GATE EC 2006 Electromagnetics Solution Q 2

GATE EC 2006 Electromagnetics Solution Q 2

When a plane wave travelling in free-space is incident normally on a medium having  \in_r=4.0, the fraction of power transmitted into the medium is given by

(a) 8/9

(b) 1/2

(c) 1/3

(d) 5/6

Ans : a)

Explanation

\Gamma=\frac{\eta_2-\eta_1}{\eta_2+\eta_1}=\frac{\sqrt{\displaystyle\frac{\mu_0}{\in_0\in_r}}-\sqrt{\displaystyle\frac{\mu_0}{\in_0}}}{\sqrt{\displaystyle\frac{\mu_0}{\in_0\in_r}}+\sqrt{\displaystyle\frac{\mu_0}{\in_0}}} \Gamma=\frac{{\displaystyle\frac12}-1}{{\displaystyle\frac12}+1}=\frac{-1}3 T=1-\Gamma^2=1-\frac19=\frac89 \therefore P_t=T.P_i \frac{P_t}{P_i}=\frac89

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