Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 7

The space between two parallel conducting plates each having an area S is filled with an inhomogeneous ohmic medium whose conductivity varies linearly from 1 at one plate ( y = 0) to 2 at the other plate ( y = d ). A d-c voltage V 0 is applied across the plates as in Fig. Determine
a) the total resistance between the plates,
b) the surface charge densities on the plates,
c) the volume charge density and the total amount of charge between the plates.
Figure: Inhomogeneous ohmic medium with conductivity ( y )