The radius of a circular ring of wire is $R$ and it carries a current of $I\,ampere$. At its centre a smaller ring of radius $r$ with current $i$ and $N\, turns$ is placed. Assuming that the planes of two rings are perpendicular to each other and the magnetic induction produced at the centre of bigger ring is constant, then the torque acting on smaller ring will be
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$T=N I A B \sin \theta$
$\mathrm{T}=\mathrm{Ni} \pi \mathrm{r}^{2}\left(\frac{\mu_{0} \mathrm{I}}{2 \mathrm{R}}\right) \sin 90^{\circ}$
$\mathrm{T}=\mathrm{Ni} \pi \mathrm{r}^{2}\left\{\frac{\mu_{0} \mathrm{I}}{2 \mathrm{R}}\right\}$
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