Which statement concerning the electric potential of a solid object made out of a perfectly conducting medium is most correct?
Answer:
It is the electric field which is zero anywhere in a perfect conductor. The electric potential does not have to be zero but it does have to be single-valued. The two facts are reliable with each other. If the electric potential which is the electric potential energy per charge has the same value everywhere in as well as on the conductor then the change in potential energy of a test charge moved from one point in/on the conductor to another point in/on the conductor has to be zero. Since the work prepared on the particle by the electric field is equal to the negative of the change in potential energy of the test charge the work done is zero. By definition the work complete on the test charge is as well the force along the path times the length of the path. For this to be zero intended for any path within the conductor the electric force on the particle must always be zero. However the force is the charge of the particle times the electric field and we stipulated that the particle had some charge so the electric field has to be zero everywhere in the conductor. This demonstrates that if the electric potential has one and the same value everywhere in/on a perfect conductor then the electric field is zero everywhere in the conductor. The converse is true also.