$A$ circular coil of area $2 \,cm^2$ has $1000$ turns. If the current through the coil is $1 \,A$, then its magnetic moment is (in $\,Am^2$)

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

$A$ loop in the form of four connected semi-circular wires carrying current $I$ lies in the $x-y$ plane as shown in the figure. The unit vector $\hat{k}$ is coming out of the plane of the paper. The magnetic moment of the current loop 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 $....$ .

$A$ 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 in a circular orbit of radius $0.05 \,nm$ performs $10^{16}$ revolutions per second. What is the magnetic moment due to the rotation of the electron? $(e = 1.6 \times 10^{-19} \,C)$