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 loop of radius $R$ carries a current $I$. Another circular loop of radius $r (r \ll R)$ carries a current $i$ and is placed at the centre of the larger loop. The planes of the two circles are at right angles to each other. Find the torque acting on the smaller loop.

Write an expression for the torque acting on a current-carrying loop suspended in a uniform magnetic field.

$A$ small coil of $N$ turns has an effective area $A$ and carries a current $I$. It is suspended in a horizontal magnetic field $\overrightarrow{B}$ such that its plane is perpendicular to $\overrightarrow{B}$. The work done in rotating it by $180^\circ$ about the vertical axis is

$A$ rectangular coil $20\,cm \times 20\,cm$ has $100$ turns and carries a current of $1\,A$. It is placed in a uniform magnetic field $B = 0.5\,T$ with the direction of the magnetic field parallel to the plane of the coil. The magnitude of the torque required to hold this coil in this position is ........ $N-m$.

$A$ thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass $m$ and radius $r$ and it is in a uniform vertical magnetic field $B_0$,as shown in the figure. Initially,it hangs vertically downwards,because of acceleration due to gravity $g$,on two conducting supports at $P$ and $Q$. When a current $I$ is passed through the loop,the loop turns about the line $PQ$ by an angle $\theta$ given by