Answer
Zero. No.
Work Step by Step
Equation 23.18 calculates the potential difference between 2 points by using the electric field along a path that joins the 2 points. If the electric field is zero everywhere along the path, the potential difference is zero.
The potential difference is zero, but that only tells us that the net work done by the electric field along any path is zero. The electric field doesn’t have to be zero at every point along every path.
For example, a nonzero electric field could do positive work on a test charge in some portion of the path, and negative work along some other portion, as long as the total work equals zero.
