question_answer

The electric field of a plane electromagnetic wave is given by \[\vec{E}={{E}_{0}}\hat{i}\cos (kz)cos(\omega t)\]

The corresponding magnetic field \[\vec{B}\]is then given by:      [JEE Main 10-4-2019 Morning]

A) \[\vec{B}=\frac{{{E}_{0}}}{C}\hat{j}\sin (kz)cos(\omega t)\]

B) \[\vec{B}=\frac{{{E}_{0}}}{C}\hat{j}\sin (kz)sin(\omega t)\]

C) \[\vec{B}=\frac{{{E}_{0}}}{C}\hat{k}\sin (kz)cos(\omega t)\]

D) \[\vec{B}=\frac{{{E}_{0}}}{C}\hat{j}\sin (kz)sin(\omega t)\]

Correct Answer: B

Solution :

[b]

Given that wave is propagating along positive z-axis and along positive x-axis. Hence along y-axis.

From Maxwell equation

i.e.and