$A$ 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

$A$ circular loop and a square loop are formed from two wires of same length and cross-section. The same current is passed through them. The ratio of their dipole moments 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: (Where $N_A, I_A$ and $N_B, I_B$ are the number of turns and current of $A$ and $B$ respectively)

$A$ 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 . . . . . . .

$A$ 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 $....$ .

$A$ 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