Electric field of a plane electromagnetic wave varies with time of amplitude 2, Vm^{-1} p

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8.Electromagnetic waves

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The electric field of a plane electromagnetic wave varies with time of amplitude $2\, Vm^{-1}$ propagating along $z$ -axis. The average energy density of the magnetic field (in $J\, m^{-3}$) is

A

$13.29 \times 10^{-12}$

B

$8.86 \times 10^{-12}$

C

$17.72 \times 10^{-12}$

D

$4.43 \times 10^{-12}$

Solution

Amplitude of electric field and magnetic field are related by the relation

$\frac{E_{0}}{B_{0}}=c$

Average energy density of the magnetic field is

$\mathrm{u}_{\mathrm{B}} =\frac{1}{4} \frac{\mathrm{B}_{0}^{2}}{\mu_{0}} $

$=\frac{1}{4} \frac{\mathrm{E}_{0}^{2}}{\mu_{0} \mathrm{c}^{2}} $ $\left(\because B_{0}=\frac{E_{0}}{c}\right)$

$=\frac{1}{4} \varepsilon_{0} \mathrm{E}_{0}^{2} $ $\left(\because c=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}\right)$

$=\frac{1}{4} \times 8.854 \times 10^{-12} \times(2)^{2} $

$ \approx 8.86 \times 10^{-12} \mathrm{\,J} \mathrm{m}^{-3}$

Standard 12

Physics

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