In the figure shown a coil of single turn is wound on a sphere of radius $R$ and mass $m.$ The plane of the coil is parallel to the plane and lies in the equatorial plane of the sphere. Current in the coil is $i$. The value of $B$ if the sphere is in equilibrium is
Diffcult
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The gravitational torque must be counter balanced by the magnetic torque about $o,$ for equilibrium of the sphere. The gravitational torque $=\tau_{g r}=|\overrightarrow{m g} \times \vec{r}|$
$\Rightarrow \tau_{g r}=m g \sin \theta$
The magnetic moment of the coil $=\mu=\left(i \pi r^{2}\right)$
$\Rightarrow \tau_{m}=\pi r^{2} B \sin \theta$
$\pi i r^{2} B \sin \theta=m g r^{\prime} \sin \theta \Rightarrow B=m g / \pi i r$
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