Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 61

The electric and magnetic fields of a general TEM wave traveling in the + z-direction along a transmission line may have both x - and y -components, and both components may be functions of the transverse dimensions.
(a) Find the relations among E x (x, y), E y (x, y), H x (x, y), and H y (x, y).
(b) Verify that all the four field components in part (a) satisfy the two-dimensional Laplace's equation for static fields.