Q125 / 180 · KCET 2021 · Physics
Suppose that the electric field amplitude of electromagnetic wave is $E_{0}=120 \mathrm{NC}^{-1}$ and its frequency $f=50 \mathrm{MHz}$. Then, which of the following value is incorrectly computed?
- AMagnetic field amplitude is $400 \mathrm{nT}$.
- BAngular frequency of EM wave is $\pi \times 10^{8} \mathrm{rad} / \mathrm{s}$.
- Correct answerCPropagation constant (angular wave number) is $2.1 \mathrm{rad} / \mathrm{m}$.
- DWavelength of EM wave is $6 \mathrm{~m}$.
Solution
Given, $E_{0}=120 \mathrm{NC}^{-1}$
$f=50 \mathrm{MHz}=50 \times 10^{6} \mathrm{~Hz}$
(a) magnetic field amplitude,
$\begin{aligned}
B_{0} &=\frac{E_{0}}{c}=\frac{120}{3 \times 10^{8}}=40 \times 10^{-8} \mathrm{~T} \\
&=400 \mathrm{n} \mathrm{T}
\end{aligned}$
(b) Angular frequency, $\omega=2 \pi f=2 \pi \times 50 \times 10^{6}$
$=\pi \times 10^{8} \mathrm{rad} / \mathrm{s}$
(c) Propagation constant,
$k=\frac{\omega}{c}=\frac{\pi \times 10^{8}}{3 \times 10^{8}}=1.047 \mathrm{rad} / \mathrm{m}$
(d) Wavelength, $\lambda=\frac{c}{f}=\frac{3 \times 10^{8}}{50 \times 10^{6}}=\frac{30}{5}=6 \mathrm{~m}$
Hence, the correct answer is option: 'C'.