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I know that if a charge q is place inside a conducting shell, a charge -q is induced on the inner surface of the shell and then we take a spherical gaussian surface with radius equal to that of the shell and say that since the net charge enclosed is zero (+q-q) the electric field is zero. But what if we take a gaussian surface with a radius smaller than that of the shell? The charge enclosed in this case would be equal to q giving a non zero electric field Where am I going wrong and how exactly do spherical capacitors have a potential difference?

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The core charge is +q. The inner surface charge is -q. There is a field between the outer surface of the core charge and the inner surface of the spherical conductor. The charge seperation on the conductor would, in and of itself, produce an electric field, but what it produces is the exact opposite of the field due to the core charge, and so the net field in the conductor is zero. This is the only way that the charges in the conductor can settle down, of course - any field would result in conduction. That's the definition of a (perfect) conductor.

So a surface between the core charge and the inner spherical surface would register the charge of the core. Inside the material of the spherical shell, the net zero charge, and outside the spherical shell, the net positive, from +q-q+q.

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