Question 117: EM waves

Question

The electric field of a plane electromagnetic wave is given by
$$\overrightarrow E  = {E_0}\left( {\widehat x + \widehat y} \right)\sin \left( {kz - \omega t} \right)$$
Its magnetic field will be given by :

Accepted Answer

Given, $$\overrightarrow E  = {E_0}\left( {\widehat x + \widehat y} ight)\sin \left( {kz - \omega t} ight)$$
We know, direction of propagation, $$\overrightarrow C  = \overrightarrow E  	imes \overrightarrow B $$
Here direction of propagation = $$\widehat k$$
$$ 	herefore $$ $$\widehat k$$ = $$\overrightarrow E  	imes \overrightarrow B $$
and $$\widehat E = {{\widehat i + \widehat j} \over {\sqrt 2 }}$$
$$ 	herefore $$ $$\widehat k = \left( {{{\widehat i + \widehat j} \over {\sqrt 2 }}} ight) 	imes \overrightarrow B $$
$$ \Rightarrow $$ $$\widehat B = {{ - \widehat i + \widehat j} \over {\sqrt 2 }}$$
$$ 	herefore $$ $$\widehat B$$ = $${{{E_0}} \over c}\left( { - \widehat x + \widehat y} ight)\sin \left( {kz - \omega t} ight)$$

Answer

$${{{E_0}} \over c}\left( {\widehat x + \widehat y} \right)\sin \left( {kz - \omega t} \right)$$

Answer

$${{{E_0}} \over c}\left( {\widehat x - \widehat y} \right)\sin \left( {kz - \omega t} \right)$$

Answer

$${{{E_0}} \over c}\left( {\widehat x - \widehat y} \right)\cos \left( {kz - \omega t} \right)$$

Answer

$${{{E_0}} \over c}\left( { - \widehat x + \widehat y} \right)\sin \left( {kz - \omega t} \right)$$

EM waves

The electric field of a plane electromagnetic wave is given by $\overrightarrow E = {E_0}\left( {\widehat x + \widehat y} \right)\sin \left( {kz - \omega t} \right)$ Its magnetic field will be given by :

Choose the correct answer: