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Electric field of a plane electromagnetic wave ....

Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by $E = 20\cos (2 \times {10^{10}}t - 200x)V/m$. The dielectric constant of the medium is equal to: (Take $\mu _r = 1 $)

(A) $\frac {1}{3}$
(B) 3
(C) 2
(D) 9

Solution

We have, $E = 20\cos \left[ {200\left( {\frac{{2 \times {{10}^{10}}}}{{200}}t - x} \right)} \right]V/m$

So, $v = \frac{{2 \times {{10}^{10}}}}{{200}} = 1 \times {10^8}m/s$

$\mu  = \sqrt {{\mu _r}{\epsilon_r}}  = \frac{c}{v} = \frac{{3 \times {{10}^8}}}{{1 \times {{10}^8}}} = 3$

$ \Rightarrow \sqrt {1 \times {\epsilon_r}}  = 3$

$ \Rightarrow {\epsilon_r} = 9$ = Dielectric Constant

Answer: (D)