Topic: Electromagnetics
Plane wave travelling in free space has an average Poynting vector of $3~\text{W/m}^{2}$. Average energy density $\text{nJ/m}^{3}$ of the wave is
- A. 10
- B. 5
- C. 1
- D. 3
Answer: A. 10
Explanation: Average Poynting vector $P_{\text{avg}} = \frac{1}{2}\frac{E^{2}}{\eta}$.
$3 = \frac{E^{2}}{2 \times 120\pi} \Rightarrow E^{2} = 240 \times 3 \times \pi = 720\pi$.
Average energy density $= \frac{1}{2}\epsilon_{0} E^{2} = \frac{1}{2} \times \frac{1}{36\pi \times 10^{9}} \times 720\pi$.
$= \frac{720}{72 \times 10^{9}} = 10 \times 10^{-9}~\text{J/m}^{3} = 10~\text{nJ/m}^{3}$.