In a plane electromagnetic wave, the electric field oscillates with amplitude  20Vm−1, then the energy density of magnetic field is (in J/m3 )

# In a plane electromagnetic wave, the electric field oscillates with amplitude  $20V{m}^{-1}$, then the energy density of magnetic field is (in $J/{m}^{3}$ )

1. A

$1×{10}^{-10}$

2. B

$5×{10}^{-10}$

3. C

$8.85×{10}^{-5}$

4. D

$8.85×{10}^{-10}$

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### Solution:

Average energy density of magnetic field  $=\frac{{B}_{rms}^{2}}{2{\mu }_{0}}=\frac{{\left({B}_{0}/\sqrt{2}\right)}^{2}}{2{\mu }_{0}}=\frac{1}{4}\frac{{B}_{0}^{2}}{{\mu }_{0}}$
But  ${B}_{0}=\frac{{E}_{0}}{C}$
Average energy density of electric field=  $\frac{1}{4}×\frac{{E}_{0}^{2}}{{C}^{2}{\mu }_{0}}$
But
= $8.85×{10}^{-10}J/{m}^{3}$

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