$A$ coil having $100$ turns, area of $5 \times 10^{-3} \, m^2$, carrying current of $1 \, mA$ is placed in a uniform magnetic field of $0.20 \, T$ such that the plane of the coil is perpendicular to the magnetic field. The work done in turning the coil through $90^{\circ}$ is . . . . . . $\mu J$.

$A$ $250$-turn rectangular coil of length $2.1\, cm$ and width $1.25\, cm$ carries a current of $85\, \mu A$ and is subjected to a magnetic field of strength $0.85\, T.$ The work done to rotate the coil by $180^o$ against the torque is .............. $\mu J$.

$A$ conducting ring of mass $2 \ kg$ and radius $0.5 \ m$ is placed on a smooth horizontal plane. The ring carries a current $i = 4 \ A$. $A$ horizontal magnetic field $B = 10 \ T$ is switched on at time $t = 0$ as shown in the figure. The initial angular acceleration of the ring will be:

The expression for the torque acting on a coil having area of cross-section $A$,number of turns $n$,placed in a magnetic field of strength $B$,making an angle $\theta$ with the normal to the plane of the coil,when a current $i$ is flowing in it,will be

$A$ circular coil of $30$ turns and radius $8.0\, cm$ carrying a current of $6.0\, A$ is suspended vertically in a uniform horizontal magnetic field of magnitude $1.0\, T$. The field lines make an angle of $60^o$ with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning. (in $, Nm$)

$A$ magnetic dipole with magnetic moment $p_m$ is placed parallel to an infinitely long straight wire carrying current $I$,as shown in the figure. Which of the following statements is correct?