$A$ thin disc of radius $R$ and mass $M$ has charge $q$ uniformly distributed on it. It rotates with angular velocity $\omega$. The ratio of magnetic moment and angular momentum for the disc is

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 $(\mu_0 = \text{permeability of free space})$

$A$ 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

Write the unit and formula of the magnetic dipole moment due to a current-carrying loop.

$A$ wire of length $2\,m$ is bent into a circular loop. When a current of $1\,A$ is passed through the loop,then the magnetic moment of the loop is

$A$ uniform conducting wire of length $24a$ and resistance $R$ is wound up as a current-carrying coil in the shape of an equilateral triangle of side $a$ and then in the form of a square of side $a$. The coil is connected to a voltage source $V_{0}$. The ratio of the magnetic moment of the coils in the case of the equilateral triangle to that of the square is $1 : \sqrt{y}$, where $y$ is ..... .