Since the equipotential is calculated by $V = q\cdot \frac{k}{r}$ I suppose that the charge is the same at any point on an equipotential surface but I'm not sure.
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$\begingroup$ This makes no sense. What system are you considering? Is there a single point charge, or are there many charges? Equipotential surface is an imaginary surface in space that has the same potential everywhere, this is defined even if there is only single point charge. $\endgroup$– Ján LalinskýCommented Sep 2, 2023 at 10:41
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$\begingroup$ This is the full question in my textbook but I suppose they are considering a single point charge. Does that mean that the charges strength IS the same on all points on one of its equipotential surfaces? $\endgroup$– lonelyhikerCommented Sep 2, 2023 at 10:44
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1$\begingroup$ What is "charge strength"? $\endgroup$– Ján LalinskýCommented Sep 2, 2023 at 10:45
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$\begingroup$ Maybe the charge strength is just the charge amount? I might have copied the question wrong, it might be strength of electric field which would then be a false statement. Sorry for the confusion $\endgroup$– lonelyhikerCommented Sep 2, 2023 at 10:50
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$\begingroup$ Well, electric field strength need not be the same on equipotential surface. Only in special cases, such as field due to spherically symmetric charge distribution, has electric field that has the same magnitude on the equipotential surface. $\endgroup$– Ján LalinskýCommented Sep 2, 2023 at 10:51
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1 Answer
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No. The charge density can easily vary on an equipotential surface.
Consider, for example, a conductive sphere placed in a uniform static external E field. The sphere will gain negative charge density on one side, and positive charge density on the other. But since the E field is zero inside the sphere, the surface is equipotential.
