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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

### Sum of the coefficients in the expansion of $(x+y)^n$ ....
If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$