The dimensional formula for magnetic moment is:

$A$ spherical shell of radius $R$ carries a uniformly distributed charge $Q$ and is rotated about its diameter with angular speed $\omega$. Find its magnetic moment.

$A$ circular coil of $1000$ turns and area of cross-section $1.5 \times 10^{-4} \, m^2$ is carrying a current of $2 \, A$. What is the magnetic moment associated with the coil in $Am^2$?

$A$ coil of $n$ turns and radius $R$ carries a current $I$. It is unwound and rewound to make a new coil of radius $\frac{R}{3}$ and the same current is passed through it. The ratio of the magnetic moment of the new coil to that of the original coil is

$A$ 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.

$A$ square loop is carrying a steady current $I$ and the magnitude of its magnetic dipole moment is $m$. If this square loop is changed to a circular loop and it carries the same current,the magnitude of the magnetic dipole moment of the circular loop will be