Question

A plane electromagnetic wave propagating in x-direction is described by \( E_y = (200 \, \text{V/m}) \sin(1.5 \times 10^7 t - 0.05 x) \). The intensity of the wave is:

• A. 35.4 W/m²
• B. 53.1 W/m²
• C. 26.6 W/m²
• D. 106.2 W/m²

Answer 1

The Correct Option is B

The intensity \(I\) of an electromagnetic wave is given by:

\[ I = \frac{1}{2} \epsilon_0 c E_0^2 \]

where \(\epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2\), \(c = 3 \times 10^8 \, \text{m/s}\), and \(E_0 = 200 \, \text{V/m}\).

Substituting the values:

\[ I = \frac{1}{2} \times 8.85 \times 10^{-12} \times (3 \times 10^8) \times (200)^2 \] \[ I = 53.1 \, \text{W/m}^2 \]