$A$ straight wire carrying current $i$ is turned into a circular loop. If the magnitude of the magnetic moment associated with it in $MKS$ units is $M$,the length of the wire 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.

An electron moves with a constant speed $v$ along a circle of radius $r$. Its magnetic moment will be ($e$ is the electron's charge).

$A$ ring of radius $R$,made of an insulating material,carries a charge $Q$ uniformly distributed on it. If the ring rotates about the axis passing through its centre and normal to the plane of the ring with a constant angular speed $\omega$,then the magnitude of the magnetic moment of the ring is:

$A$ small bar magnet experiences a torque of $0.016 \ Nm$ when placed with its axis at $30^{\circ}$ with an external magnetic field of $0.04 \ T$. If the bar magnet is replaced by a solenoid of cross-sectional area $1 \ cm^2$ and $1000$ turns, having the same magnetic moment as that of the bar magnet, then the current flowing through the solenoid is: (in $A$)

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