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I have a doubt about the electric potential of a body. Well, I know that given a continuous distribution of charge we can find the potential at a point $a$ using the following relation:

$$V(x,y,z)=\frac{1}{4\pi\epsilon_0}\iiint_{S} \rho(a') \frac{1}{|a-a'|}dV'$$

However, this gives a function that at each point tells me the electrostatic potential energy divided by charge. The difference of potential between two points can be found then calculating this function at those points and subtracting.

My problem is that I've found exercises that asked something like: "find the difference of potential between two concentric spheres with uniform charge density and radii $a$ and $b$". However, what does it means calculate the difference of potential between two spheres? How do we deal with problems like this? And last but not least, what it means the potential of a sphere? The potential of a charge as the difference of potential between infinity and the place of the charge I understand, but what should be the potential of a whole sphere?

Thanks in advance for the help.

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@DouglasB.Staple that should probably be an answer ;-) – David Z Apr 19 '13 at 1:46
@David Thanks! Done. – Douglas B. Staple Apr 19 '13 at 1:47

In a conductor at equilibrium the electric potential is equal everywhere, for, if it were not, then the electrons would experience a force proportional to the gradient of the potential, causing them to redistribute themselves until the potential became homogeneous.

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