Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 62

The vector magnetic potential A and scalar electric potential V defined in Section 7- 4 are not unique in that it is possible to add to A the gradient of a scalar , , with no change in B from Eq. (7- 55).
A' =A +
In order not to change E in using Eq. (7-57), V must be modified to V '.
a) Find the relation between V ' and V.
b) Discuss the condition that must satisfy so that the new potentials A' and V ' remain governed by the uncoupled wave equations (7 - 63) and (7- 65).