## Physics: Principles with Applications (7th Edition)

Assume that the test charge begins and ends at rest. The external work done in moving a test charge q from one point to the other is $q \Delta V$, so if the change in potential is zero then the work done by the electric field is zero, the work done by the external force is also zero, and the net work is zero. If the test charge is moved along an equipotential line, then no work is done along any segment of the path. However, it is possible that, for some portion of the path, positive work is done by the external force but enough negative work is done to cancel it along other portions of the path. Draw a parallel between electric potential energy and gravitational PE. If you slide frictionlessly on the floor, you can move between 2 points of equal potential with no force. However, you might also choose to go up a flight of stairs (exerting a force and doing positive work), then return to your original floor (exerting a force and doing negative work).