Question

Electromagnetic wave with intensity \( I = 4 \times 10^{14} \, \text{watt/m}^2 \) is propagating in free space. Find the amplitude of magnetic field \( B_0 \). Given: \( c = 3 \times 10^8 \, \text{m/s}, \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2 \).

• A. 1.83 Tesla
• B. 0.5 Tesla
• C. 4.5 Tesla
• D. 1 Tesla

Hint:

In free space, the intensity of an electromagnetic wave is related to the amplitude of the electric field, which in turn is related to the amplitude of the magnetic field.

Answer 1

The Correct Option is A

Step 1: Formula for intensity and magnetic field.
The intensity \( I \) of an electromagnetic wave is related to the amplitude of the electric and magnetic fields by: \[ I = \frac{1}{2} \epsilon_0 c E_0^2, \] where \( E_0 \) is the amplitude of the electric field. The amplitude of the magnetic field \( B_0 \) is related to the amplitude of the electric field by: \[ B_0 = \frac{E_0}{c}. \] Step 2: Calculate the electric field.
Rearranging the intensity formula to solve for \( E_0 \): \[ E_0 = \sqrt{\frac{2I}{\epsilon_0 c}}. \] Substituting the given values: \[ E_0 = \sqrt{\frac{2 \times 4 \times 10^{14}}{8.85 \times 10^{-12} \times 3 \times 10^8}} \approx 6.6 \times 10^3 \, \text{V/m}. \] Step 3: Calculate the magnetic field.
Now, using the relation between \( E_0 \) and \( B_0 \): \[ B_0 = \frac{E_0}{c} = \frac{6.6 \times 10^3}{3 \times 10^8} \approx 1.83 \, \text{Tesla}. \] Final Answer: \[ \boxed{1.83 \, \text{Tesla}}. \]