First slide

Electromagnetic waves and its nature

Question

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

Moderate

A

$13.29 \times 10^{- 12}$
B

$4.43 \times 10^{- 12}$
C

$17.72 \times 10^{- 12}$
D

$8.85 \times 10^{- 12}$

Solution

Average energy density of magnetic field $= \frac{{(B_{r m s})}^{2}}{2 μ_{0}} = \frac{{(B_{0} / \sqrt{2})}^{2}}{2 μ_{0}} = \frac{1}{4} \frac{B_{0}^{2}}{μ_{0}}$
But $B_{0} = \frac{E_{0}}{C}$
Average energy density of magnetic field is $\frac{1}{4} \frac{E_{0}^{2}}{C^{2} μ_{0}} = \frac{1}{4} \in_{0} E_{0}^{2} (∴ \in_{0} = \frac{1}{C^{2} μ_{0}})$
Average energy density of magnetic field $= \frac{1}{4} \times 8.85 \times 10^{- 12} \times 2^{2} = 8.85 \times 10^{- 12} J / m^{3}$

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