JEE MAIN - Physics (2020 - 2nd September Evening Slot - No. 20)
In a plane electromagnetic wave, the directions
of electric field and magnetic field are
represented by $$\widehat k$$ and $$2\widehat i - 2\widehat j$$, respectively.
What is the unit vector along direction of
propagation of the wave?
$${1 \over {\sqrt 5 }}\left( {\widehat i + 2\widehat j} \right)$$
$${1 \over {\sqrt 5 }}\left( {2\widehat i + \widehat j} \right)$$
$${1 \over {\sqrt 2 }}\left( {\widehat i + \widehat j} \right)$$
$${1 \over {\sqrt 2 }}\left( {\widehat j + \widehat k} \right)$$
Explanation
$$\overrightarrow E \times \overrightarrow B = \widehat k \times \left( {2\widehat i - 2\widehat j} \right)$$
= $$2\widehat k \times \widehat i - 2\widehat k \times \widehat j$$
= $$\left( {2\widehat j + 2\widehat i} \right)$$
Unit vector along $$\overrightarrow E \times \overrightarrow B $$ = $${{\left( {2\widehat j + 2\widehat i} \right)} \over {2\sqrt 2 }}$$
= $${1 \over {\sqrt 2 }}\left( {\widehat i + \widehat j} \right)$$
= $$2\widehat k \times \widehat i - 2\widehat k \times \widehat j$$
= $$\left( {2\widehat j + 2\widehat i} \right)$$
Unit vector along $$\overrightarrow E \times \overrightarrow B $$ = $${{\left( {2\widehat j + 2\widehat i} \right)} \over {2\sqrt 2 }}$$
= $${1 \over {\sqrt 2 }}\left( {\widehat i + \widehat j} \right)$$
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