Question

If the amplitude of the magnetic field in a travelling plane electromagnetic wave is \(2.2 \times 10^{-4} \, \text{T}\), then the intensity of the wave is nearly:

• A. \(5.8 \times 10^6 \, \text{W/m}^2\)
• B. \(4.2 \times 10^6 \, \text{W/m}^2\)
• C. \(1.2 \times 10^7 \, \text{W/m}^2\)
• D. \(8.8 \times 10^5 \, \text{W/m}^2\)

Hint:

For EM waves, intensity \(I = c B_0^2 / 2\mu_0\) relates magnetic field amplitude to energy flux.

Answer 1

The Correct Option is A

Step 1: Convert the magnetic field amplitude into an electric field amplitude first.
For an EM wave, $E_0 = cB_0$:
\[ E_0 = (3\times10^8)(2.2\times10^{-4}) = 6.6\times10^4\ \text{V/m} \]
Step 2: Use the standard intensity formula in terms of $E_0$.
\[ I = \frac12\epsilon_0 c E_0^2 \]
Step 3: Substitute and compute.
\[ E_0^2 = (6.6\times10^4)^2 = 4.356\times10^9 \]
\[ I = \frac12(8.854\times10^{-12})(3\times10^8)(4.356\times10^9) \approx 5.8\times10^6\ \text{W/m}^2 \]
\[ \boxed{5.8\times10^6\ \text{W/m}^2} \]