An electron revolving in a circular orbit of radius $r$ with velocity $v$ and frequency $f$ has an orbital magnetic moment $M$. If the frequency of revolution is doubled,then the new magnetic moment will be:

An insulating thin rod of length $l$ has a linear charge density $\rho(x) = \rho_0 \frac{x}{l}$ on it. The rod is rotated about an axis passing through the origin $(x = 0)$ and perpendicular to the rod. If the rod makes $n$ rotations per second,then the time-averaged magnetic moment of the rod is:

The unit of magnetic moment is . . . . . . .

$A$ closely wound solenoid of $800$ turns and area of cross-section $2.5 \times 10^{-4} \; m^2$ carries a current of $3.0 \; A$. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?

$A$ 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 $\alpha$ particle is revolving in a circle of radius $r$ with frequency $f$. Find the value of its magnetic dipole moment.