Total charge, Q = Surface charge density × surface area.
Surface area of sphere, S = 4πr2
S = 18.08 m2
Q = 80 × 10-6Cm-2 × 18.08m-2
⇒ Q = 1.447 × 10-3C
b) Let total electric flux leaving the surface of sphere =
We know that,
Flux, Φ = q/ε0 …(1)
Where, Q = net charged.
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
By, plugging the values of q and ε0 in equation (1), we get,
⇒
⇒ Φ = 1.63 × 108 Nm2C-1
The total flux through the sphere is 1.63 × 108 Nm2C-1 .
Question 26.
An infinite line charge produces a field of 9 × 104 N/C at a distance of 2 cm. Calculate the linear charge density.
Answer:
Given:
E = 9 × 104 NC-1
d = 2 cm
Let the linear charge density = λ Coulomb/metre
We know that, Electric field produced by a line charge with a linear charge density σ, at a distance d is given by,
…(1)
Where, λ = linear charge density.
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
d = distance
From equation (1) we have,
⇒ λ = E × 2 × π × ε0 × d
⇒ λ = 9 × 104 NC-1 × 2 × π × 8.85 × 10-12N-1 m-2C2 × 0.02m
⇒ λ = 10 ×10-8 Cm-1
The linear charge density is 10-7 Cm-1.
Question 27.
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0 × 10–22 C/m2. What is E: (a) in the outer region of the first plate, (b) in the outer region of the second plate, and (c) between the plates?
Answer:
Given:
Surface charge density on plate A, σA = -17.0 × 10-22 Cm-2
Surface charge density on plate B, σB = 17.0 × 10-22 Cm-2
The arrangement of plates are as shonw:
Let electric field in region 1 = E1
Region 2 = E2
Region 3 = E3
The electric field in region I and region III is zero because no charge is present in these regions.
E1 = 0
E3 = 0
We know that,
E2 = σ/ε0 ...(1)
Where, σ Surface charge density
ε0 = permittivity of free space
ε0 = 8.85 × 10-12N-1 m-2C2
Now, plugging the Values in equation (1).
⇒
⇒ E2 = 1.92 × 10-10 NC-1
The electric field in the region enclosed by the plates is found to be 1.92 × 10-10 NC-1.
The electric field in region II is 1.92 × 10-10 NC-1.
Additional Exercises
Question 1.An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55 × 104 NC–1 in Millikan’s oil drop experiment. The density of the oil is 1.26 gcm-3. Estimate the radius of the drop.
(g = 9.81 m s–2; e = 1.60 × 10–19 C).
Answer:If the oil drop is stationary, the net force on it must be Zero or the resultant of all the forces on oil drop is zero.
There are two forces acting on the oil drop, its weight or force due to Earth’s gravity which is pulling it vertically downwards, and Electrostatic force which is acting in vertically upward direction.
Both forces should be equal in magnitude and opposite direction so that they cancel each other.
The arrangement is shown in the figure
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Note: Electric Field is in vertically downward direction, because force on an negatively charged body in opposite direction of the field, so force on the drop is in vertically upward direction, which balances weight of the drop acting in vertically downward direction.
There are nine excess electrons which make the drop negatively charged because the electron is negatively charged, the net magnitude charge on a body is given by
q = n × E
n is the excess of electrons or protons on the body,
the charge of an electron is denoted by e
e = 1.60 × 10–19 C
here since there are twelve excess electrons so
n = 12
i.e. q = 12 × 1.60 × 10–19 C
= 1.92 × 10-18 C
Now the magnitude electrostatic force on a charged particle held in an electric field is given by
F = q × E
where, F force is acting on a particle having charge q held in an electric field of magnitude E
here, charge on the oil drop is
q = 1.92 × 10-18 C
magnitude of Electric field is
E = 2.55 × 104
NC–1
So Electrostatic force on the oil drop is
F = 1.92 × 10-18 C × 2.55 × 104
NC–1
= 4.896 × 10-14 N
This force is acting in vertically upward direction, so Weight should have same magnitude of Force and is acting in vertically downward direction.
Let us assume oil drop to be Spherical in shape, so the volume of drop will be
(Volume of Sphere)
Where r is the radius of the Spherical drop
Now we know mass of an object whose volume and density are known is given by
m = V × d
where, m is the mass
V is the volume and d is the density
Here density of the drop is
d = 1.26 gcm-3
= 1.26 × 103 Kgm-3
so mass of the drop is
m =
× 1.26 × 103
Now the downward pull on a body due to earth’s gravitational force is the weight of body given by
W = m × g
Where W is the weight of a body having mass m
The acceleration due to gravity is denoted by g
g = 9.81 ms-2
so the weight or the downward gravitational force on oil drop is
W =
× 1.26 × 103 Kgm-3× 9.81ms-2
Both the forces should be equal in magnitude so equating them
i.e. putting F = W
4.896 × 10-14 N = (4/3 πr3) × 1.26 × 103 Kgm-3 × 9.81ms-2
we get ,
(1N = 1kgms-2)
![](data:image/png;base64,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)
So, r ![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒r = 0.981
10-6 m
= 9.81 × 10-7 m
= 981 × 10-4 mm
i.e. radius of the oil drop is 981
10-4 mm
Question 2.Which among the curves shown in Fig. 1.35 cannot possibly represent electrostatic field lines?
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)
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)
Answer:Electrostatic field lines have some properties and characteristics, which should be taken into account while drawing Electrostatic field lines, the Characteristic of electrostatic field lines are :-
1. They start from a positively charged body and end at a negatively charged body.
2. Tangent to the electrostatic field line at any point gives the direction of the electric intensity at that point.
3. Electrostatic field lines cannot intersect each other.
4. The electrostatic field lines are always normal to the surface of a conductor. There is no component of the electric filed intensity parallel to the surface of the conductor.
5. Electrostatic field lines do not form any closed loops.
These properties and characteristics must be taken into account while drawing electrostatic field lines, if any of these are violated then the following representation will be incorrect.
![](data:image/png;base64,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)
Hence, only (c) is the correct representation of electrostatic field lines and (a),(b),(d),(e) are incorrect representations of electrostatic field lines .
Question 3.In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 105 NC–1 per meter. What are the force and torque experienced by a system having a total dipole moment equal to 10–7 Cm in the negative z-direction?
Answer:A dipole is a system consisting of two charges equal in magnitude and opposite in nature i.e. a positive charge + q and a negative charge –q separated by some distance d
Electric dipole moment of a dipole is given by,
P = q × d
Where, ‘q’ is magnitude of either of charge (in column)
And ‘d’ is separation between the pair of charges (in metres)
Dipole moment is a vector quantity and its direction is from negative charge to positive charge
We are given dipole moment of the system,
P = 10-7
Cm , along negative Z axis
Here Electric Field is varying at the rate of 105 NC–1 per metre in positive Z direction
i.e. dE/dl = 105 NC–1m-1 along Z direction
so the electric field at any point on z axis at distance of a metres is ![](data:image/png;base64,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)
Now the total dipole moment equal to 10–7 Cm in the negative z-direction.
The system and the Forces on it are as shown in the figure
![](data:image/jpeg;base64,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Force on a charged particle in an electric field is given by
F = q × E
Where q is the magnitude of charge and E is the magnitude of Electric Field and the force is same as the direction of electric field in case of a positively charged particle and opposite to the direction of field in case of negatively charged particle
so Force on the + q charge located at a distance l from origin will be
![](data:image/png;base64,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)
directed towards positive Z axis
(since the electric field on z axis at distance of l metres from origin )
Force on the -q charge located at a distance l + d from origin will be
directed towards negative Z axis
(since the electric field on z axis at distance of l + d metres from origin)
So net force on the system would be
F = F + q – F-q
(since F + q is directed towards positive Z axis and F-q is directed towards negative Z axis )
So net force will be
![](data:image/png;base64,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)
Solving we get
![](data:image/png;base64,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)
We know,
q × d = P which is the dipole moment of the system so we get
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH0AAAArCAMAAABiiXf9AAAAAXNSR0IArs4c6QAAAIpQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6Ojo6OjqQOmaQOma2OpC2OpDbZgAAZgBmZjoAZjpmZmaQZma2ZpCQZpDbZrbbZrb/kDoAkGYAkGY6kLbbkNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm29u22////7Zm/9uQ/9u2//+2///bfgy/hgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACQ0lEQVRYR+1X21KDMBAlKhattXhXqqYq1pKS//89k90kBMQmoTSOo/tQmOnunuz1kCT5l/1loM7JZH/enZ7rfJ4kFUE5Xjv1x1Vg2YNwWB48JwkvoqehOnyT6PBL5UGiySoj6SNkm0aPWqT7XlRc4sri80XUyFkm+g3LzjLRcpD8aEIlXCXbDcrOpjEbHjtctVv0UYNBxyP8wKgB+jsRP6r49UXEwouA16vbfM5usPibuLumyg7uEkpma5bjnpVp+L3CX6Yj1K48e9Up0PTjswp5cS5nFk2OngZnkZ2atQf0Aw3qEl4oJWnCF7BHhgk70ba4D5YerpCu9AqpSLO36yv8Z6OezjOVav34bwKjyQtpa6PzIpXwdT5z4qKCDh7op/ChHyQMAJEVgDWuBQ5U5z7NAya6iNBCHfqh6kOIELu2SBhCZNR82R5fAf9xOfHnEUX4QD9eCTPopTxc2ml5XnS+2kwErRedLIqFVw+PemF7fmfyBX27R4TtHbXtme8tL2Q+gEcR3bSSO3id+T4T3XXehce6U2tqHQfQqD0mOIMBTY8pFw3kvbLUvPeZbK4xaKaedhx4m6HtuWqWnTvnSsPsOm8LULQ+coyh3nUBnsyeD7DRrdW2HRC63FDAcYECKWu1qsVxIb6C+d3cZuyqWfweAh6s29xmBhQ6GK1j0Nxm/Jl0V8zGvrnNeH29jAcsPVm3mUFNvttprEE3DLWbxxBr6zbjz6QhAFt1m9uMeNPLeDTvTkfmNiP4JDXf8E6zv6DwCfd4MuOAtsRfAAAAAElFTkSuQmCC)
Putting the values of P = 10–7 Cm and
= 105 NC–1m-1 We get
F = - (10-7C × 105NC-1m-1)
i.e. F = -10-2 N
Negative sign states that force is along negative Z axis , so the net force on the system is 10-2 N in negative Z direction.
