GATE 2021 PH – Question 15
A small current loop carries a time-dependent sinusoidal current. At a distance $r$ much larger than the loop size, the time-averaged integral of the Poynting vector over a sphere of radius $r$ is constant. The amplitude of the magnetic field varies as
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Correct answer: (C) $r^{-1}$
Explanation
Constant total radiated power through a sphere implies $4\pi r^2\langle S\rangle=\text{constant}$, hence $\langle S\rangle\propto r^{-2}$. In the radiation zone $E=cB$ and $\langle S\rangle\propto B_0^2$. Taking the square root gives $B_0\propto r^{-1}$. The faster inverse powers describe near fields rather than the far-zone radiation amplitude.
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