Zero electric potential related to electric field.

[bennyq]

Homework Statement

Which one of the following statements concerning electrostatic situations is false?
a) No work is required to move a charge along an equipotential surface.
b) If the electric potential with a region of space is zero volts, the electric field within that region must also be zero V m-1.
c) If a charge is moved along an equipotential surface, there is no component of the force acting along the charge’s path.
d) The electric field is always perpendicular to equipotential surfaces.
e) The electric field is zero V m-1 everywhere inside a conductor.

Homework Equations

The Attempt at a Solution

The answer given to this problem is C.

My problem with this question is part B, I also think that this is also false. My understanding is that you can have a zero electric potential and still have an electric field. For instance if I had a charge of +q and -q separated by some distance R, then at R/2 there will be zero potential but obviously there is an electric field. The analogy I think of for potential is the rate of change of potential energy over distance, like velocity can be zero but acceleration is not.

 

[NascentOxygen]

b) If the electric potential with a region of space is zero volts,

Is that meant to be "within" or what?

 

[HallsofIvy]

The electric field is given by the gradient of the potential. The potential can be 0 at a given point and have an electric field, just as a non-constant function can have gradient 0 at a point, but this problem has the potential 0 in a "region".