Question:
The rms electric field of an EM wave is $30\sqrt{\pi}\ \text{V m}^{-1}$. Find its intensity in free space.}
The rms electric field of an EM wave is $30\sqrt{\pi}\ \text{V m}^{-1}$. Find its intensity in free space.}
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Intensity ∝ square of electric field amplitude.
Updated On: Jun 17, 2026
- 30 W m$^{-2}$
- 3.75 W m$^{-2}$
- 15 W m$^{-2}$
- 7.5 W m$^{-2}$
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The Correct Option is D
Solution and Explanation
Step 1: Intensity of EM wave: \[ I = \epsilon_0 c E_{\text{rms}}^2 \]
Step 2: Substitute values: \[ E_{\text{rms}}^2 = (30\sqrt{\pi})^2 = 900\pi \]
Step 3: \[ \epsilon_0 c = 8.85\times10^{-12} \times 3\times10^8 = 2.655\times10^{-3} \]
Step 4: \[ I = 2.655\times10^{-3} \times 900\pi \]
Step 5: \[ I = 2.3895 \pi \approx 7.5\ \text{W m}^{-2} \]
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