First slide

Average energy density of electromagnetic wave

Question

The electric field on an electromagnetic wave is given by $E = (50 N / C) \sin ω (t - \frac{x}{c})$ The energy contained in a cylinder of cross-section 10 cm² and length 50 cm along the x-axis will be

Moderate

A

$5 \cdot 5 \times 10^{- 9} J$
B

$5 \cdot 54 \times 10^{- 10} J$
C

$5 \cdot 5 \times 10^{- 12} J$
D

$5 \cdot 5 \times 10^{- 15} J$

Solution

The average average density is given by
$u_{a v} = \frac{1}{2} ϵ_{0} E_{0}^{2}$
Total volume of cylinder
$V = Al$
Total energy contained in the cylinder
$U = (u_{a v}) (V) = (\frac{1}{2} \in_{0} E_{0}^{2}) \times A l = [\frac{1}{2} \times 8 .86 \times 10^{- 12} \times (50)^{2}] \times [(10 \times 10^{- 4}) \times (50 \times 10^{- 2})] J = 5 \cdot 5 \times 10^{- 12} J$

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