JEE MAIN - Physics (2012 - No. 6)
An electromagnetic wave in vacuum has the electric and magnetic field $$\mathop E\limits^ \to $$and $$\mathop B\limits^ \to $$, which are always perpendicular to each other. The direction of polarization is given by $$\mathop X\limits^ \to $$ and that of wave propagation by $$\mathop k\limits^ \to $$. Then
$$\mathop X\limits^ \to ||\mathop B\limits^ \to $$ and $$\mathop X\limits^ \to ||\mathop B\limits^ \to \times \mathop E\limits^ \to $$
$$\mathop X\limits^ \to ||\mathop E\limits^ \to $$ and $$\mathop k\limits^ \to ||\mathop E\limits^ \to \times \mathop B\limits^ \to $$
$$\mathop X\limits^ \to ||\mathop B\limits^ \to $$ and $$\mathop k\limits^ \to ||\mathop E\limits^ \to \times \mathop B\limits^ \to $$
$$\mathop X\limits^ \to ||\mathop E\limits^ \to $$ and $$\mathop k\limits^ \to ||\mathop B\limits^ \to \times \mathop E\limits^ \to $$
Explanation
as The $$E.M.$$ wave are transverse in nature i.e.,
$$ = {{\overrightarrow k \times \overrightarrow E } \over {\mu \omega }} = \overrightarrow H \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)$$
where $$\overrightarrow H = {{\overrightarrow B } \over \mu }$$
and $${{\overrightarrow k \times \overrightarrow H } \over {\omega \varepsilon }} = - \overrightarrow E \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)$$
$$\overrightarrow k $$ is $$ \bot \,\,\overrightarrow H $$ and $$\overrightarrow k $$ is also $$ \bot $$ to $$\overrightarrow E $$
or In other words $$\overrightarrow X ||\overrightarrow E $$ and $$\overrightarrow k ||\overrightarrow E \times \overrightarrow B $$
$$ = {{\overrightarrow k \times \overrightarrow E } \over {\mu \omega }} = \overrightarrow H \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)$$
where $$\overrightarrow H = {{\overrightarrow B } \over \mu }$$
and $${{\overrightarrow k \times \overrightarrow H } \over {\omega \varepsilon }} = - \overrightarrow E \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)$$
$$\overrightarrow k $$ is $$ \bot \,\,\overrightarrow H $$ and $$\overrightarrow k $$ is also $$ \bot $$ to $$\overrightarrow E $$
or In other words $$\overrightarrow X ||\overrightarrow E $$ and $$\overrightarrow k ||\overrightarrow E \times \overrightarrow B $$
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