Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 15

Given a vector function F = a x ( x + c 1 z) + a y ( c 2 x -3z) + a z ( x + c 3 y + c 4 z ).
a) Determine the constants c 1 , c 2 , and c 3 if F is irrotational.
b) Determine the constant c 4 if F is also solenoidal.
c) Determine the scalar potential function V whose negative gradient equals F.