We know Torque on an Electric Dipole is Vector or cross product of dipole moment P and electric field E and is given as
= P
E
which can be further evaluated as
= PE.sin(θ)![](data:image/png;base64,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)
is the Torque of the dipole
Where P is the magnitude of dipole moment
E is the magnitude of electric field
is the angle between Dipole moment and electric field
is a unit vector perpendicular to plane containing P and E
Here dipole moment P is along negative z axis and electric field E along positive Z axis so angle between them ![](data:image/png;base64,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)
So, Sin
= Sin180
= 0
So whatever be the magnitude of P and E putting
in the equation
= PESin![](data:image/png;base64,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)
We get the torque τ = 0 Nm
So the torque of the system is zero
Question 4.(a) A conductor A with a cavity as shown in Fig. 1.36(a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor.
(b) Another conductor B with charge q is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q + q [Fig. 1.36(b)].
(c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.
![](data:image/png;base64,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)
Answer:In Electrostatic we deal with charges at rest so there is no current inside or on the surface of the conductor i.e. in the static situation, the electric field is zero everywhere inside the conductor. This is the basic property of a conductor. A conductor has free electrons. As long as electric field is not zero, the free charge carriers would experience force and drift and re distribute themselves in such a way so that net electric field inside a conductor is zero.
We will use the above stated property to solve the problems
(a) Here in this situation a conductor with a cavity having no charge inside is given a charge Q on outer surface, we have to show that all charge resides on the external surface only and there is no charge on the inner surface.
From Gauss Theorem we know, net electric flux through an Gaussian surface enclosing a charge is equal to net charge enclosed by surface divided by permittivity of free space
Mathematically ![](data:image/png;base64,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)
Where E is the electric field so
denotes the net Electric flux through the surface q is the net charge enclosed by the Gaussian surface and
is permittivity of free space which is a constant
Now if electric field at all the points on a Gaussian surface is zero
i.e. flux is zero or ![](data:image/png;base64,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)
this means q/ϵ0 = 0 or q = 0
i.e if electric field at all the points on a Gaussian surface is zero then the net charge enclosed by the Gaussian surface is also zero, or there is no charge inside the Gaussian surface
Now if we consider a Gaussian surface enclosing the cavity inside the conductor as shown in the figure
![](data:image/jpeg;base64,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)
we know that net electric field everywhere inside a conductor is zero
so the electric flux through this Gaussian surface would also be zero, this means no charge is enclosed by the Gaussian surface, since cavity does not contain any charge so no charge should be induced on the cavity’s metal surface as well so whole of the charge Q is distributed on the outer surface only.
(b) Again using Gauss Theorem we know,
If electric field at all the points on a Gaussian surface is zero then the net charge enclosed by the Gaussian surface is also zero, or there is no charge inside the Gaussian surface
Now if we consider a Gaussian surface enclosing the cavity inside the conductor as shown in the figure
![](data:image/jpeg;base64,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)
we know that net electric field everywhere inside a conductor is zero
so the electric flux through this Gaussian surface would also be zero, this means no charge is enclosed by the Gaussian surface, but the cavity has a charge q , this means a charge –q must be induced on the inner metal surface because net charge enclosed by Gaussian surface must be zero (q + (-q) = 0) , but the metal surface has only been given charge Q so net charge of system must only be q + Q , i.e. a charge q is induced on outer surface of the conductor as which makes the total charge on the conductor equal to Q only Q + (-q) + q = Q
and total charge of the system as
Q + (-q) + q + q = Q + q
This arrangement is also in accordance with the law of conservation of charge
note: Only Q charge has been given on the conductor’s outer surface , the charge appearing (Q + q) on it is only due to induction due to charge inside the cavity.
(c) To shield the sensitive instrument from strong electrostatic fields in its environment. We need to enclose it inside a metal piece’s Cavity, this process is also known as electrostatic shielding.
we consider a metal Block with a cavity having no charge inside and Instrument inside it as shown in the figure
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any cavity inside a metal surface the electric field is zero no matter in which environment it is placed.
So in order to save the Instrument from External Electrostatic fiels we need to keep it inside a metal Cavity.
Question 5.A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is (
/2
)
, where
is the unit vector in the outward normal direction, and σ is the surface charge density near the hole.
Answer:Now in order to find the electric field inside the tiny hole on the surface of a charged hollow conductor, we will assume the hole to be filled up with the same conductor with same charge density i.e. Hollow conductor without any hole and will find out electric field at the point of hole on the conductor due to the whole conductor and due to the hole element and thus finding the contribution in electric field due the hole element and subtracting it with the total electric field of the conductor without any hole we will get the electric field of the rest of the conductor with hole.
Now consider a hollow spherical conductor with surface charge density
C/m2 with a tiny on its surface now considering two points one just outside the surface of conductor near the hole say A and other inside the hollow cavity say B
As shown in the figure
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Now finding the electric field at point A due to the whole conductor assuming hole to be filled up now the total charge on the conductor with total surface area S and surface charge density
will be
q =
× S
From Gauss Theorem we know, net electric flux through an Gaussian surface enclosing a charge is equal to net charge enclosed by surface divided by permittivity of free space
Mathematically: ![](data:image/png;base64,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)
Where E is the electric field so
denotes the net Electric flux through the surface q is the net charge enclosed by the Gaussian surface and
is permittivity of free space which is a constant
Now assuming an Gaussian surface just enclosing the conductor
As shown in the figure
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)
So we will have
![](data:image/png;base64,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)
Since electric field is always normal to a conductor surface so E and ds are in same direction i.e.
= 0![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAXBAMAAAA1qkh7AAAAAXNSR0IArs4c6QAAADBQTFRFAAAAAAAAADpmADqQOgAAOjqQOma2ZgBmkNv/ttv/tv//27Zm2////7Zm/9uQ//+2XNrvcwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAI0lEQVQYV2NgwAV4HTUZGL43bD7A8Izh+wIga+sBBrAYpQAAzlIJQrHIx3UAAAAASUVORK5CYII=)
So, cos(θ) = 1 and due to spherical symmetry magnitude of electric field will same everywhere so we have
= E × S = q/![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAXCAMAAADa6lTVAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6ZgAAZjoAZpDbZrbbZrb/kDoAkNv/tmYAtmY6ttv/tv//25A625Bm27Zm29v/2////7Zm/9uQ/9u2//+2///bWWXwYAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAbUlEQVQoU82QyxKAIAhF0V7aw7QyK8v//8yoTWgzrbtLhgMHAP4X3zCWjcTL8XaNNL1QibYp4w4IPcNk09N31Cn0roQe54QFISdYoS94R5u8A9i4hoFuuWlLK14iYSqi5qUCiyDJjIPpcV//PwFSNgQjkV/2LgAAAABJRU5ErkJggg==)
i.e. E × S = (
× S) /![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAXCAMAAADa6lTVAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6ZgAAZjoAZpDbZrbbZrb/kDoAkNv/tmYAtmY6ttv/tv//25A625Bm27Zm29v/2////7Zm/9uQ/9u2//+2///bWWXwYAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAbUlEQVQoU82QyxKAIAhF0V7aw7QyK8v//8yoTWgzrbtLhgMHAP4X3zCWjcTL8XaNNL1QibYp4w4IPcNk09N31Cn0roQe54QFISdYoS94R5u8A9i4hoFuuWlLK14iYSqi5qUCiyDJjIPpcV//PwFSNgQjkV/2LgAAAABJRU5ErkJggg==)
or E =
/ϵ0
now since electric field is always normal to the surface of a charged conductor we have
E = (
/ϵ0)![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAXCAMAAAAMT46wAAAAAXNSR0IArs4c6QAAADZQTFRFAAAAAAAAOgAAOjpmOma2OpDbZgAAZjo6Zrb/kLbbkNv/tmYA25A625Bm2////7Zm/9uQ//+2Gxu0rAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAUklEQVQoU2NgoAbgZuRAMoafkYUPwRVk58RlBT8jIwcvEyMLTF6AiZmLgQdulgAT0FQBJlaoNJgryEYWlx9kKNwoASagxYJsjIwws6gRBmhmAABy6wIrmGKyeAAAAABJRU5ErkJggg==)
Where ń is the outward normal to the surface of conductor
Now let us assume contribution of the tiny hole to this electric field is E1 and Electric field due to rest of the conductor is E2
So, we have E = E1 + E2 (Just outside the conductor)
Now inside the hollow cavity inside the conductor at point B we know electric field is zero because of electrostatic shielding
Again assuming the electric field at that point to be contribution of the tiny hole to this electric field is E1 and Electric field due to rest of the conductor is E2 now since the hole will act as a point sized charge so field would be directed outwards i.e. in vertically downward direction, and rest of the conductor is below the point so field would be in vertically upward direction, i.e. field due to both hole and rest of conductor are opposite in direction and net field is zero inside a cavity in a conductor
So, we have,
0 = E1 - E2 (Just inside the hollow cavity of conductor)
Or E1 = E2
i.e. Electric field due to hole and rest of conductor are equal in magnitude and in same direction outside the conductor and equal in magnitude and opposite in direction in the hollow cavity.
