A rod is rotating $n$ times per second about an axis passing through one of its ends $(x=0)$ . Its linear charge density is varying with distance as $\rho =\frac{{\rho }_{0}x}{l}$ , where ${\rho }_0$ is positive constant and $l$ is the total length of the rod. Find the net magnetic moment of the rod.

The ratio of the magnetic field at the centre of a current-carrying circular coil to magnetic moment is $x$. If the current and the radius both are doubled. The new ratio will become

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 $a$.
The magnetic dipole moments of the coil in each case respectively are:

A particle of mass $M$ and charge $q$ is moving in a circle of radius $R$ with speed $v$, where $v\ll$ speed of light. The ratio of the magnetic moment of the particle to its angular momentum is

A wire carrying current $\mathrm{I}$ is bent in the shape$\mathrm{ABCDEFA}$ as shown, where rectangle $\mathrm{ABCDA}$ and $\mathrm{ADEFA}$ are perpendicular to each other. If the sides of the rectangles are of lengths $\mathrm{a}$ and $\mathrm{b}$, then the magnitude and direction of magnetic moment of the loop $\mathrm{ABCDEFA}$ is :