$A$ charged particle (charge $= q$; mass $= m$) is rotating in a circle of radius $R$ with uniform speed $V$. The ratio of its magnetic moment $(\mu)$ to the angular momentum $(L)$ 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

$A$ straight wire carrying current $i$ is turned into a circular loop. If the magnitude of the magnetic moment associated with it in $MKS$ units is $M$,the length of the wire will be

$A$ loop carrying current $I$ lies in the $x$-$y$ plane as shown in the figure. The unit vector $\hat{k}$ is coming out of the plane of the paper. The magnetic moment of the current 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 ..... .

$A$ current-carrying small loop behaves like a small magnet. If $A$ is its area and $M$ is its magnetic moment,the current in the loop will be