Now using, E1 = E2 and E = E1 + E2
We have, 2E1 = E and 2E2 = E
Or, E1 = E/2 and E2 = E/2
Also we know E = (
/
)![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAXCAMAAAAMT46wAAAAAXNSR0IArs4c6QAAADZQTFRFAAAAAAAAOgAAOjpmOma2OpDbZgAAZjo6Zrb/kLbbkNv/tmYA25A625Bm2////7Zm/9uQ//+2Gxu0rAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAUklEQVQoU2NgoAbgZuRAMoafkYUPwRVk58RlBT8jIwcvEyMLTF6AiZmLgQdulgAT0FQBJlaoNJgryEYWlx9kKNwoASagxYJsjIwws6gRBmhmAABy6wIrmGKyeAAAAABJRU5ErkJggg==)
i.e. the electric field due to the hole only is
E1 = (
/2
)![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAXCAMAAAAMT46wAAAAAXNSR0IArs4c6QAAADZQTFRFAAAAAAAAOgAAOjpmOma2OpDbZgAAZjo6Zrb/kLbbkNv/tmYA25A625Bm2////7Zm/9uQ//+2Gxu0rAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAUklEQVQoU2NgoAbgZuRAMoafkYUPwRVk58RlBT8jIwcvEyMLTF6AiZmLgQdulgAT0FQBJlaoNJgryEYWlx9kKNwoASagxYJsjIwws6gRBmhmAABy6wIrmGKyeAAAAABJRU5ErkJggg==)
And electric field due to rest of surface when hole is made is also
E2 = (
/2
)![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAXCAMAAAAMT46wAAAAAXNSR0IArs4c6QAAADZQTFRFAAAAAAAAOgAAOjpmOma2OpDbZgAAZjo6Zrb/kLbbkNv/tmYA25A625Bm2////7Zm/9uQ//+2Gxu0rAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAUklEQVQoU2NgoAbgZuRAMoafkYUPwRVk58RlBT8jIwcvEyMLTF6AiZmLgQdulgAT0FQBJlaoNJgryEYWlx9kKNwoASagxYJsjIwws6gRBmhmAABy6wIrmGKyeAAAAABJRU5ErkJggg==)
i.e. the electric field in the hole of a charged hollow conductor is (
/2
)![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAXCAMAAAAMT46wAAAAAXNSR0IArs4c6QAAADZQTFRFAAAAAAAAOgAAOjpmOma2OpDbZgAAZjo6Zrb/kLbbkNv/tmYA25A625Bm2////7Zm/9uQ//+2Gxu0rAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAUklEQVQoU2NgoAbgZuRAMoafkYUPwRVk58RlBT8jIwcvEyMLTF6AiZmLgQdulgAT0FQBJlaoNJgryEYWlx9kKNwoASagxYJsjIwws6gRBmhmAABy6wIrmGKyeAAAAABJRU5ErkJggg==)
Where
is a unit vector in the outward normal direction.
Question 6.Obtain the formula for the electric field due to a long thin wire of uniform linear charge density λ without using Gauss’s law. [Hint: Use Coulomb’s law directly and evaluate the necessary integral.]
Answer:Let AB be a long thin wire of uniform linear charge density λ.
Let us consider the electric field intensity due to AB at point P at a distance h from it as shown in the figure.
![](data:image/png;base64,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)
The charge on a small length dx on the line AB is q which is given as q = λdx.
So, according to Coulomb’s law, electric field at P due to this length dx is
![](data:image/png;base64,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)
where, ϵ0 is the vacuum permittivity of the medium
But ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
This electric field at P can be resolved into two components as dEcosθ and dEsinθ. When the entire length AB is considered, then the dEsinθ components add up to zero due to symmetry. Hence, there is only dEcosθ component.
So, the net electric field at P due to dx is
dE' = dE cosθ
⇒
………………….(1)
In ΔPOC,
![](data:image/png;base64,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)
⇒ x = h tan θ
Differentiating both sides w.r.t. θ,
![](data:image/png;base64,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)
⇒ dx = h sec2θ dθ …………………….(2)
Also, h2 + x2 = h2 + h2tan2θ
⇒ h2 + x2 = h2(1+ tan2θ)
⇒ h2 + x2 = h2 sec2θ ………….(3)
(Using the trigonometric identity, 1+ tan2θ = sec2θ)
Using equations (2) and (3) in equation (1),
![](data:image/png;base64,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)
⇒,![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIAAAAAhCAMAAAAmoFOyAAAAAXNSR0IArs4c6QAAAK5QTFRFAAAA///b//+22///tv//tv/b/9u2/9uQ29u2ttv/29uQkNv//7Zm27a227aQ27ZmkLb/kLbbtrZmkLa2Zrb/Zrbb25Bm25A6kJC2ZpDbZpC2ZpCQOpDbtmY6kGaQtmYAZma2kGY6kGYAOma2OmaQkDo6ZjqQAGa2kDoAAGaQZjpmOjqQZjoAOjoAADqQADpmZgBmADo6ZgA6ZgAAOgBmOgA6OgAAAABmAAA6AAAAZ/Ia4QAAAAF0Uk5TAEDm2GYAAAJASURBVHja7Vddc5swEDwQteKi5qty1LSkNCWu3JrarYkx9///WOdOCBMnYZg08lPuBTSyZ0+7e7oD4C3+OyZlcz74g6sai5AJfBAmG9o362m8SYNyoIYSkNsUooUOiR8tXAKnJaIGOKtxnQLEJeJPAWAsQGAGDHICqrmI5imoJoWblYC8AFlQdoiIuySkALvLjHlgmuNKA5iVALX9LPrrl0RcjfhjXGn2gLxPvOSQW6qO21Xi2OckxsChPfBPrUcYwIKykykjmwzkVoNpUjAzkKR8vEmj3A7C9LboJApdEIsjpMt3Ccj6TgDcYHPtqn49JWO4JXmyEI9hvFefODDlzwdjA79+OBhm6UDh9sCGH7kOVb0MQ7XygGEi5NYl1CkW/xCvDe5hmGCXRVvKzQyUMwdJFH0Pc3N1MFwr7B8vS9ZZQNbPXBw5+mjSl6rvYUxn9L2VPSFkAbkcTT6OjIcwOUHHle3Vsjef2wvUMzyM6x4Kdb8y3bZ/QAAJ9jDtWyc0r69cS3FOiP8E6B57GH5TmPW4EWdfqkx+ayWaLGwYCTxMboWsexiqbq4hpytTVo7lLMgV1MFMyvaiDhwKgzn6mRv+kXGzY+FH89/6KdX1sRIwM8Jy8xdNhjQfZhBvPpZ4FBJUwYc9nRrNtKvl1HngToTp6YcV/iuJFrOvAqJ56mYwROo5dOsdxQbGtxa5FDQbtvMhgYf+Jjnwm7Fg7MkFf4wIHkbl/btPR0ngfc3DoQZFA6JB/HvORMh6ncBbDMQ/YohWgFHZ2agAAAAASUVORK5CYII=)
The wire extends from
to
since it is very long.
