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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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Detailed Solution

Let number of turns in length $l$ is $n$ . so,

$τ_{max} = M B = n i π r^{2} B$

$[l = n (2 π r) \Rightarrow r = \frac{l}{2 π n}]$

$\Rightarrow τ_{max} = \frac{n i π B l^{2}}{4 π^{2} n^{2}} = \frac{l^{2} i B}{4 π n_{min}}$

$\Rightarrow τ_{max} \propto \frac{1}{n_{min}}$

$\Rightarrow n_{min} = 1$

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