Question 140: 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

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