$A$ charge $q$ is spread uniformly over an insulated loop of radius $r$. If it is rotated with an angular velocity $\omega$ with respect to the normal axis,then the magnetic moment of the loop is:

In a hydrogen atom,an electron of mass $m$ and charge $e$ revolves in an orbit of radius $r$ making $n$ revolutions per second. If the mass of hydrogen nucleus is $M$,the magnetic moment associated with the orbital motion of the electron is

The magnetic dipole moment of a current loop is independent of

$A$ $100$-turn closely wound circular coil of radius $5 \text{ cm}$ has a magnetic field of $3.14 \times 10^{-3} \text{ T}$ at its centre. The current flowing through the coil, and the magnitude of the magnetic moment of this coil are, respectively: (Take $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$)

$A$ uniform conducting wire of length $12 a$ 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 $a$.
The magnetic dipole moments of the coil in each case respectively are:

The current associated with an electron of charge $e$ moving in a circular orbit of radius $r$ with speed $v$ around the positively charged nucleus is given by