# Solved Problems-7

Problem-7

(a) A plane wave is incident on a good conductor at
(b) Due to this current density, find the magnitude of the total current through a strip of the conductor of infinite depth along

*z*= 0. Find the current density in the conductor.*z*and width*w*along*y*.Solution

(a) we get,

Using Ohmâ€™s law,

*=***J***Ïƒ*, we get in time-harmonic form,**E**Since
Solving,
Since the current is finite as z â†’ âˆž, K
Also, for a good conductor,
where
This current density can be written as,
where

(b) Total current is given as,
The magnitude of the current is

**has only the***E**x*-component which is a function of*z*only the above equation reduces to an ordinary differential equation given as,_{2}= 0*Î´*is the skin depth.*J*(0) is the current density at*z*= 0, i.e., on the surface of the conductor.(b) Total current is given as,