$A$ current-carrying small loop behaves like a small magnet. If $A$ is its area and $M$ is its magnetic moment,the current in the loop will be

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 $q$) is moving in a circle of radius $R$ with uniform speed $v.$ The associated magnetic moment $\mu$ is given by

$A$ 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 $....$ .

Due to the flow of current in a circular loop of radius $R$,the magnetic field produced at the centre of the loop is $B$. The magnetic moment of the loop is:

What is the magnetic dipole moment for a coil? Write its $SI$ unit and dimensional formula,and explain its stable and unstable equilibrium.