# Solved Problems-7

Problem-7
(a) A plane wave  is incident on a good conductor at z = 0. Find the current density in the conductor.

(b) Due to this current density, find the magnitude of the total current through a strip of the conductor of infinite depth along z and width w along y.
Solution
(a) we get,

Using Ohmâ€™s law, J = ÏƒE, we get in time-harmonic form,

Since E has only the x-component which is a function of z only the above equation reduces to an ordinary differential equation given as,

Solving,

Since the current is finite as z â†’ âˆž, K2 = 0

Also, for a good conductor,

where Î´ is the skin depth.

This current density can be written as,

where J(0) is the current density at z = 0, i.e., on the surface of the conductor.

(b) Total current is given as,

The magnitude of the current is