Question

The average value of electric energy density in an electromagnetic wave is ( $E_0$ is peak value)

• A. $\frac{1}{2}{\epsilon }_0{E}_0^2$
• B. $\frac{E_0^2}{2{\epsilon }_0}$
• C. ${\epsilon }_0{E}_0^2$
• D. $\frac{1}{4}{\epsilon }_0{E}_0^2$

Answer 1

Answer: (D)

Electric energy density
$u_e=\frac{1}{2}{\epsilon }_0{E}_{rms}^2$
$E_{\text{rms }}=\frac{E_0}{\sqrt{2}}$
$\therefore u_e=\frac{1}{4}{\epsilon }_0{E}_0^2$