Integrating both sides,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOkAAAAiCAMAAACNxg6mAAAAAXNSR0IArs4c6QAAAL1QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZjqQZpDbZrbbZrb/kDoAkDo6kGYAkGY6kGZmkGaQkJBmkJC2kLa2kLbbkLb/kNv/tmYAtmY6tpBmtrZmtrbbttv/tv/btv//25A625Bm27Zm27aQ27a229uQ29u22////7Zm/7aQ/9uQ/9u2//+2///bDqmp/QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADrElEQVRoQ+1Z61YTMRDOUrArIq20okKLigpdL9gIyMbs5v0fi8ltu+0m6STdc9RzyK+eNvMlc/tmMiXkaT1Z4F+yQPXxxnsdNi77vGp1unfdJ14cFj9aBAToy2UcXHD3fUlPeoSLg6ons6AAfdarV9nf07QYhi0j5n3eLR1NzDO1wn4J6MKfu2K3DcsGPcYvzVLtdndDZ6RIlQYLuF3ahk13Q9fAbPA9+a7iYlFPQ5QSjk2eu6OhDUu9Tq0ncUkMnJCep/y45Ifp4eXTog3rswYh/l+c9hXzIWHDylPTxLfjth7FphHpkNDhwxWKbzvCELwep7Rh6wlEHB3ZCzLNDBlIRqZwAcHB85Gby8X8VfsHaZW1Ja3KfMIb6neECaknbuZdgxVzaQ5+ZOOc7kG2KDCwR1+rTzZw3YnnGIKQvgBVLUvriC9moG0y5XcuExke0QZmqPKknAgeNJHe0HX9rremoom36jTL9s8IzcCc4iukyG2+h7ZnQDhKU+NUmbbiPfp0nPUtt9WTcVnJxJAE8mvBBp/OdfJgVkjYeGsLDNWeN6nEc6AjV+EpDFVlmY6BmMWMiNIYemPjY9VobOvimnNCwjhNref1kTJNoQhh9WjUd36wKFZToEiFrPgelJQxrNvRRrw5uGNZvzDc2lp/Q2odttFUhZGvMGFVd+5r6jrPD2RA6ExRSkYU7YBwVJ5qHR21yty9j+glpPogc0VrrpSMYWW/cIKm2sT1a3mT/paJXj42ptSBo75Fx1BQGBcZup4aalCnK3rsc5mLsMECHKkIqbostWeLobhEmTUojOwcNM0rluATncOYjiPCFCYn/rwB4j4DOZod3JhEUR8xKyjsT7oWtN3kfspi7uDaw2TjvFox2Zh0JCYJrOOT5yzuHFl/VSP63gdonyCPE5etYx3xFqxlC+d0AnGuuHjh6Kg2m+aNt0wXt55ekdv4nsQCmQrdwW3Dar+v3jII5da20HP5ElgNbO7ANyeknn45Xcv2jfep85RdEigQkk2fKz2yep/GKsrGyn3NwIYdK4Jh2aiMfvXtMkMNDEENbHJ6apPUb5difg4lwwxsakne8m0LFSR2AHabnqbSWb6XgoHdNg/e5mJqBxRmYGNnQaBl7ACM7qSo96lgYBGcuE1X82I3AxuZE6KE4jwj/PDn563CrUIEirJdXoviwvXfC9Ow8GPEXTxbf+dqgGTmQODk/WvQUn51sMSjq7BHTQ78mPfd8yxs9QN/laed/6cFHgGG634gj7NKegAAAABJRU5ErkJggg==)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
This is the net electric field due to a long wire with linear charge density λ at a distance h from it.
NOTE: In the given case, it has been assumed that the length of the wire tends to infinity. In case of wires of finite lengths, the sin(θ) components cancel out only along the perpendicular bisector of the wire. At any other point, the net electric field will have both sin(θ) and cos(θ) components.
Question 7.It is now believed that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called ‘up’ quark (denoted by u) of charge + (2/3) e, and the ‘down’ quark (denoted by d) of charge (–1/3) e, together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron.
Answer:Let there be n up quarks.
Number of down quarks = 3-n (Since there are 3 quarks in a proton)
Charge on n up quarks =
where e is the charge of a proton
Charge on 3-n down quarks = ![](data:image/png;base64,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)
In case of a proton:
Since the charge on a proton is e,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ n = 2
So, 3-n = 3-2 = 1
Hence, there can be two up quarks ⇒, 2u and one down quark ⇒, 1d in a proton.
In case of a neutron:
Since a neutron is electrically neutral,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI8AAAAgCAMAAAAc99uaAAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6AABmADo6ADqQAGaQAGa2OgAAOgA6OjoAOjpmOjqQOmZmOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///bBATQ7AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABjElEQVRYR+2WyWKDIBCGIU1bu6U1drFWm2DSuPD+71fGpTFKEJg55NA5cBF+v1mBsX8jisBPxPkzkVYnI79vvQXr9RfbLVLv85qD+VPkzwN65R0pD2MCxyNeKMOjtHA8O+LyQfIIchxUfAqFU3yQJkxmN4eJoEw4f9zM/qcOuTJbnv2rReULUByXpIyvD1V8tZ0FcthQRXwqKGMrZwqYKYW14zZU5WojvHkyOFmHLoOgUHnLA+OwduMZCEK6gAdWayuDh5QJU0zdeNhRsOVp194yqLPGztwPZaBKoQwM09GZpxfU8Wjj1BE23xqeOux4dPgjHq2HA8WjYJ8vl/oZ8ejwfeLTOtjV8zD2dvn6iw8tT1OWjv1+mi9aHmit03Keb7MG31zP004wzcOhoBqmfOXS7YpEDSC4P840mEzUBr58O3XMwDMnOB+hC9iR3/PFyGUkFUpRflK/n/GK5O9n3Iu8St6RGRofRylmfEnMg1Xcw71Fav6K9Tpt7y0yQyqqFxh1v5MrksXqUoV+ASuVJFhqPo0qAAAAAElFTkSuQmCC)
⇒ n = 1
So, 3-n = 3-1 = 2
Hence, there can be one up quark i.e. 1u and two down quarks i.e. 2d in a neutron.
Question 8.(a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (⇒, where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.
(b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.
Answer:(a) At a null point, the net electrostatic field is zero. If a small test charge is placed at the null point, it experiences no electrostatic force. But if it is displaced from the null point, it tends to move in the direction which is tangential to the field lines ⇒, towards the negative charge and away from the positive charge. So, if the test charge is displaced from the equilibrium position at the null point, it tends to move away from the equilibrium position. Hence, a null point is necessarily unstable.
(b) Let us consider the case of two charges of equal magnitude and opposite sign. The null point occurs at the midpoint of the line joining the two charges. If the test charge is moved away from this null point, it experiences a force towards the negative charge and away from the positive charge. This results in the movement of the charge away from the null point. Hence, the null point is an unstable equilibrium position.