A charge $q$ is uniformly distributed on a hollow sphere of radius $R$. It is rotated with an angular speed $\left(\omega \right)$ about an axis passing through the centre of mass of the hollow sphere. The magnetic moment of the hollow sphere is :-

A rectangular loop of sides $10 \mathrm{cm}$ and $5 \mathrm{cm}$, carrying a current $I$ of $12 \mathrm{A}$, is placed in different orientations as shown in the figure below.
(a)  (b)

(c)  (d)

If there is a uniform magnetic field of $0.3 \mathrm{T}$ in the positive $z$ direction, in which orientations the loop would be in $\left(\mathrm{i}\right)$ stable equilibrium and $\left(\mathrm{ii}\right)$ unstable equilibrium?

Two short magnets are placed along the same axis with their like-poles, facing each other. The magnets repel each other with a force that varies inversely as

Torque acting on a coil is $2\times {10}^{-5} \mathrm{N} \mathrm{m}$. If the torque produces angular deflection of $10°$ in the coil, then the torsional rigidity of the suspension fibre (in $\mathrm{N} \mathrm{m}$/$\mathrm{degree}$) connected to coil is