GATE 2014 EC (EC4) – Question 34
An antenna radiates in free space. Electric-field magnitude at 1 km is 12 mV/m. Given intrinsic impedance $120\pi$ Ω, find average power-density magnitude at 2 km (nW/m²).
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Show answer and explanation
Correct answer: 47.6 to 47.8
Explanation
In the radiation far field, electric-field amplitude decreases as1/r. The peak field at2km is therefore6mV/m. Average power density is Epeak²/(2η)=(0.006)²/(240π)=4.77465×10⁻⁸W/m²=**47.7465nW/m²**. The official answer treats the quoted field as peak amplitude; an rms field convention would give twice this power.