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAcwAAAChCAYAAABKxo+2AAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABY+SURBVHhe7d0JmI71/sfxzyzGYBhMTbJlJ2SrTuqcCl1HSUjHHqqjUuochKRyZEmUkcoeHVGy1LRcbXRKCi2HNpzssv0tITszlvk/vzuDGbMx89P9/J73fV1dV8b9fO/f9/W7x+e5l+d+IlMCi1gQQAABBBBAIEuBSHwQQAABBBBAIHsBAjN7I9ZAAAEEEEBABCY7AQIIIIAAAjkQIDBzgMQqCCCAAAIIEJjsAwgEpcBh7Vw6V5Ne+UTr9uxX0onTTURfXF7Nuz2lphWCsjEGjYBvBQhM304NA0MgK4FD+r8l72vyqP+oUre2ql349Lr54y5WTBR6CCCQ1wIEZl6LUg+BCySQEhajy6rdon+OGqYm+S7QRtkMAiEsQGCG8OTTOgIIIIBAzgUIzJxbsSYCPhIIV1R0inZv+URD23fS9AKnhxYdX0EtHhqo27iG6aP5YiguCBCYLswiPYSkgHlGV0S+QrqoVFmVjTlNEFXsEhXhGmZI7hM0bVeAwLTrS3UELAmc0NGkMMXGX6f7RzzNNUxLypRF4EwBApP9AQEEEEAAgRwIEJg5QGIVBPwoEK4DWrfiXf2rzT69VjDtNcyW/xjMNUw/ThpjCmoBAjOop4/Bh65AjMr8paMGJFTWpr1pH1wQVayUYvOHrgydI2BLgMC0JUtdBKwK5FfRijfqrkdutLoViiOAwGkBApO9AQEEEEAAgRwIEJg5QGIVBGwL7Nu3T08++eSpzVSoUEE9evSwstlly5Zp5syZGjx4sJX6FEXAVQEC09WZpa+gEEgNyi1btigxMfHUmKOifv8gpY3QLFiwoHbt2qX+/fsTmkGxlzBIvwgQmH6ZCcYRcgIbN25Uz5490wRlKkJycrL69u1rJTTN0evYsWM1YMAAjRgxQr179w45expG4HwECMzzUeM1COSBQPqjyvQlTWj26tVL33zzTR5sLW0JcwS7fft2zZkzR+vWrVPx4sU1ZMiQPN8OBRFwSYDAdGk26SWoBCIjs//1K1GihKpUqWKlrxo1aqhmzZpKSEjQhAkTrGyDogi4JJD9b6xL3dILAj4SOHbsWLajiY2N1cCBA7Nd73xWSEpK8q6Rzp49W61atTqfErwGgZASIDBDarpp1k8CFStW9K5hPv/88xkOy2ZYbt682QvLJk2aEJZ+2ikYi68FCExfTw+Dc1kgPj5ew4YN81pMH5omLKdMmaLbb789zwnMx0qeeuopLyy7dOmS5/UpiICrAgSmqzNLX0EhYG6+MaFpjjZXrlzp3THbr18/lSpVykpYGpRChQoRlkGxdzBIvwkQmH6bEcYTcgImNB966CEtXrxYCxcu9P7f5lK+fHmOLG0CU9tZAQLT2amlsWAT2Lt3r3JyI1Cw9cV4EXBFgMB0ZSbpAwEEEEDAqgCBaZWX4ggggAACrggQmK7MJH0ggAACCFgVIDCt8lIcAQQQQMAVAQLTlZmkDwQQQAABqwIEplVeiiOAAAIIuCJAYLoyk/SBAAIIIGBVgMC0yktxBBBAAAFXBAhMV2aSPhBAAAEErAoQmFZ5KY4AAggg4IoAgenKTNIHAggggIBVAQLTKi/FEUAAAQRcESAwXZlJ+kAAAQQQsCpAYFrlpTgCCCCAgCsCBKYrM0kfCCCAAAJWBQhMq7wURwABBBBwRYDAdGUm6QMBBBBAwKoAgWmVl+IIIIAAAq4IEJiuzCR9IIAAAghYFSAwrfJSHAEEEEDAFQEC05WZpA8EEEAAAasCBKZVXoojgAACCLgiQGC6MpP0gQACCCBgVYDAtMpLcQQQQAABVwQITFdmkj4QQAABBKwKEJhWeSmOAAIIIOCKAIHpykzSBwIIIICAVQEC0yovxRFAAAEEXBEgMF2ZSfpAAAEEELAqQGBa5aU4AggggIArAgSmKzNJHwgggAACVgUITKu8FEcAAQQQcEWAwHRlJukDAQQQQMCqAIFplZfiCCCAAAKuCBCYrswkfSCAAAIIWBUgMK3yUhwBBBBAwBUBAtOVmaQPBBBAAAGrAgSmVV6KI4AAAgi4IkBgujKT9IEAAgggYFWAwLTKS3EEEEAAAVcECExXZpI+EEAAAQSsChCYVnkpjgACCCDgigCB6cpM0gcCCCCAgFUBAtMqL8URQAABBFwRIDBdmUn6QAABBBCwKkBgWuWlOAIIIICAKwIEpiszSR8IIIAAAlYFCEyrvBRHAAEEEHBFgMB0ZSbpAwEEEEDAqgCBaZWX4ggggAACrggQmK7MJH0ggAACCFgVIDCt8lIcAQQQQMAVAQLTlZmkDwQQQAABqwIEplVeiiOAAAIIuCJAYLoyk/SBAAIIIGBVgMC0yktxBBBAAAFXBAhMV2aSPhBAAAEErAoQmFZ5KY4AAggg4IoAgenKTNIHAggggIBVAQLTKi/FEUAAAQRcESAwXZlJ+kAAAQQQsCpAYFrlpTgCCCCAgCsCBKYrM0kfCCCAAAJWBQhMq7wURwABBBBwRYDAdGUm6QMBBBBAwKoAgWmVl+IIIIAAAq4IEJiuzCR9IIAAAghYFSAwrfJSHAEEEEDAFQEC05WZpA8EEEAAAasCBKZVXoojgAACCLgiQGC6MpP0gQACCCBgVYDAtMpLcQQQQAABVwQITFdmkj4QQAABBKwKEJhWeSmOAAIIIOCKAIHpykzSBwIIIICAVQEC0yovxRFAAAEEXBEgMF2ZSfpAAAEEELAqQGBa5aU4AggggIArAgSmKzNJHwgggAACVgUITKu8FEcAAQQQcEWAwHRlJukDAQQQQMCqAIFplZfiCCCAAAKuCBCYrswkfSCAAAIIWBUgMK3yUhwBBBBAwBUBAtOVmaQPBBBAAAGrAgSmVV6KI4AAAgi4IkBgujKT9IEAAgggYFWAwLTKS3EEEEAAAT8JHFiTqKH3jdL8w8k6HhhYWGScqtV/UE+PuE0lsxnoeQfm0e1zNKz9UM05nKRjKYGNRsTqsppd9MyENirvJx3GggACCCAQdAJr165V165d04y7du3aSkhIOL9eTuzWqnef1d0DpmrdxnJq90IfXR+zX+vmvqLBCd209rd56jMwQc1KZ17+7MA8vkerE4ep+5u/ql3/yepcM92LUw5oy9wEtXvi31rxQxG1HDNAN190WNsWTdWTI7tr/d7/6JGnJ6ptxex72rZtmzp27JhmxcqVK2vcuHHZv5g1EEAAAQScFDBh2apVK/3www9p+ps/f77353MPzaP6dfl7GvHPUfrq1zi1HD5eQ++qpYKm2DWldeCXFhr0ystSyg264pUWKpeJagZHmMnau3qBPvpwo+p0S/+q49rzyxwlPPisFqyPVMNB05XQ9ToVNqs1qKLkdU30yMwpGprcSHUS26lqFlNpwrJZs2ZavHhxmrU+/fRT78+EppO/BzSFAAIIZCmQWViaFx07dkwvvvjieYTmIe1ctVifbE5S8Vp/1d9anwxLU6l0PbVsfZvGzZ2lH76cpM/WttDfMzngOzswIwqqUOEiio6NVUyh9H0d0b61/9Wc9YcUU66FWrc/GZZmtbgaan5nSz3/zmStWDBaHy8PBGaNjF22bt2q5s2bnxWWqWuPHz+e0OSXKuQEwsLCQq5nGkbgTIHly5d7Zx3TH1meuU5qaB4/flyjRo06/VfJ2/TjzOHqOuarUz8Lj6+qO/pOUO9rD2rvhvXaFPibS6OKqnjMmRXDlb/wJTJxdzB8p3bvyXxOvMA8tHWhJvfqqWlrvAzXoW3rlLwjWWM7/0nvmMIFLlGle57T9LvidfCXdVod+FGRyGK6yDu0TF1SFBXYaJHAH3dE/qrduzLeqHn30KZNG3333XdZ7ikmNE+cOKEJEyawRyEQEgLR0dEKDw8PiV5pEoGMBA4cOJBlWKa+xoRm6unZU3Uii6j0Na3VN+aGUz8KKxCr8hXzBW6yyaf8RYp6+ZSSkhL4L93Wzc/Mj1LClNX7Vi8wo2IrqmGXfiq9L/CH43u17oMX1O+9XfpLx35qe3ngZ5EFVKRqicBGw5QvsNHigR8dDZQ/n43u3bs327BMbWXixIlavdrEMwsC7gv89ttvWrNmjRo1auR+s3SIQAYCJh9yusTEpDlMlMILKq7KdWpZJaMKhRRbrqIqB/7q+93LtPh/Sbr12vy/r3h4j35ZvkhbFaWLC/1FdTJ8/e+reoEZWbCEat7UUr/f33NEq7bP0hNzj6nOrS3Vss6ZG09WofKVZTL0y33L9M2y/WpT4uRhZvIhbV66QOsVoQLRN6perYzbjoiIyKmHt968efPOaX1WRiDYBdjng30GGf+FEDBHijlfCqhU3eZ6+O5EdZ7yuWY8O15N3+quK8NPaPvXb+iZ8d8pOa6a2vR7RH9Ol8NnbuPsa5jH9mrf/oNKOnRQ+88K+3y6qFpT9ew2U5+PXaLZQ0fq9usG6PrArUb7f5qtISO/1OECJdXhyX/pptict8KaCCCAAAIInIvAkSNHzmH1MOWPq6fWw19TRI0EPdvnMd1x9QyViYnQka2btaNYV02e/pCa1Suh6CyqZnDTT3FVu/Mlzb8xSWWrp39l4JRs4epqOmSqEuuO1rD7BqtN/Q9Vrkg+Hd+9SRvVSWM+76k76pXyLqBmtJjrkjldSpYsqddffz2nq7MeAggggECQC/z444/q0aNHll1UqlRJL78c+BjIOS3hio6vow49ElS7bietXrNI0wYPVOKW0rpuyIP6+1VXZFvt7MAMXByNKVNLN5TJ/LURxaqr5b1Pq3qFllq1aalmD+kVuGGoqKr16qpuf6qb5UbN5yzNtcn7778/y/VMWL7//vuqWzfretl2yAoIIIAAAkEjcP3113tjzSw0TVgmJibqiiuyD7gMm46MV42bGgf+u14VCm7Q6s5T9N8JHVX/ncA10Mtbqe/oPrrB3B2UwXLeT/qRiqlqo78GPmt5k6rHrdPKZmP07Rv369r5hRRT9lb1Gv+Ubrn47C2aC7X33Xef9xeZhSZhGTT7NgNFAAEE8lTA3Ofy8MMPZxiauQ7LNCMtoJqth2tGmU7aeuSQDiSdUIGi5VUli3OyuQjM1C2Hq2KTQZo272/anHRI+48cV1RMadVM85GTsz0zC03CMk/3PYohgAACQSeQGprmUXhnLnFxced/ZJmBQnh0vKo3aKSzrj5mIpYHgRmoHFFcVRo0VBZ342a4eROa5hTtmUts4IEJnIYNuv2bASOAAAJ5KmBCs0GDBnlaM7fF8iYwczEKv4HkohVeigACCCDgsMAfHpgO29IaAggggIBDAgSmQ5NJKwgggAAC9gQITHu2VEYAAQQQcEjA14G5bNkyDR8+XNOmTXOInFYQQAABBIJRwNeBaZ5cP3fu3GB0ZcwI5KnATz/9pKFDh2rGjBl5WtflYvs3fKaJvQbonaMV1OKRF9T7xqIut+tEbwsWLPAebDN16lRf9uPbwDRHl88884w++ugjX8IxKASyEzDf7de5c2fVqFEjV/8AmK/C69+/vx577LHsNsnfnyFw9MBWLftsgRYkbVGFDsnYBIFAlSpVVLNmTXXp0kWTJ0/23Yh9G5j79+/3vmC6Xr16vkML9gEd3PylJvV+XG8eKKtbe76kfjeZL2xjyWuBUqVKadCgQdqyZYuuuuoqVa9e/byC03ztl3kDmfrIsLwep6v1wsLzqYB5gEpUjArk48u5g2Ge4+PjVadOHZnvQ/bj4svAXLp0qXd0aZ4ly5L3AscObdP/5gXeee8ppdLtkvJ+A1T0BIoWLaqmTZvKfDN8mTJltHnzZu8NoDnizOl1efPN888995zeffddVBEICYGrr75avXr1UqdOnXL8e3KhYHwZmObapTkNxRN/7OwG5p13tHnnfYJ33naE01Y1Tyxp0qSJzLfEly5dOsfBab61