A wire of length $L$ is bent in the form of a circular coil and current $i$ is passed through it. If this coil is placed in a magnetic field then the torque acting on the coil will be maximum when the number of turns is
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(d) ${\tau _{\max }} = MB$ or ${\tau _{\max }} = ni\pi {r^2}B$.
Let number of turns in length $l$ is $n$ so $l = n\,(2\pi r)$ or $\alpha = \frac{l}{{2\pi n}}$
$ \Rightarrow {\tau _{\max }} = \frac{{ni\pi B{l^2}}}{{4{\pi ^2}{n^2}}} = \frac{{{l^2}iB}}{{4\pi \,{n_{\min }}}} $
$\Rightarrow {\tau _{\max }} \propto \frac{1}{{{n_{\min }}}} \Rightarrow {n_{\min }} = 1$
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