Consider you have a point charge. For symmetry I can think that there is a sphere of a certain radii around it. It is an equipotential surface. I can see that is due to all the points on the sphere's surface is equidistant from the point charge. As we have the formula of potential as v= kq/r. But why does all the points inside the sphere have same potential. Would you please write me how to figure out which is the reason?
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asked Mar 14, 2018 at 4:07
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$\begingroup$ What are your thoughts on this? How much could you proceed? $\endgroup$– Yuzuriha InoriCommented Mar 14, 2018 at 4:25
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1 Answer
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This is only true for the points inside a conducting sphere, for example a sphere made of metal. To see why the inside of a conducting sphere is all at the same potential, first assume that it isn't. Then because there's a difference in potential, there must be an electric field in the sphere (from Gauss' law). This electric field exerts a force on the charges in the conductor, causing them to move. This contradicts the assumption that our situation is electrostatic, so our assumption that the potential varies inside the sphere must be wrong. So we must have that the potential is constant, i.e. the inside of the sphere is an equipotential.
Also note that this isn't the case for an insulating sphere, which might have an inhomogeneous charge distribution scattered throughout it.
