$A$ 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:

An electron moves in a circular orbit with a uniform speed $v$. It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is proportional to

The magnetic field at the centre of a current carrying circular coil of area $A$ is $B$. The magnetic moment $(M)$ of the coil is $(\mu_0 = \text{permeability of free space})$

The magnetic moment vectors $\mu_{s}$ and $\mu_{l}$ associated with the intrinsic spin angular momentum $S$ and orbital angular momentum $L$ respectively,of an electron are predicted by quantum theory (and verified experimentally to a high accuracy) to be given by $\mu_{s} = -(e/m)S$ and $\mu_{l} = -(e/2m)L$. Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result.

The magnetic field at the centre of a current carrying circular coil of an area $A$ is $B$. The magnetic moment of the coil is (where $\mu_0$ is the permeability of free space).

$A$ 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