Question

Suppose that the electric field amplitude of electromagnetic wave is \(E_o=120\ NC^{-1}\) and its frequency if f = 50 MHz. Then which of the following value is incorrectly computed ?

• A. Magnetic field amplitude is 400nT.
• B. Angular frequency of EM wave is π × 10⁸ rad/s
• C. Propagation constant (angular wave number) is 2.1 rad/m
• D. Wavelength of EM wave is 6m.

Answer 1

The Correct Option is C

(A) Magnetic field amplitude is 400nT.

The relationship between the electric field amplitude ($E_0$) and magnetic field amplitude ($B_0$) in an electromagnetic wave is given by:

$B_0 = \frac{E_0}{c}$

where $c$ is the speed of light ($3 \times 10^8\,\text{m/s}$). Substituting the given value of $E_0$:

$B_0 = \frac{120\,\text{NC}^{-1}}{3 \times 10^8\,\text{m/s}} = 40 \times 10^{-8}\,\text{T} = 400 \times 10^{-9}\,\text{T} = 400\,\text{nT}$

This is correct.

(B) Angular frequency of EM wave is $\pi \times 10^8$ rad/s

Angular frequency ($\omega$) is related to frequency ($f$) by:

$\omega = 2\pi f$

$\omega = 2\pi (50 \times 10^6\,\text{Hz}) = \pi \times 10^8\,\text{rad/s}$

This is correct.

(C) Propagation constant (angular wave number) is 2.1 rad/m

The propagation constant ($k$), also known as the angular wave number, is given by:

$k = \frac{2\pi}{\lambda}$

where $\lambda$ is the wavelength. We know that $c = f\lambda$, so $\lambda = \frac{c}{f}$. Thus:

$k = \frac{2\pi f}{c} = \frac{\omega}{c} = \frac{\pi \times 10^8\,\text{rad/s}}{3 \times 10^8\,\text{m/s}} \approx 1.05\,\text{rad/m}$

The given value of $2.1\,\text{rad/m}$ is incorrect.

(D) Wavelength of the EM wave is 6 m.

The wavelength ($\lambda$) is given by:

$\lambda = \frac{c}{f} = \frac{3 \times 10^8\,\text{m/s}}{50 \times 10^6\,\text{Hz}} = 6\,\text{m}$

This is correct.

The correct answer is (C).