Question

An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm-1. Choose the correct equations for electric and magnetic field if the EM wave is propagating in vacuum:

• A. $E_y=60\sin⁡[\frac{π}{4}×10^3(x−3×10^8t)]\hat{j}Vm^{−1}$
  $B_y = 2\sin\left[\frac{\pi}{4} \times 10^3 (x - 3 \times 10^8 t)\right]\hat{k}T$
• B. $E_y = 60\sin\left[\frac{\pi}{4} \times 10^3 (x - 3 \times 10^8 t)\right] \hat{j} \,Vm^{-1}$
  $B_z = 2 \times 10^{-7} \sin\left[\frac{\pi}{4} \times 10^3 (x - 3 \times 10^8 t)\right] \hat{k} \, \text{T}$
• C. $E_y = 2 \times 10^{-7} \sin\left(\frac{\pi}{4} \times 10^3 (x - 3 \times 10^8 t)\right) \hat{j} \, Vm^{-1}$
  $B_z = 60 \sin\left[\frac{\pi}{4} \times 10^3 (x - 3 \times 10^8 t)\right]\hat{k} \, \text{T}$
• D. $E_y = 2 \times 10^{-7} \sin\left[\frac{\pi}{4} \times 10^4 (x - 4 \times 10^8 t)\right] \hat{j} \, Vm^{-1}$
  $B_z = 60 \sin\left[\frac{\pi}{4} \times 10^4 x - 4 \times 10^8 t)\right] \hat{k} \, \text{T}$

Answer 1

Answer: (B)

$E_y = 60\sin\left[\frac{\pi}{4} \times 10^3 (x - 3 \times 10^8 t)\right] \hat{j} \,Vm^{-1}$
$B_z = 2 \times 10^{-7} \sin\left[\frac{\pi}{4} \times 10^3 (x - 3 \times 10^8 t)\right] \hat{k} \, \text{T}$

Answer 2

The correct answer is (B) : $E_y = 60\sin\left[\frac{\pi}{4} \times 10^3 (x - 3 \times 10^8 t)\right] \hat{j} \,Vm^{-1}$
$B_z = 2 \times 10^{-7} \sin\left[\frac{\pi}{4} \times 10^3 (x - 3 \times 10^8 t)\right] \hat{k} \, \text{T}$
In first 3 options speed of light is 3 × 108 m/sec and in the fourth option it is 4 × 108 m/sec.
Using
E = CB
We can check the option is B.