Electromagnetic Waves Question 7
Question 7 - 2024 (31 Jan Shift 1)
In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5 \times 10^{10} \mathrm{~Hz}$ and an amplitude of $50 \mathrm{Vm}^{-1}$. The total average energy density of the electromagnetic field of the wave is : [Use
$\left.\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} / \mathrm{Nm}^{2}\right]$
(1) $1.106 \times 10^{-8} \mathrm{Jm}^{-3}$
(2) $4.425 \times 10^{-8} \mathrm{Jm}^{-3}$
(3) $2.212 \times 10^{-8} \mathrm{Jm}^{-3}$
(4) $2.212 \times 10^{-10} \mathrm{Jm}^{-3}$
Show Answer
Answer: (1)
Solution:
$\mathrm{U}{\mathrm{E}}=\frac{1}{2} \epsilon{0} \mathrm{E}^{2}$
$\mathrm{U}_{\mathrm{E}}=\frac{1}{2} \times 8.85 \times 10^{-12} \times(50)^{2}$
$=1.106 \times 10^{-8} \mathrm{~J} / \mathrm{m}^{3}$
