# A plane electromagnetic wave, has frequency

Question:

A plane electromagnetic wave, has frequency of $2.0 \times 10^{10}$

$\mathrm{Hz}$ and its energy density is $1.02 \times 10^{-8} \mathrm{~J} / \mathrm{m}^{3}$ in vacuum.

The amplitude of the magnetic field of the wave is close to

$\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \frac{\mathrm{Nm}^{2}}{C^{2}}\right.$ and speed of light $\left.=3 \times 10^{8} \mathrm{~ms}^{-1}\right):$

1. (1) $150 \mathrm{nT}$

2. (2) $160 \mathrm{nT}$

3. (3) $180 \mathrm{nT}$

4. (4) $190 \mathrm{nT}$

Correct Option: , 2

Solution:

(2) Energy density $=\frac{1}{2} \frac{B^{2}}{\mu_{0}}$

$\Rightarrow B=\sqrt{2 \times \mu_{0} \times \text { Energy density }}$

$\mu_{0}=\frac{1}{C^{2} \varepsilon_{0}}=4 \pi \times 10^{-7}$

\begin{aligned} \therefore B &=\sqrt{2 \times 4 \pi \times 10^{-7} \times 1.02 \times 10^{-8}}=160 \times 10^{-9} \\ &=160 \mathrm{nT} \end{aligned}