# When the electric field in an electrostatic charged conductor is zero, is the potential within also zero?

Let's say you have a point charge inside a conducting shell with an inner radius of 5cm and an outer radius of $7cm$. The point charge has a chard of $-4C$ and the shell a charge of $6C$. This means that the $-4C$ point charge attracts $4C$ worth of charge from the shell to the shell's inner surface. This leaves $2C$ of charge on the shell's outer surface. If you use the Gaussian-surface method at a radius of $6cm$, the Gaussian surface encloses both the $-4C$ point charge and the shell's $4C$ inner surface, so the net enclosed charge is $0C$, and therefore there is no electric field inside the shell (between the inner surface and outer surface).

But is there a potential there? My first intuition was "no", but then I was thinking that if you put a positive point charge there, the positive charge would join the other positive charges on the shell's outer surface, which makes it seem there'd have to be some potential energy being converted to kinetic energy somehow...

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The potential of a metal shell due to its own charge $q_1$ is $\frac{kq_1}{r_{shell}}$ If you add a point charge $q_2$ at the center, then the potential becomes $\frac{kq_1}{r_{shell}} + \frac{kq_2}{r_{shell}}$.
And your example has a potential (relative to infinity) of $200k/7$. – Manishearth Feb 21 '12 at 4:02