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 :
Solution
Given, $$\overrightarrow E = {E_0}\left( {\widehat x + \widehat y} \right)\sin \left( {kz - \omega t} \right)$$
<br><br>We know, direction of propagation, $\overrightarrow C = \overrightarrow E \times \overrightarrow B$
<br><br>Here direction of propagation = $\widehat k$
<br><br>$\therefore$ $\widehat k$ = $\overrightarrow E \times \overrightarrow B$
<br><br>and $\widehat E = {{\widehat i + \widehat j} \over {\sqrt 2 }}$
<br><br>$\therefore$ $$\widehat k = \left( {{{\widehat i + \widehat j} \over {\sqrt 2 }}} \right) \times \overrightarrow B $$
<br><br> $\Rightarrow$ $\widehat B = {{ - \widehat i + \widehat j} \over {\sqrt 2 }}$
<br><br>$\therefore$ $\widehat B$ = $${{{E_0}} \over c}\left( { - \widehat x + \widehat y} \right)\sin \left( {kz - \omega t} \right)$$
About this question
Subject: Physics · Chapter: Electromagnetic Waves · Topic: Maxwell's Equations
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