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:

Two wires of the same length are used to form a circle and a square. They carry the same current. The ratio of the magnetic moment of the circle to that of the square is:

$A$ thin circular wire carrying a current $I$ has a magnetic moment $M$. The shape of the wire is changed to a square and it carries the same current. It will have a magnetic moment

$A$ circular loop and a square loop are formed from two wires of same length and cross-section. The same current is passed through them. The ratio of their dipole moments is

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.

In the given diagram,a rod is rotating with angular velocity $\omega$. The mass of this rod is $m$,the charge is $q$,and the length is $l$. Find the magnetic moment of this rod.