oXfv3hoyZIj3rpsFgVAQKFasmO655x6ZHPBbaPouMM2pp2HDhumDDz4IhX2DHkNIIDIy0gtO8xV35ohz06ZNmR5xLlmyxLtuacKyfv36IaREqwhIBQsWVPfu3TV69Gjde++9mjRpki9YfBeYBw8e9K7XpH/ori+0GAQCeSAQHh6uW265xQvOsmXLekec5hqnOVX76quvelvYt2+ffv75Z8IyD7xNibAwrmHmEeUFKxMdHa1GjRqpT58+MmdpJkyYcMG2ndmGfBOYq1atUocOHXT48GFt2LBBV1555R+O48oAqlWrlusv4l6xYoXuvPNOV0j+8D7MnYAmHG+++WZvLBUrVvQCslu3bt5XG7300kv68MMP//BxBvcAUpRivq8+JRCYEfly1Ir5+I45HcjiDwFzAGUW83ETPyy+CcxLL71UrVu39h5U8PXXX2vXrl1+8HFiDEWKZPJtqOfwztt87Zr5HCBL3giYo8rUa/RRUVEyc2TupjWh+fHHH2v9+vXauXOnzN3iLNkL1KpV69TReeraKYG0PGEOLHcs0+v/+LO+GnAyNMMvVpU7HtP4JxoFvtU37WKO+NnPs/e+UGt8++23eu211zRr1qwLtckst+ObwCxcuLB36G1uijDnq/16W7EvZi3Xgzj3d97mH/TUo6Fcb54C3g1A5jqmOT1rrleau8Lfeust5c+fX1988YXGjRungQMHeuuZU7csWQuYO5LTL0XKN1a/9xbp7kMndPTIQR0+GjjUNEtYfhUuXV2FMihp6rCf+2dvM9cy33zzTe9yhR8W3wSmwTD/eJgPrj766KMEps29I/DO2/unY9dKzep5g5YMOfnOOyxO5Vs8qokDGusim9untswNQI0bN9batWs1duxY75STOU1rFnOTT4kSJbyn+vjhuk2wTldkgTiVq3OtygVrAyE+7kWLFikhIcFXHy3xVWCa/cNcbzN3yZrrmdOnTw/xXcZO+4XKNFTvtxepw0HzzvtQ4J33ySOYwDvvmJLVZD5xwmJf4Pvvv/fOqphTgKlhabZqwtRcLzanYzt27OidkmJBINQEzCUJc2+LOd3ul8V3gWlOzV5++eU8BsziHhIRXVyX1b5Wl1ncBqWzFjCfMzZhad4cmg9qp1/MqVnzkIORI0dCiUBICpjfAXN3rJ8W3wWmwalatap380/79u31xhtv+MmLsSCQa4HswjJ1A+ajVeazmG3bttXMmTNzvV0KIBAsAuZ07JgxY3z3778vA9McZZrQ5GHTwbJ7M86cCuQ0LE09c6OVedKJubWe0MypMOu5IGCen2w+ynbmpQo/9OXLwDQwqdcy27Vrx1ca+WFPYQy5FjiXsEzdmDkt9cADD3h/NB+7mj17dq7HQQEE/CywcOFC76bPxMRE3w3Tt4FpjjJNaPbt29d3aAwIgXMVMJ8ne/zxxzO9ZplVvdTQvOaaa851s6yPQNAJ7NixQytXrvTd0aWB9G1gph5lzpkzJ+gmnAEjkF6gUqVK3nX5832ClQlNninLfhUKAg0bNtTbb7/ty1Z9HZgxMTG+fJfhy5lkUL4WKF68uMx/LAggkLWAeXhERg+i8IObrwPTD0CMAQEEEEAAAd+fkmWKEEAAAQQQ8IsAR5h+mQnGgQACCCDgawEC09fTw+AQQAABBPwiQGD6ZSYYBwIIIICArwUITF9PD4NDAAEEEPCLAIHpl5lgHAgggAACvhYgMH09PQwOAQQQQMAvAv8P5FDemC+U8/cAAAAASUVORK5CYII=)
NOTE: A test charge is a positive charge of unit magnitude. A null point or neutral point is a point where magnitude of electric field is zero. A pair of charges of equal magnitude and opposite sign is known as a dipole.
Question 9.A particle of mass m and charge (–q) enters the region between the two charged plates initially moving along x-axis with speed vx(like particle 1 in Fig. 1.33). The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is ![](data:image/png;base64,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)
Compare this motion with motion of a projectile in gravitational field discussed in Section 4.10 of Class XI Textbook of Physics.
Answer:Given,
Mass of the particle = m
Charge of the particle = -q
Velocity of the particle = vx
Length of the plate = L
Electric field between the plates = E
From Newton’s second law of motion,
![](data:image/png;base64,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)
Where, F = Force on the particle
m = mass of the particle
a = acceleration of the particle
⇒ ![](data:image/png;base64,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)
⇒
(Since F = qE)
Time taken by the particle to cover the distance L is given by
(Time = Displacement/Velocity)
For the movement in vertical direction, initial velocity (u) is zero.
According to Newton’s second equation of motion,
![](data:image/png;base64,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)
⇒![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKkAAAAoCAMAAACy5ypgAAAAAXNSR0IArs4c6QAAAKJQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmZmOmaQOma2OpDbZgAAZgA6ZjoAZjpmZrbbZrb/kDoAkDo6kGYAkGY6kGZmkLbbkLb/kNv/tmYAtmY6tpA6tpBmtrbbttvbttv/tv+2tv//25A625Bm27Zm27aQ27a229u22////7Zm/9uQ/9u2//+2///bO5BMhgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADV0lEQVRYR+2YiXLTMBCG7RRKTA+amhISSlul0IIbID70/q/G6t6VbDVOYs9kwDPuYf+WPv1arY4k+X/9iw78uUnT2TE0vPl4l6wnD8eACozV+2MhLa5HsbT++uzXU8429FGowZL1OGFanbueq7JUXNdJcfETo2oNvD61TXCSYjBQvpo6jCb/jJheToBQ9GXhkJLEako8coykBNASF3KwSHj5cINIGfobahSk4uILFHpWY18jSZOLbhiEFAxzdHrU1pATz+GpQGGyVgTlRjYhxZKD2egVhEiVXXwx3cANfNYfZKqznZIS34dhdaRVJg2UromnztOkMIGgNZ7R4l8rGQZT1GB7X9dFSJNShqgFRDzS08LGJGrDMKycvTO5hqkh3uSzTS17H1A4k6RNrseU1hhP+RL8V5eV9Obkt2l6GaRxv5hCpUxVlXa3zNKrxyn4KPOpNI0vTCtsD6jXLlMZSX9QKLtemPAyn/NFdwapMpSL0DiT3zJVEtF4TFrSm1Tm5dJPbTFSInYxoWoulHlBgYhLS9yTegme+1Nx2BDZQtuh23iKKSBB0XXGDqQiHPgXPL212q2ipsk9YczTwBNccKF6J6bREvuVHGLVJWCYi8nAp+Gth0AQ5TuTasNjpEFkrNKLp9ejVjES0rYW6SbiUExsw/FLj5RqFE4Yw+uz9C1ZhrVxm94nSw6B3j32Y6NlpxEFXL8yDNDa+yqtBNl4TFIZomim6AoEGd+9slR0OrT5tLtP/HxaZfOkxmvKDlQx7MNpY+vM75eqvYlmfi/P1EuYxa7Q0O8yVawyA12MVK70Oi7zLqKJff56BuiniMSU9bJbE7O7H0e7Gp95kI0RldtX3ZrI14cAJWcekXWbtbJbs8Uo35fY7YzsBjM9/ZZN7h7Tyb0qHO1ZlYbBcg/WBigR0G3tvkzt37szD1ubmDSZuPUYQ9topZHWksMSstMeBhSfeZjqxG95K1Lil9LAz+YTmilHsJSeeWgTKam37ZQaIBNbqCI9+ZGD+SPsTL0zD76UK19DuhJ7LHhGelNpijdisuRsylfzQDJA74dnHr+hS2GLNBVrabWerr/7FSuN3mCJzUAoGYB1zyL57dk4h5B7ckK3PzT5fN9SxvieiRA5mtPyFkf+AsxVXUghUi0NAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
This is the vertical displacement of the particle at the far edge of the plate.
This motion is very similar to the motion of a projectile in a gravitational field. In a gravitational field, the force acting on the particle is mg and in the given case it is qE. The trajectory followed by the object will be similar in both the cases.
NOTE: A projectile is any object thrown into space by the exertion of a force. The path followed by a projectile is known as its trajectory.
Question 10.Suppose that the particle in Exercise in 1.33 is an electron projected with velocity vx= 2.0 × 106 m s–1. If E between the plates separated by 0.5 cm is 9.1 × 102 N/C, where will the electron strike the upper plate? (|e| = 1.6 × 10–19 C, me= 9.1 × 10–31 kg.)
