Skip to main content

Visit this link for 1 : 1 LIVE Classes.

For a plane electromagnetic wave propagating in x-direction ....

For a plane electromagnetic wave propagating in x-direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively?

(1) $\hat j + \hat k, \hat j + \hat k $
(2) $-\hat j + \hat k, -\hat j - \hat k $
(3) $\hat j + \hat k, -\hat j - \hat k $
(4) $-\hat j + \hat k,-\hat j+\hat k $

Solution

The direction of propagation $\hat i$ is the same as the direction of $\vec E \times \vec B$.

Or, $\hat i = \frac {\vec E \times \vec B}{| \vec E \times \vec B |}$

Options (1) & (4)  have identical vectors making their cross product 0.

Option (3) has vectors in opposite directions making their cross product 0 again.

For Option (2), $( - \hat j + \hat k) \times ( - \hat j - \hat k) = \hat j \times \hat k - \hat k \times \hat j = 2\hat i$

$\therefore \frac{{\vec E \times \vec B}}{{|\vec E \times \vec B|}} = \frac{{2\hat i}}{2} = \hat i$

Answer: (2)

Popular posts from this blog

${\log _{\sqrt 5 }}\left[ {3 + \cos \left( {\frac{{3\pi }}{4} + x} \right) + \cos \left( {\frac{\pi }{4} + x} \right) + \cos \left( {\frac{\pi }{4} - x} \right) - \cos \left( {\frac{{3\pi }}{4} - x} \right)} \right]$

The range of the function $f(x) = {\log _{\sqrt 5 }}\left[ {3 + \cos \left( {\frac{{3\pi }}{4} + x} \right) + \cos \left( {\frac{\pi }{4} + x} \right) + \cos \left( {\frac{\pi }{4} - x} \right) - \cos \left( {\frac{{3\pi }}{4} - x} \right)} \right]$ is: (A) $[ - 2,2]$ (B) $\left[ {\frac{1}{{\sqrt 5 }},\sqrt 5 } \right]$ (C) $(0,\sqrt 5 )$ (D) $[ 0,2]$ Solution We have, $f(x) = {\log _{\sqrt 5 }}\left( {3 - 2\sin \frac{{3\pi }}{4}\sin x + 2\cos \frac{\pi }{4}\cos x} \right)$ $ \Rightarrow f(x) = {\log _{\sqrt 5 }}\left[ {3 + \sqrt 2 (\cos x - \sin x)} \right]$ Now, $ - \sqrt 2  \le \cos x - \sin x \le \sqrt 2 $ $\therefore - 2 \le \sqrt 2 (\cos x - \sin x) \le 2$ $\therefore 1 \le 3 + \sqrt 2 (\cos x - \sin x) \le 5$ $\therefore{\log _{\sqrt 5 }}1 \le {\log _{\sqrt 5 }}[3 + \sqrt 2 (\cos x - \sin x)] \le {\log _{\sqrt 5 }}5$ $ \Rightarrow 0 \le f(x) \le 2$ Answer: (D)