Question 16

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $$5 \times 10^{10}$$ Hz and an amplitude of $$50 \text{ V m}^{-1}$$. The total average energy density of the electromagnetic field of the wave is : [Use $$\varepsilon_0 = 8.85 \times 10^{-12} \text{ C}^2 \text{N}^{-1}\text{m}^{-2}$$]

The total average energy density ($$u_{\text{avg}}$$) contains equal contributions from both the electric and magnetic fields:

$$u_{\text{avg}} = \varepsilon_0 E_{\text{rms}}^2 = \frac{1}{2}\varepsilon_0 E_0^2$$

$$\implies u_{\text{avg}} = \frac{1}{2} \times (8.85 \times 10^{-12}) \times (50)^2$$

$$\implies u_{\text{avg}} = 1.106 \times 10^{-8}\text{ J m}^{-3}$$

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