A plane electromagnetic wave, has frequency of 2.0 × 1010 Hz and its… | JEE Main 2020 (2 Sep, Shift 1)

Q26JEE Main 2020 · 2 SEP · SHIFT 1Medium

Energy Density & Intensity

A plane electromagnetic wave, has

frequency of 2.0 $\times$ 1010 Hz and its energy density is 1.02 $\times$ 10–8 J/m3 in vacuum. The amplitude of the magnetic field of the wave is close to

( $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9} \frac{Nm^2}{C^2}$ and speed of light

= 3 $\times$ 108 ms–1)

Show answer and solution

Answer: (c)

Average energy density $u = \dfrac{B_0^2}{2\mu_0} \Rightarrow B_0 = \sqrt{2\mu_0 u}$
$\mu_0 = \dfrac{1}{\varepsilon_0 c^2} = \dfrac{4\pi \times 9 \times 10^{9}}{9 \times 10^{16}} = 4\pi \times 10^{-7}$
$B_0 = \sqrt{2 \times 4\pi \times 10^{-7} \times 1.02 \times 10^{-8}} = \sqrt{2.56 \times 10^{-14}} = 1.6 \times 10^{-7}$ T
So the answer is (c) 160 nT.

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