Two wires of same length are bent to form a circular loop with two turns and a square loop of one turn. Both of them carry the same current. The ratio of the magnetic moment of the circular loop of two turns to that of the square loop is

Magnetic induction at the centre of a circular loop of area $\pi \ m^2$ is $0.1 \ T$. The magnetic moment of the loop is ( $\mu_0 = \text{permeability of air}$ ).

Magnetic field at the centre of a circular loop of area $A$ is $B$. Then the magnetic moment of the loop is ($\mu_0$ is the permeability of free space).

$A$ conducting solid sphere of radius $R$ and mass $M$ carries a charge $Q$. The sphere is rotating about an axis passing through its center with a uniform angular speed $\omega$. The ratio of the magnitudes of the magnetic dipole moment to the angular momentum about the same axis is given as $\alpha \frac{Q}{2 M}$. 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 . . . . . . .

The number of turns of two circular coils $A$ and $B$ are $300$ and $200$ respectively. The magnetic moments of the two coils $A$ and $B$ are in the ratio $1:2$. If the two coils carry equal currents, then the ratio of radii of coils $A$ and $B$ is