GATE EC 1996 Electromagnetics Solution Q 3

# GATE EC 1996 Electromagnetics Solution Q 3

Some unknown material has a conductivity of 106 mho/m and a permeability of $latex \;4\pi\times10^{-7}H/m$.
The skin depth for the material at 1 GHz is

(a) 15.9 µm

(b) 20.9 µm

(c) 25.9 µm

(d) 30.9 µm

Ans : a)

Explanation

\frac\sigma{\omega\in}=18\times10^6

As it is very much higher than 1; the material is a good conductor. So the skin depth is given by-

\delta=\frac1{\sqrt{\pi f\mu\sigma}}=\frac1{\sqrt{\pi\times10^9\times4\pi\times10^{-7}\times10^6}} \delta=\frac{10^{-4}}{2\pi} \delta=15.9\mu m

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