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
( ${1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9}{{N{m^2}} \over {{C^2}}}$ and speed of light
=
3 $\times$ 108 ms–1)
Solution
Energy density, ${{dU} \over {dV}} = {{B_0^2} \over {2{\mu _0}}}$
<br><br>$\Rightarrow$ 1.02 $\times$ 10<sup>–8</sup> = ${{B_0^2} \over {2{\mu _0}}}$
<br><br>Also, c = ${1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}$
<br><br>$\Rightarrow$ ${\mu _0} = {1 \over {{c^2}{\varepsilon _0}}}$
<br><br>$\therefore$ ${B_0^2}$ = 1.02 $\times$ 10<sup>–8</sup> $\times$ 2 $\times$ ${1 \over {{c^2}{\varepsilon _0}}}$
<br><br>= 1.02 $\times$ 10<sup>–8</sup> $\times$ 2 $\times$ ${{4\pi \times 9 \times {{10}^9}} \over {9 \times {{10}^{16}}}}$
<br><br>$\Rightarrow$ B<sub>0</sub> = 16 $\times$ 10<sup>-8</sup> T = 160 nT
About this question
Subject: Physics · Chapter: Electromagnetic Waves · Topic: Properties of EM Waves
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