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Solved Problems-7

(a) A plane wave Description: 40449.png 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.
(a) we get,
Description: 40442.png
Using Ohm’s law, J = σE, we get in time-harmonic form,
Description: 40435.png
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,
Description: 40426.png
Description: 40416.png
Since the current is finite as z → , K2 = 0
Description: 40408.png
Also, for a good conductor, Description: 40397.png
where δ is the skin depth.
Description: 40388.png
This current density can be written as,
Description: 40380.png
where J(0) is the current density at z = 0, i.e., on the surface of the conductor.

(b) Total current is given as,
Description: 40373.png
The magnitude of the current is
Description: 40365.png

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