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Question 15

The ratio of average electric energy density and total average energy density of electromagnetic wave is:

We need to find the ratio of average electric energy density to the total average energy density of an electromagnetic wave. For an electromagnetic wave, the electric energy density is $$u_E = \frac{1}{2}\epsilon_0 E^2$$ and the magnetic energy density is $$u_B = \frac{B^2}{2\mu_0}$$.

In an electromagnetic wave, the electric and magnetic densities are equal. Using $$E = cB$$ and $$c = \frac{1}{\sqrt{\mu_0\epsilon_0}}$$, we get $$u_E = \frac{1}{2}\epsilon_0 E^2 = \frac{1}{2}\epsilon_0 c^2 B^2 = \frac{1}{2}\epsilon_0 \cdot \frac{1}{\mu_0\epsilon_0} \cdot B^2 = \frac{B^2}{2\mu_0} = u_B$$.

It follows that the total energy density is $$u_{total} = u_E + u_B = 2u_E$$.

The ratio of the electric energy density to the total energy density is $$\frac{u_E}{u_{total}} = \frac{u_E}{2u_E} = \frac{1}{2}$$, which matches Option D.

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