Current $i$ is carried in a wire of length $L$. If the wire is turned into a circular coil, the maximum magnitude of torque in a given magnetic field $B$ will be
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(c) ${\tau _{\max }} = NiAB = 1 \times i \times (\pi {r^2}) \times B$ $\left( {2\pi r = L,\,\, \Rightarrow r = \frac{L}{{2\pi }}} \right)$
${\tau _{\max }} = \pi i{\left( {\frac{L}{{2\pi }}} \right)^2}B = \frac{{{L^2}iB}}{{4\pi }}$
${\tau _{\max }} = \pi i{\left( {\frac{L}{{2\pi }}} \right)^2}B = \frac{{{L^2}iB}}{{4\pi }}$
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