Question

A plane electromagnetic wave, has frequency of $2.0\times {10}^{10}\text{Hz}$ and its energy density is $1.02\times {10}^{–8}{\text{Jm}}^{-3}$ in vacuum.
The amplitude of the magnetic field of the wave is close to:
$(\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9\frac{{\text{Nm}}^2}{C^2})\text{and speed of light}c=3\times {10}^8{\text{ms}}^{-1}$

• A. $150\text{nT}$
• B. $160\text{nT}$
• C. $180\text{nT}$
• D. $190\text{nT}$

Answer 1

The correct option is B $160\text{nT}$

The energy density of the electromagnetic wave in terms of magnetic field is given by,

$U=\frac{1}{2}\frac{B_0^2}{{\mu }_0}$

$\Rightarrow B_0=\sqrt{2\times {\mu }_0\times U}$

From electromagnetic theory,
${\mu }_0=\frac{1}{c^2{\epsilon }_0}$

$=\frac{4\pi \times 9\times {10}^9}{(3\times {10}^8{)}^2}=4\pi \times {10}^{-7}$

$\therefore B_0=\sqrt{2\times 4\pi \times {10}^{-7}\times 1.02\times {10}^{-8}}$

$\Rightarrow B_0=160\times {10}^{-9}\text{T}$

$\Rightarrow B_0=160\text{nT}$.

Hence, option $\left(B\right)$ is correct.