GATE EC 2014 Electromagnetics Solution Q 15

# GATE EC 2014 Electromagnetics Solution Q 15

For an antenna radiating in free space, the electric field at a distance of 1 km is found to be 12 mV/m. Given that intrinsic impedance of the free space is 120\pi\;\Omega, the magnitude of average power density due to this antenna at a distance of 2 km from the antenna (in nW/m^2)is _.

Ans :- 44.7

Explanation

We know that E\propto\frac1r, where r is the distance where electric field is to be measured.

So, electric field, E at a distance of 2 km = \frac{12\;mV/m}2=6\;mV/m

Also, power density due to the antenna will be,

P_{avg}=\frac12\frac{E^2}\eta=\frac12\times\frac{6\times6\times10^{-6}}{120\pi}=47.7\;nW/m^2

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