A plane electromagnetic wave travels in free space along the x-direction.

Question:

A plane electromagnetic wave travels in free space along the $x$-direction. The electric field component of the wave at a particular point of space and time is $\mathrm{E}=6 \mathrm{Vm}^{-1}$ along $y$-direction. Its corresponding magnetic field component, B would be:

1. (1) $2 \times 10^{-8} \mathrm{~T}$ along $z$-direction

2. (2) $6 \times 10^{-8} \mathrm{~T}$ along $x$-direction

3. (3) $6 \times 10^{-8} \mathrm{~T}$ along $z$-direction

4. (4) $2 \times 10^{-8} \mathrm{~T}$ along $y$-direction

Correct Option: 1

Solution:

(1) The relation between amplitudes of electric and magnetic field in free space is given by

$B_{0}=\frac{E_{0}}{c}=\frac{6}{3 \times 10^{8}}=2 \times 10^{-8} T$

Propagation direction $=\hat{E} \times \hat{B}$

$\hat{i}=\hat{j} \times \hat{B}$

$\Rightarrow \hat{B}=\hat{k}$

$\therefore$ The magnetic field component will be along $z$ direction.