Question

In a plane electromagnetic wave, the maximum value of the electric field component is \(4.4 \, \text{V/m}\). Find the intensity of the wave.

• A. 22.4 mW/m\(^2\)
• B. 25.7 mW/m\(^2\)
• C. 65.5 mW/m\(^2\)
• D. 45.6 mW/m\(^2\)

Hint:

Intensity of EM wave: \(I = \frac{1}{2} c \epsilon_0 E_0^2\). Always convert units consistently.

Answer 1

The Correct Option is B

Step 1: Use the impedance of free space instead of separate constants.
The intensity of an EM wave can be written as
\[ I = \frac{E_0^2}{2Z_0}, \qquad Z_0 = \mu_0 c \approx 377\ \Omega \]
which bundles $\mu_0$ and $c$ into one familiar number.
Step 2: Substitute the given field.
\[ I = \frac{(4.4)^2}{2(377)} = \frac{19.36}{754} \]
Step 3: Divide.
\[ I \approx 0.0257\ \text{W/m}^2 = 25.7\ \text{mW/m}^2 \]
\[ \boxed{25.7\ \text{mW/m}^2} \]