Question

The magnetic field of a plane electromagnetic wave is given by: \[ \vec{B} = 2 \times 10^{-8} \sin \left(0.5 \times 10^3 x + 1.5 \times 10^{11} t \right) \hat{j} \, {T}. \] {The amplitude of the electric field would be:}

• A. \( 6 \, {V/m} \, {along x-axis} \)
• B. \( 3 \, {V/m} \, {along z-axis} \)
• C. \( 6 \, {V/m} \, {along z-axis} \)
• D. \( 2 \times 10^{-8} \, {V/m} \, {along z-axis} \)

Hint:

In an electromagnetic wave, the electric field and magnetic field are perpendicular to each other, and the amplitude of the electric field is related to the magnetic field by \( E = c B \).

Answer 1

The Correct Option is A

Step 1: The relationship between the electric field \( E \) and the magnetic field \( B \) in a plane electromagnetic wave is given by: \[ E = c B \] where \( c = 3 \times 10^8 \, {m/s} \) is the speed of light. 
Step 2: Given that the amplitude of the magnetic field is \( 2 \times 10^{-8} \, {T} \), we can calculate the amplitude of the electric field as: \[ E = (3 \times 10^8) \times (2 \times 10^{-8}) = 6 \, {V/m}. \] 
Step 3: Since the magnetic field is along the \( \hat{j} \)-axis (the \( y \)-axis), the electric field must be perpendicular to it and, therefore, must be along the \( x \)-axis.