Answer:Given,
Velocity of the electron, vx = 2.0 × 106 m s–1
Separation of plates, l = 0.5cm = 0.5 × 10-2 m
Electric field between the plates, E = 9.1 × 102 N C-1
Charge on the electron, q = |e| = 1.6 × 10-19 C
Mass of the electron, me = 9.1 × 10-31 kg
The vertical deflection of the particle (s) is given by
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ L = √(2.5 × 10-4) m
hence, L = 1.58 × 10-2m = 1.58cm
Hence, the electron will strike the upper plate after travelling 1.58cm.
An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55 × 104 NC–1 in Millikan’s oil drop experiment. The density of the oil is 1.26 gcm-3. Estimate the radius of the drop.
(g = 9.81 m s–2; e = 1.60 × 10–19 C).
Answer:
If the oil drop is stationary, the net force on it must be Zero or the resultant of all the forces on oil drop is zero.
There are two forces acting on the oil drop, its weight or force due to Earth’s gravity which is pulling it vertically downwards, and Electrostatic force which is acting in vertically upward direction.
Both forces should be equal in magnitude and opposite direction so that they cancel each other.
The arrangement is shown in the figure
Note: Electric Field is in vertically downward direction, because force on an negatively charged body in opposite direction of the field, so force on the drop is in vertically upward direction, which balances weight of the drop acting in vertically downward direction.
There are nine excess electrons which make the drop negatively charged because the electron is negatively charged, the net magnitude charge on a body is given by
q = n × E
n is the excess of electrons or protons on the body,
the charge of an electron is denoted by e
e = 1.60 × 10–19 C
here since there are twelve excess electrons so
n = 12
i.e. q = 12 × 1.60 × 10–19 C
= 1.92 × 10-18 C
Now the magnitude electrostatic force on a charged particle held in an electric field is given by
F = q × E
where, F force is acting on a particle having charge q held in an electric field of magnitude E
here, charge on the oil drop is
q = 1.92 × 10-18 C
magnitude of Electric field is
E = 2.55 × 104NC–1
So Electrostatic force on the oil drop is
F = 1.92 × 10-18 C × 2.55 × 104NC–1
= 4.896 × 10-14 N
This force is acting in vertically upward direction, so Weight should have same magnitude of Force and is acting in vertically downward direction.
Let us assume oil drop to be Spherical in shape, so the volume of drop will be
(Volume of Sphere)
Where r is the radius of the Spherical drop
Now we know mass of an object whose volume and density are known is given by
m = V × d
where, m is the mass
V is the volume and d is the density
Here density of the drop is
d = 1.26 gcm-3
= 1.26 × 103 Kgm-3
so mass of the drop is
m = × 1.26 × 103
Now the downward pull on a body due to earth’s gravitational force is the weight of body given by
W = m × g
Where W is the weight of a body having mass m
The acceleration due to gravity is denoted by g
g = 9.81 ms-2
so the weight or the downward gravitational force on oil drop is
W = × 1.26 × 103 Kgm-3× 9.81ms-2
Both the forces should be equal in magnitude so equating them
i.e. putting F = W
4.896 × 10-14 N = (4/3 πr3) × 1.26 × 103 Kgm-3 × 9.81ms-2
we get ,
(1N = 1kgms-2)
So, r
⇒r = 0.98110-6 m
= 9.81 × 10-7 m
= 981 × 10-4 mm
i.e. radius of the oil drop is 98110-4 mm
Question 2.
Which among the curves shown in Fig. 1.35 cannot possibly represent electrostatic field lines?
Answer:
Electrostatic field lines have some properties and characteristics, which should be taken into account while drawing Electrostatic field lines, the Characteristic of electrostatic field lines are :-
1. They start from a positively charged body and end at a negatively charged body.
2. Tangent to the electrostatic field line at any point gives the direction of the electric intensity at that point.
3. Electrostatic field lines cannot intersect each other.
4. The electrostatic field lines are always normal to the surface of a conductor. There is no component of the electric filed intensity parallel to the surface of the conductor.
5. Electrostatic field lines do not form any closed loops.
These properties and characteristics must be taken into account while drawing electrostatic field lines, if any of these are violated then the following representation will be incorrect.
Hence, only (c) is the correct representation of electrostatic field lines and (a),(b),(d),(e) are incorrect representations of electrostatic field lines .
Question 3.
In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 105 NC–1 per meter. What are the force and torque experienced by a system having a total dipole moment equal to 10–7 Cm in the negative z-direction?
Answer:
A dipole is a system consisting of two charges equal in magnitude and opposite in nature i.e. a positive charge + q and a negative charge –q separated by some distance d
Electric dipole moment of a dipole is given by,
P = q × d
Where, ‘q’ is magnitude of either of charge (in column)
And ‘d’ is separation between the pair of charges (in metres)
Dipole moment is a vector quantity and its direction is from negative charge to positive charge
We are given dipole moment of the system,
P = 10-7Cm , along negative Z axis
Here Electric Field is varying at the rate of 105 NC–1 per metre in positive Z direction
i.e. dE/dl = 105 NC–1m-1 along Z direction
so the electric field at any point on z axis at distance of a metres is
Now the total dipole moment equal to 10–7 Cm in the negative z-direction.
The system and the Forces on it are as shown in the figure
Force on a charged particle in an electric field is given by
F = q × E
Where q is the magnitude of charge and E is the magnitude of Electric Field and the force is same as the direction of electric field in case of a positively charged particle and opposite to the direction of field in case of negatively charged particle
so Force on the + q charge located at a distance l from origin will be
directed towards positive Z axis
(since the electric field on z axis at distance of l metres from origin )
Force on the -q charge located at a distance l + d from origin will be
directed towards negative Z axis
(since the electric field on z axis at distance of l + d metres from origin)
So net force on the system would be
F = F + q – F-q
(since F + q is directed towards positive Z axis and F-q is directed towards negative Z axis )
So net force will be
Solving we get
We know,
q × d = P which is the dipole moment of the system so we get
Putting the values of P = 10–7 Cm and = 105 NC–1m-1 We get
F = - (10-7C × 105NC-1m-1)
i.e. F = -10-2 N
Negative sign states that force is along negative Z axis , so the net force on the system is 10-2 N in negative Z direction.
We know Torque on an Electric Dipole is Vector or cross product of dipole moment P and electric field E and is given as
= P
E
which can be further evaluated as
= PE.sin(θ)
is the Torque of the dipole
Where P is the magnitude of dipole moment
E is the magnitude of electric field
is the angle between Dipole moment and electric field
is a unit vector perpendicular to plane containing P and E
Here dipole moment P is along negative z axis and electric field E along positive Z axis so angle between them
So, Sin = Sin180
= 0
So whatever be the magnitude of P and E putting in the equation
= PESin
We get the torque τ = 0 Nm
So the torque of the system is zero
Question 4.
(a) A conductor A with a cavity as shown in Fig. 1.36(a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor.
(b) Another conductor B with charge q is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q + q [Fig. 1.36(b)].
(c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.
Answer:
In Electrostatic we deal with charges at rest so there is no current inside or on the surface of the conductor i.e. in the static situation, the electric field is zero everywhere inside the conductor. This is the basic property of a conductor. A conductor has free electrons. As long as electric field is not zero, the free charge carriers would experience force and drift and re distribute themselves in such a way so that net electric field inside a conductor is zero.
We will use the above stated property to solve the problems
(a) Here in this situation a conductor with a cavity having no charge inside is given a charge Q on outer surface, we have to show that all charge resides on the external surface only and there is no charge on the inner surface.
From Gauss Theorem we know, net electric flux through an Gaussian surface enclosing a charge is equal to net charge enclosed by surface divided by permittivity of free space
Mathematically
Where E is the electric field so denotes the net Electric flux through the surface q is the net charge enclosed by the Gaussian surface and
is permittivity of free space which is a constant
Now if electric field at all the points on a Gaussian surface is zero
i.e. flux is zero or
this means q/ϵ0 = 0 or q = 0
i.e if electric field at all the points on a Gaussian surface is zero then the net charge enclosed by the Gaussian surface is also zero, or there is no charge inside the Gaussian surface
Now if we consider a Gaussian surface enclosing the cavity inside the conductor as shown in the figure
we know that net electric field everywhere inside a conductor is zero
so the electric flux through this Gaussian surface would also be zero, this means no charge is enclosed by the Gaussian surface, since cavity does not contain any charge so no charge should be induced on the cavity’s metal surface as well so whole of the charge Q is distributed on the outer surface only.
(b) Again using Gauss Theorem we know,
If electric field at all the points on a Gaussian surface is zero then the net charge enclosed by the Gaussian surface is also zero, or there is no charge inside the Gaussian surface
Now if we consider a Gaussian surface enclosing the cavity inside the conductor as shown in the figure
we know that net electric field everywhere inside a conductor is zero
so the electric flux through this Gaussian surface would also be zero, this means no charge is enclosed by the Gaussian surface, but the cavity has a charge q , this means a charge –q must be induced on the inner metal surface because net charge enclosed by Gaussian surface must be zero (q + (-q) = 0) , but the metal surface has only been given charge Q so net charge of system must only be q + Q , i.e. a charge q is induced on outer surface of the conductor as which makes the total charge on the conductor equal to Q only Q + (-q) + q = Q
and total charge of the system as
Q + (-q) + q + q = Q + q
This arrangement is also in accordance with the law of conservation of charge
note: Only Q charge has been given on the conductor’s outer surface , the charge appearing (Q + q) on it is only due to induction due to charge inside the cavity.
