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. $\vec{B}=60sin(0.5\times 10^{3}x+1.5\times 10^{11}t\hat{k}$

Answer 1

Answer: (C)

Magnetic field when electromagnetic wave
propagates in $+z$ direction
$B=B_{0}sin(kz-\omega t)$
where
$B_0=\frac{60}{3\times 10^8}=2\times 10^{-7}$
$k=\frac{2\pi }{\lambda }=0.5\times 10^3$
$k=\frac{2\pi }{\lambda }=0.5\times 10^3$
$\omega =2\pi f=1.5\times 10^{11}$