# Electrostatic potential within a conductor

It states that electric field inside a hollow conductor is zero due to reasons of rearrangement of charges on the surface of a conductor whenever there is an excess charge placed on it and the hollow region (say air) encloses no charge.

How can the work done to move a test charge placed in the interior of the conductor be zero? This is what my textbook says. After all, Work is simply force times displacement and since the test charge would have a mass and there is no field in the conductor or any other force to oppose the motion of a charge should it be set in motion, then the only force acting on the charge is the force you apply to push it through a distance. Shouldn't there be an impulse acting on the object? And hence a force?

Or am I just over thinking it and my textbook simply means there is no work done due to an electric field?

• i hardly understood your question – Lelouch Jul 31 '16 at 11:01
• You might be over thinking it, you still need to do mechanical, as opposed to electrical, work in moving the test charge around. I hope I understand your point though. – user108787 Jul 31 '16 at 11:27
• And in addition to what count_to_10 said, the mechanical work will be zero. If you wish (it is not necessary) to think the test charge as a dynamical object, you will accelerate it and then deaccelerate it and the total mechanical work done will be zero too. – Mikael Kuisma Jul 31 '16 at 11:30

If the electric field $\vec E$ is zero that means that the potential $V$ is equal to a constant and that constant is not necessarily zero.
So you bring a charge $q$ from infinity $(V=0)$ up to the sphere with work being done $(=qV)$ and then you can move that charge anywhere within the conductor and do no work in doing so.