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### A plane electromagnetic wave of frequency 500 MHz ....

A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time, $\vec B = 8.0 \times 10^{-8} \hat z T$. The value of electric field at this point is:

(speed of light = $3 \times 10^8 ms^{-1}$)

$\hat x , \hat y , \hat z$ are unit vectors along x, y and z directions.

(A) $24 \hat x V/m$
(B) $2.6 \hat x V/m$
(C) $-24 \hat x V/m$
(D) $-2.6 \hat y V/m$

Solution

We have, $\frac{{\vec E \times \vec B}}{{|\vec E \times \vec B|}} = \hat y$ or $\hat E \times \hat B = \hat y$

$\therefore \hat E \times \hat z = \hat y$

$\therefore \hat E = -\hat x$

Also, $c=\frac {E}{B}$ or E = c.B

$\therefore E = 3 \times 10^8 \times 8.0 \times 10^ {-8} = 24 V/m$

So, $\vec E = E (-\hat x ) = -24 \hat x V/m$

### 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 = ${}^{12}{C_6} = 924$