$A$ 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

The magnetic moments associated with two closely wound circular coils $A$ and $B$ of radius $r_A = 10 \ cm$ and $r_B = 20 \ cm$ respectively are equal. If $N_A, I_A$ and $N_B, I_B$ are the number of turns and current of $A$ and $B$ respectively,then which of the following relations is correct?

$A$ 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:

$A$ current $I$ is flowing in a conductor of length $L$. When it is bent in the form of a circular loop,its magnetic moment will be

$A$ 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 ..... .

$A$ wire of length $L \ m$ carrying a current $I \ A$ is bent in the form of a circle. The magnitude of its magnetic moment is