GATE EC 1999 Electromagnetics Solution Q 3

GATE EC 1999 Electromagnetics Solution Q 3

A plane wave propagation through a medium \left[\in_r=8,\;\;\mu_r=2,\;\;and\;\;\sigma=0\right]

has its electric field given by

\overrightarrow E=0.5\;\sin\left(10^8t-\beta z\right)V/m.

The wave impedance, in ohms is

(a) 377

(b) 198.5\angle180^0

(c) 182.9\angle14^0

(d) [/latex]latex 188.5[/latex]

Ans : d)

Explanation

\eta=\sqrt{\frac{j\omega\mu}{\sigma+j\omega\in}}\;\;\;\;\sigma=0 \eta=\sqrt{\frac\mu\in}\angle0^0 =\sqrt{\frac{\mu_0\mu_r}{\in_0\in_r}}=\sqrt{\frac{\mu_0}{\in_0}}\sqrt{\frac{\mu_r}{\in_r}} =377\sqrt{\frac28}=\frac{377}2=188.5

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