GATE 2021 EC – Question 65
An antenna with a directive gain of 6 dB is radiating a total power of 16 kW. The amplitude of the electric field in free space at a distance of 8 km from the antenna in the direction of 6 dB gain (rounded off to three decimal places) is ________ V/m.
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Correct answer: 0.23 to 0.25
Explanation
The 6 dB gain is $G=10^{0.6}=3.98$. The power density at $r=8$ km is $S=\frac{P_tG}{4\pi r^2}=\frac{16000\times3.98}{4\pi(8000)^2}=7.92\times10^{-5}\ \text{W/m}^2$. With $S=\frac{E_0^2}{2\eta_0}$ and $\eta_0=377\ \Omega$, the peak field amplitude is $E_0=\sqrt{2\eta_0S}=\sqrt{2\times377\times7.92\times10^{-5}}\approx0.244$ V/m.