Magnetic induction produced at the centre of a circular loop of radius $R$ carrying a current is $B$. The magnetic moment of the loop is $(\mu_0 = \text{permeability of free space})$

$A$ circular and a square coil are prepared from two identical metal wires and a current is passed through them. The ratio of the magnetic dipole moment associated with the circular coil to that with the square coil 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 . . . . . . .

$A$ conducting ring of radius $R$ and one turn is formed from a conducting wire of length $L$ and on passing current $I$ the obtained magnetic dipole moment is $m$. If this wire is then converted to a ring of two turns and on passing electric current $I$,the new magnetic dipole moment obtained is . . . . . . .

$A$ coil of $n$ turns and radius $R$ carries a current $I$. It is unwound and rewound again to make another coil of radius $\frac{R}{3}$,with the current remaining the same. The ratio of the magnetic moment of the new coil to that of the original coil is:

The magnetic field at the centre of a single-turn circular coil of a given length of wire carrying a current $I$ is $B$. If the same wire is bent into a circular coil of two turns and the same current $I$ is passed through it,the new magnetic field at the centre will be: