A charge, Q, is located a distance, d, above a grounded conducting plane. Two st
ID: 2070823 • Letter: A
Question
A charge, Q, is located a distance, d, above a grounded conducting plane. Two students are asked to compute the amount of work that would have to be done to move this charge to infinite distance from the plane. One student claims that the answer is just the work neccessary to separate two charges that are 2d apart i.e. W=kQ^2/2d. The other student calculates the force that acts on the charge as it moves and then integrates it to obtain the work done. He gets a different answer. What is the answer and which student is right?
Explanation / Answer
The second student is right and he gets the answer W = kQ2/4d
Although the potential configuration of a charge above a grounded conducting plane is the same above the plane as if the plane were replaced by another charge equidistant beneath the plane (method of images), the energy is different.
It is different because instead of bringing two charges together and doing work on both of them, you are bringing one charge in and doing no work on the grounded plane. Thus the energy is half as much.
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