(c) To shield the sensitive instrument from strong electrostatic fields in its environment. We need to enclose it inside a metal piece’s Cavity, this process is also known as electrostatic shielding.
we consider a metal Block with a cavity having no charge inside and Instrument inside it as shown in the figure
any cavity inside a metal surface the electric field is zero no matter in which environment it is placed.
So in order to save the Instrument from External Electrostatic fiels we need to keep it inside a metal Cavity.
Question 5.
A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is (/2
)
, where
is the unit vector in the outward normal direction, and σ is the surface charge density near the hole.
Answer:
Now in order to find the electric field inside the tiny hole on the surface of a charged hollow conductor, we will assume the hole to be filled up with the same conductor with same charge density i.e. Hollow conductor without any hole and will find out electric field at the point of hole on the conductor due to the whole conductor and due to the hole element and thus finding the contribution in electric field due the hole element and subtracting it with the total electric field of the conductor without any hole we will get the electric field of the rest of the conductor with hole.
Now consider a hollow spherical conductor with surface charge density C/m2 with a tiny on its surface now considering two points one just outside the surface of conductor near the hole say A and other inside the hollow cavity say B
As shown in the figure
Now finding the electric field at point A due to the whole conductor assuming hole to be filled up now the total charge on the conductor with total surface area S and surface charge density will be
q = × S
From Gauss Theorem we know, net electric flux through an Gaussian surface enclosing a charge is equal to net charge enclosed by surface divided by permittivity of free space
Mathematically:
Where E is the electric field so denotes the net Electric flux through the surface q is the net charge enclosed by the Gaussian surface and
is permittivity of free space which is a constant
Now assuming an Gaussian surface just enclosing the conductor
As shown in the figure
So we will have
Since electric field is always normal to a conductor surface so E and ds are in same direction i.e. = 0
So, cos(θ) = 1 and due to spherical symmetry magnitude of electric field will same everywhere so we have
= E × S = q/
i.e. E × S = ( × S) /
or E = /ϵ0
now since electric field is always normal to the surface of a charged conductor we have
E = (/ϵ0)
Where ń is the outward normal to the surface of conductor
Now let us assume contribution of the tiny hole to this electric field is E1 and Electric field due to rest of the conductor is E2
So, we have E = E1 + E2 (Just outside the conductor)
Now inside the hollow cavity inside the conductor at point B we know electric field is zero because of electrostatic shielding
Again assuming the electric field at that point to be contribution of the tiny hole to this electric field is E1 and Electric field due to rest of the conductor is E2 now since the hole will act as a point sized charge so field would be directed outwards i.e. in vertically downward direction, and rest of the conductor is below the point so field would be in vertically upward direction, i.e. field due to both hole and rest of conductor are opposite in direction and net field is zero inside a cavity in a conductor
So, we have,
0 = E1 - E2 (Just inside the hollow cavity of conductor)
Or E1 = E2
i.e. Electric field due to hole and rest of conductor are equal in magnitude and in same direction outside the conductor and equal in magnitude and opposite in direction in the hollow cavity.
Now using, E1 = E2 and E = E1 + E2
We have, 2E1 = E and 2E2 = E
Or, E1 = E/2 and E2 = E/2
Also we know E = (/
)
i.e. the electric field due to the hole only is
E1 = (/2
)
And electric field due to rest of surface when hole is made is also
E2 = (/2
)
i.e. the electric field in the hole of a charged hollow conductor is (/2
)
Where is a unit vector in the outward normal direction.
Question 6.
Obtain the formula for the electric field due to a long thin wire of uniform linear charge density λ without using Gauss’s law. [Hint: Use Coulomb’s law directly and evaluate the necessary integral.]
Answer:
Let AB be a long thin wire of uniform linear charge density λ.
Let us consider the electric field intensity due to AB at point P at a distance h from it as shown in the figure.
The charge on a small length dx on the line AB is q which is given as q = λdx.
So, according to Coulomb’s law, electric field at P due to this length dx is
where, ϵ0 is the vacuum permittivity of the medium
But
⇒
This electric field at P can be resolved into two components as dEcosθ and dEsinθ. When the entire length AB is considered, then the dEsinθ components add up to zero due to symmetry. Hence, there is only dEcosθ component.
So, the net electric field at P due to dx is
dE' = dE cosθ
⇒ ………………….(1)
In ΔPOC,
⇒ x = h tan θ
Differentiating both sides w.r.t. θ,
⇒ dx = h sec2θ dθ …………………….(2)
Also, h2 + x2 = h2 + h2tan2θ
⇒ h2 + x2 = h2(1+ tan2θ)
⇒ h2 + x2 = h2 sec2θ ………….(3)
(Using the trigonometric identity, 1+ tan2θ = sec2θ)
Using equations (2) and (3) in equation (1),
⇒,
The wire extends from to
since it is very long.
Integrating both sides,
⇒
⇒
⇒
⇒
This is the net electric field due to a long wire with linear charge density λ at a distance h from it.
NOTE: In the given case, it has been assumed that the length of the wire tends to infinity. In case of wires of finite lengths, the sin(θ) components cancel out only along the perpendicular bisector of the wire. At any other point, the net electric field will have both sin(θ) and cos(θ) components.
Question 7.
It is now believed that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called ‘up’ quark (denoted by u) of charge + (2/3) e, and the ‘down’ quark (denoted by d) of charge (–1/3) e, together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron.
Answer:
Let there be n up quarks.
Number of down quarks = 3-n (Since there are 3 quarks in a proton)
Charge on n up quarks = where e is the charge of a proton
Charge on 3-n down quarks =
In case of a proton:
Since the charge on a proton is e,
⇒
⇒
⇒
⇒ n = 2
So, 3-n = 3-2 = 1
Hence, there can be two up quarks ⇒, 2u and one down quark ⇒, 1d in a proton.
In case of a neutron:
Since a neutron is electrically neutral,
⇒
⇒
⇒
⇒ n = 1
So, 3-n = 3-1 = 2
Hence, there can be one up quark i.e. 1u and two down quarks i.e. 2d in a neutron.
Question 8.
(a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (⇒, where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.
(b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.
Answer:
(a) At a null point, the net electrostatic field is zero. If a small test charge is placed at the null point, it experiences no electrostatic force. But if it is displaced from the null point, it tends to move in the direction which is tangential to the field lines ⇒, towards the negative charge and away from the positive charge. So, if the test charge is displaced from the equilibrium position at the null point, it tends to move away from the equilibrium position. Hence, a null point is necessarily unstable.
(b) Let us consider the case of two charges of equal magnitude and opposite sign. The null point occurs at the midpoint of the line joining the two charges. If the test charge is moved away from this null point, it experiences a force towards the negative charge and away from the positive charge. This results in the movement of the charge away from the null point. Hence, the null point is an unstable equilibrium position.
NOTE: A test charge is a positive charge of unit magnitude. A null point or neutral point is a point where magnitude of electric field is zero. A pair of charges of equal magnitude and opposite sign is known as a dipole.
Question 9.
A particle of mass m and charge (–q) enters the region between the two charged plates initially moving along x-axis with speed vx(like particle 1 in Fig. 1.33). The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is
Compare this motion with motion of a projectile in gravitational field discussed in Section 4.10 of Class XI Textbook of Physics.
Answer:
Given,
Mass of the particle = m
Charge of the particle = -q
Velocity of the particle = vx
Length of the plate = L
Electric field between the plates = E
From Newton’s second law of motion,
Where, F = Force on the particle
m = mass of the particle
a = acceleration of the particle
⇒
⇒ (Since F = qE)
Time taken by the particle to cover the distance L is given by
(Time = Displacement/Velocity)
For the movement in vertical direction, initial velocity (u) is zero.
According to Newton’s second equation of motion,
⇒
⇒
This is the vertical displacement of the particle at the far edge of the plate.
This motion is very similar to the motion of a projectile in a gravitational field. In a gravitational field, the force acting on the particle is mg and in the given case it is qE. The trajectory followed by the object will be similar in both the cases.
NOTE: A projectile is any object thrown into space by the exertion of a force. The path followed by a projectile is known as its trajectory.
Question 10.
Suppose that the particle in Exercise in 1.33 is an electron projected with velocity vx= 2.0 × 106 m s–1. If E between the plates separated by 0.5 cm is 9.1 × 102 N/C, where will the electron strike the upper plate? (|e| = 1.6 × 10–19 C, me= 9.1 × 10–31 kg.)
Answer:
Given,
Velocity of the electron, vx = 2.0 × 106 m s–1
Separation of plates, l = 0.5cm = 0.5 × 10-2 m
Electric field between the plates, E = 9.1 × 102 N C-1
Charge on the electron, q = |e| = 1.6 × 10-19 C
Mass of the electron, me = 9.1 × 10-31 kg
The vertical deflection of the particle (s) is given by
⇒
⇒
⇒ L = √(2.5 × 10-4) m
hence, L = 1.58 × 10-2m = 1.58cm
Hence, the electron will strike the upper plate after travelling 1.58cm.