$A$ charge $q$ is spread uniformly over an isolated ring of radius $R$. The ring is rotated about its natural axis with an angular velocity $\omega$. Magnetic dipole moment of the ring 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 $....$ .

$A$ current-carrying loop consists of $3$ identical quarter circles of radius $R$,lying in the positive quadrants of the $xy$,$yz$,and $zx$ planes with their centers at the origin,joined together. Find the direction and magnitude of the magnetic field $\vec{B}$ at the origin.

$A$ closely wound solenoid of $1000$ turns and area of cross-section $2 \times 10^{-4} \ m^2$ carrying a current of $5.0 \ A$. The magnetic moment is . . . . . . $A \ m^2$.

$A$ rod of length $l$ having uniformly distributed charge $Q$ is rotated about one end with constant frequency $f$. Its magnetic moment is:

In the given diagram,a rod is rotating with angular velocity $\omega$. The mass of this rod is $m$,the charge is $q$,and the length is $l$. Find the magnetic moment of this rod.