Question 142: EM waves

Question

The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by an expression $\overrightarrow E \left( {x,y} \right) = 10\widehat j\cos \left[ {\left( {6x + 8z} \right)} \right].$ The magnetic field $\overrightarrow B $(x,z, t) is given by $-$ (c  is the velocity of light)

Accepted Answer

$\overrightarrow E  = 10\widehat j\cos \left[ {\left( {6\widehat i + 8\widehat k} ight).\left( {x\widehat i + z\widehat k} ight)} ight]$
$ = 10\widehat j\,\cos \left[ {\overrightarrow K .\overrightarrow r } ight]$
$ 	herefore $   $\overrightarrow K  = 6\widehat i + 8\widehat k;$ direction of waves travel.
i.e.,  direction  of  'c'.
$ 	herefore $   Direction of $\widehat B$ will be along
$\widehat C 	imes \widehat E = {{ - 4\widehat i + 3\widehat k} \over 5}$
Mag.  of  $\overrightarrow B $  will  be  along
$\widehat C 	imes \widehat E = {{ - 4\widehat i + 3\widehat k} \over 5}$
Mag.  of  $\overrightarrow B  = {E \over C} = {{10} \over C}$
$ 	herefore $   $\overrightarrow B  = {{10} \over C}\left( {{{ - 4\widehat i + 3\widehat k} \over 5}} ight) = {{\left( { - 8\widehat i + 6\widehat k} ight)} \over C}$

Answer

${1 \over c}\left( {6\hat k + 8\widehat i} \right)\cos \left[ {\left( {6x + 8z - 10ct} \right)} \right]$

Answer

${1 \over c}\left( {6\widehat k - 8\widehat i} \right)\cos \left[ {\left( {6x + 8z - 10ct} \right)} \right]$

Answer

${1 \over c}\left( {6\hat k + 8\widehat i} \right)\cos \left[ {\left( {6x - 8z + 10ct} \right)} \right]$

Answer

${1 \over c}\left( {6\hat k - 8\widehat i} \right)\cos \left[ {\left( {6x - 8z + 10ct} \right)} \right]$

EM waves

Choose the correct answer: