Q90 / 90 · JEE Main 2019 (12 Apr Shift 2) · Physics

A plane electromagnetic wave having a frequency $f = 23.9 G H z$ 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?

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

Solution

B = \frac{E}{c} = \frac{60}{3 \times 10^{8}} = 2 \times 10^{- 7}

The magnetic field can be written as,

k = \frac{2 π}{λ} = \frac{2 π}{c / f} \approx 500

ω = 2 π f \approx 1.5 \times 10^{11}

\vec{B} = 2 \times 10^{- 7} \sin (0.5 \times 10^{3} z - 1.5 \times 10^{11} t) \hat{i}

Hence, the correct answer is option: 'A'.