Question

A plane electromagnetic wave having a frequency n = 23.9 GHz propagates along the positive z-direction in free space. The peak value of the electric field is 60 V/m. Which among the following is the acceptable magnetic field component in the electromagnetic wave ?

• A. $\vec{B} = 2 \times 10^7 \, sin(0.5 \times 10^3 z + 1.5 \times 10^{11}t \hat{i}$
• B. $\vec{B} = 2 \times 10^{-7} \, sin(1.5 \times 10^2 x + 0.5 \times 10^{11}t \hat{j}$
• C. $\vec{B} = 2 \times 10^{-7} \, sin(0.5 \times 10^3 z - 1.5 \times 10^{11}t \hat{i}$
• D. $\vec{B} = 60 sin(0.5 \times 10^3 x + 1.5 \times 10^{11}t \hat{k}$

Answer 1

Answer: (C)

Magnetic field when electromagnetic wave
propagates in $+z$ direction
$B = B_0\, sin (kz - \omega t)$
where
$B_0 \, = \, \frac{60}{3 \times 10^8} = 2 \times 10^{-7}$
$k = \frac{2\pi}{\lambda} = 0.5 \times 10^3$
$k = \frac{2 \pi}{\lambda} = 0.5 \times 10^3$
$\omega = 2\pi f = 1.5 \times 10^{11}$