First slide

Average energy density of electromagnetic wave

Question

The rms value of the electric field of a plane electromagnetic wave is 314 V/m. The average energy density of electric field and the average energy density are

Moderate

A

4.3 ×10^-7 Jm^-3 ; 2.15 ×10^-7 Jm^-3
B

4.3 ×10^-7 Jm^-3 ; 8.6 ×10^-7 Jm^-3
C

2.15 ×10^-7 Jm^-3 ; 4.3 ×10^-7 Jm^-3
D

8.6 ×10^-7 Jm^-3 ; 4.3 ×10^-7 Jm^-3

Solution

$\begin{array}{rcl} E_{rms} & = & 314 {Vm}^{- 1}; \\ E_{0} & = & E_{rms} \sqrt{2} \\ = & 314 x \sqrt{2} = 444 {Vm}^{- 1} \end{array}$
Average energy density of electric field
$\begin{array}{rcl} (u_{E}) & = & \frac{1}{4} \in_{0} {E_{0}}^{2} \\ = & \frac{1}{4} x 8.8 x 10^{- 12} {(444)}^{2} \\ = & 433699 x 10^{- 12} \\ = & 4.3 x 10^{- 7} {Jm}^{- 3} \end{array}$
$∴$ Average energy density
= 2u_E = 2 x 4.3 x10^-7 = 8.6 x 10^-7 Jm^-3

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