Topic: Electromagnetics
The electric field component of a time harmonic plane EM wave traveling in a non-magnetic lossless dielectric medium has amplitude of $2~\text{V/m}$. If the relative permittivity of the medium is 4, the magnitude of the time-average power density vector (in $\text{W/m}^2$) is
- A. $\frac{1}{30\pi}$
- B. $\frac{1}{120\pi}$
- C. $\frac{1}{60\pi}$
- D. $\frac{1}{240\pi}$
Answer: A. $\frac{1}{30\pi}$
Explanation: $E = 2~\text{V/m}, \epsilon_r = 4$.
Intrinsic impedance $\eta = \frac{120\pi}{\sqrt{\epsilon_r}} = \frac{120\pi}{2} = 60\pi~\Omega$.
Average power density $P_{avg} = \frac{1}{2} \frac{E²}{\eta} = \frac{1}{2} \frac{2^2}{60\pi} = \frac{1}{30\pi}~\text{W/m}^2$.