question_answer

               An electromagnetic wave going through vacuum is decribed by \[\varepsilon ={{\varepsilon }_{0}}\,\sin \,(KX-\cot \theta );\] and \[B={{B}_{0}}\]\[B={{B}_{0}}\sin \]\[B={{B}_{0}}\sin \,(KX-\omega t)\]. Which of the following equations is true? 

A)  \[{{\varepsilon }_{0}}K={{B}_{0}}\omega \]     

B)  \[{{\varepsilon }_{0}}\omega ={{B}_{0}}K\]

C)  \[{{\varepsilon }_{0}}K={{B}_{0}}\omega K\]       

D)  none of these       

Correct Answer: A

Solution :

    Here,  \[\frac{{{\varepsilon }_{0}}}{BO}=C\]     and    \[=\frac{\varepsilon }{K}=C\] \[\frac{{{\varepsilon }_{0}}}{{{B}_{0}}}=\frac{\omega }{K}\]         \[\Rightarrow \]   \[{{\varepsilon }_{0}}K={{B}_{0}}\omega \]