$A$ wire of length $L \ m$ carrying a current $I \ A$ is bent in the form of a circle. The magnitude of its magnetic moment is

$A$ closely wound solenoid of $800$ turns and area of cross section $2.5 \times 10^{-4} \text{ m}^2$ carries a current of $3.0 \text{ A}$. The magnetic moment associated with it is . . . . . . . (in $\text{ JT}^{-1}$)

The magnetic dipole moment of a rectangular current-carrying loop is:

$A$ charged particle (charge $= q$; mass $= m$) is rotating in a circle of radius $R$ with uniform speed $V$. The ratio of its magnetic moment $(\mu)$ to the angular momentum $(L)$ is:

$A$ conducting solid sphere of radius $R$ and mass $M$ carries a charge $Q$. The sphere is rotating about an axis passing through its center with a uniform angular speed $\omega$. The ratio of the magnitudes of the magnetic dipole moment to the angular momentum about the same axis is given as $\alpha \frac{Q}{2 M}$. The value of $\alpha$ is $....$ .

Derive an expression for the torque acting on a current-carrying loop suspended in a uniform magnetic field.