First slide

Electromagnetic waves and its nature

Question

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

Moderate

A

$1 \times 10^{- 10}$
B

$5 \times 10^{- 10}$
C

$8.55 \times 10^{- 5}$
D

$8.55 \times 10^{- 10}$

Solution

Average energy density of magnetic field $= \frac{B^{2} r m s}{2 μ_{0}} = \frac{{(B_{0} / \sqrt{2})}^{2}}{2 μ_{0}} = \frac{1}{4} \frac{B_{0}^{2}}{μ_{0}}$
But $B_{0} = \frac{E_{0}}{C}$
Average energy density of electric field= $\frac{1}{4} \times \frac{E_{0}^{2}}{C^{2} μ_{0}}$
But $C = \frac{1}{\sqrt{μ_{0} \in_{0}}} ∴ E_{0} = \frac{1}{C^{2} μ_{0}} H e n c e, A v e r a g e e n e r g y d e n s i t y o f m a g n e t i c f i e l d = \frac{1}{4} \times \in_{0} E_{0}^{2} = \frac{1}{4} \times 8.55 \times 10^{- 12} \times {(20)}^{2}$
= $8.55 \times 10^{- 10} J / m^{3}$

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