$A$ circular coil of $1000$ turns and area of cross-section $1.5 \times 10^{-4} \, m^2$ is carrying a current of $2 \, A$. What is the magnetic moment associated with the coil in $Am^2$?

$A$ 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 magnitude of magnetic induction at a point on the axis at a large distance $(r)$ from the centre of a circular coil of $n$ turns and area $A$ carrying current $I$ is given by:

In a hydrogen atom,an electron revolves around the nucleus at a frequency of $6.6 \times 10^{15} \, \text{rev/sec}$ in an orbit of radius $0.528 \, \mathring{A}$. The magnetic moment in $\text{A} \cdot \text{m}^2$ is:

An insulated wire is wound so that it forms a flat coil with $N = 200$ turns. The radius of the innermost turn is $r_1 = 3\text{ cm}$, and of the outermost turn $r_2 = 6\text{ cm}$. If $20\text{ mA}$ current flows in it, then the magnetic moment will be $\alpha \times 10^{-2}\text{ A.m}^2$. The value of $\alpha$ 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 ..... .