The average value of electric energy density in an electromagnetic wave is. [where $\mathrm{E}_0$ is peak…

The average value of electric energy density in an electromagnetic wave is. [where $\mathrm{E}_0$ is peak value]
  1. $\frac{\epsilon_0 \mathrm{E}_{\mathrm{rms}}^2}{4}$
  2. $\frac{1}{2} \epsilon_0 \mathrm{E}_0^2$
  3. $\frac{1}{2} \epsilon_0 \mathrm{E}_0$
  4. $\frac{1}{4} \epsilon_0 \mathrm{E}_0^2$

Solution

The energy density in EM wave is $\mathrm{u}=\frac{1}{2} \varepsilon_{\mathrm{o}} \mathrm{E}^2=\frac{1}{2} \varepsilon_{\mathrm{o}} \mathrm{E}_0^2 \sin ^2(\omega \mathrm{t}-\mathrm{kx})$ $\therefore \quad$ Average energy density, $ \lt \mathrm{u}\gt=\frac{1}{2} \varepsilon_0 \mathrm{E}_0^2 \lt \sin ^2(\omega \mathrm{t}-\mathrm{kx})\gt=\left(\frac{1}{2} \varepsilon_0 \mathrm{E}_0^2\right) \times \frac{1}{2}$ $=\frac{1}{4} \epsilon_0 \mathrm{E}_0^2$

Asked in: AP EAMCET 2024 (20 May Shift 1)

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