$A$ wire of length $L$ $m$ carrying a current of $I$ $A$ is bent in the form of a circle. Its magnitude of magnetic moment will be

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

An electron revolving in a circular orbit of radius $r$ with velocity $v$ and frequency $f$ has an orbital magnetic moment $M$. If the frequency of revolution is doubled,then the new magnetic moment will be:

The unit of magnetic moment is . . . . . . .

The magnetic field at the centre of a single-turn circular coil of a given length of wire carrying a current $I$ is $B$. If the same wire is bent into a circular coil of two turns and the same current $I$ is passed through it,the new magnetic field at the centre will be:

$A$ uniform conducting wire of length $12a$ and resistance $R$ is wound up as a current-carrying coil in the shape of:
$(i)$ an equilateral triangle of side $a$;
$(ii)$ a square of side $a$;
$(iii)$ a regular hexagon of side $a$.
The coil is connected to a voltage source $V_{0}$. Find the magnetic moment of the coils in each case.