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.
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.
Show Hint
Intensity of EM wave: \(I = \frac{1}{2} c \epsilon_0 E_0^2\). Always convert units consistently.
Updated On: Jul 18, 2026
- 22.4 mW/m\(^2\)
- 25.7 mW/m\(^2\)
- 65.5 mW/m\(^2\)
- 45.6 mW/m\(^2\)
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The Correct Option is B
Solution and Explanation
Step 1: Recall the intensity formula for EM wave.
\[ I = \frac{1}{2} c \epsilon_0 E_0^2 \]
where \(c = 3 \times 10^8 \, \text{m/s}\), \(\epsilon_0 = 8.854 \times 10^{-12} \, \text{F/m}\), \(E_0\) is maximum electric field.
Step 2: Substitute known values.
\[ I = \frac{1}{2} (3 \times 10^8) (8.854 \times 10^{-12}) (4.4)^2 \]
Step 3: Square electric field.
\[ 4.4^2 = 19.36 \]
Step 4: Multiply constants.
\[ \frac{1}{2} \cdot 3 \times 10^8 \cdot 8.854 \times 10^{-12} \cdot 19.36 \approx 25.7 \times 10^{-3} \, \text{W/m}^2 \]
Step 5: Convert to mW/m\(^2\).
\[ I \approx 25.7 \, \text{mW/m}^2 \]
Step 6: Final conclusion.
Hence, the intensity of the electromagnetic wave is:
\[ \boxed{25.7 \, \text{mW/m}^2} \]
\[ I = \frac{1}{2} c \epsilon_0 E_0^2 \]
where \(c = 3 \times 10^8 \, \text{m/s}\), \(\epsilon_0 = 8.854 \times 10^{-12} \, \text{F/m}\), \(E_0\) is maximum electric field.
Step 2: Substitute known values.
\[ I = \frac{1}{2} (3 \times 10^8) (8.854 \times 10^{-12}) (4.4)^2 \]
Step 3: Square electric field.
\[ 4.4^2 = 19.36 \]
Step 4: Multiply constants.
\[ \frac{1}{2} \cdot 3 \times 10^8 \cdot 8.854 \times 10^{-12} \cdot 19.36 \approx 25.7 \times 10^{-3} \, \text{W/m}^2 \]
Step 5: Convert to mW/m\(^2\).
\[ I \approx 25.7 \, \text{mW/m}^2 \]
Step 6: Final conclusion.
Hence, the intensity of the electromagnetic wave is:
\[ \boxed{25.7 \, \text{mW/m}^2} \]
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