GATE EC 1989 Electromagnetics Solution Q 2

GATE EC 1989 Electromagnetics Solution Q 2

The skin depth of copper at a frequency of 3 GHz, is 1 micron (10-6 meter). At 12 GHz, For a non-magnetic conductor whose conductivity is 1/9 times that of copper, the skin depth would be

(a) \sqrt{9\times4}microns

(b) \sqrt{9/4}microns

(c) \sqrt{4/9}microns

(d) 1/\sqrt{9\times4}microns

Ans : b)

Explanation

For good conductors,

Skin\;depth=\delta=\frac1{\sqrt{\pi\;f\;\mu\;\sigma}} \delta\propto\frac1{\sqrt{f\sigma}} \frac{\delta_2}{\delta_1}=\sqrt{\frac{f_1\sigma_1}{f_2\sigma_2}} \frac{\delta_2}1=\sqrt{\frac3{12}\times\frac91}=\sqrt{\frac94} \delta_2=\sqrt{\frac94}microns

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