Question

In a plane electromagnetic wave, the electric field oscillates with a frequency $2 \times 10^{10} s ^{-1}$ and amplitude $40\, Vm ^{-1}$, then the energy density due to electric field is $\left(\varepsilon_{0}=8.85 \times 10^{-12}\, Fm ^{-1}\right)$

• A. $ 1.52 \times 10^{-9} \, Jm^{-3} $
• B. $ 2.54 \times 10^{-9} \, Jm^{-3} $
• C. $ 3.54 \times 10^{-9} \, Jm^{-3} $
• D. $ 4.56 \times 10^{-9} \, Jm^{-3} $

Answer 1

Answer: (C)

Energy density due to electric field is
$U=\frac{1}{2} \varepsilon_{0} E^{2}$
Here, $E=\frac{E_{0}}{\sqrt{2}}=\frac{40}{\sqrt{2}}$
$\therefore U=\frac{1}{2} \times 8.85 \times 10^{-12} \times \frac{40 \times 40}{2}$
$= 3.54 \times 10^{-9}\, J / m ^{3}$