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Question

The amount of work done in moving a point charge of 10C from the point A to B, inside a spherical shell as shown is .



A
10 J
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B
20 J
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C
15 J
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D
0 J
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Solution

The correct option is D 0 J
The electric field inside a uniformly charged spherical shell is zero and the electric potential is constant.
Work done on a charge is given by q (VfVi) (where q is the charge,Vf is the potential of final point and Vi is the potential of the initial point).Here,
VfVi=0 and thus work done in moving the charge from A to B is zero
But why is the potential constant?
So if you (as an external agent) bring a unit positive charge from infinity to its surface, you’ll have to do work but once you take the charge inside, there is no electric field, so no force and hence no work is done by you. If we think about this a li’l more, we’ll realize that on moving a test charge particle inside a uniformly charged spherical shell there is no change in potential and hence the potential is constant.

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