$A$ rectangular coil has $2n$ turns,an area $2a$ and carries a current $2I$. The plane of the coil is at $60^{\circ}$ to a horizontal uniform magnetic field of flux density $B$. The torque on the coil due to magnetic force is

$A$ thin non-conducting disc of radius $R$ is rotating clockwise (see figure) with an angular velocity $\omega$ about its central axis,which is perpendicular to its plane. Both its surfaces carry positive charges of uniform surface density. Half the disc is in a region of a uniform,unidirectional magnetic field $B$ parallel to the plane of the disc,as shown. Then,

$A$ small coil $C$ with $N = 200$ turns is mounted on one end of a balance beam and introduced between the poles of an electromagnet as shown in the figure. The cross-sectional area of the coil is $A = 1.0 \, cm^2$,and the length of the arm $OA$ of the balance beam is $l = 30 \, cm$. When there is no current in the coil,the balance is in equilibrium. On passing a current $I = 22 \, mA$ through the coil,the equilibrium is restored by putting an additional counterweight of mass $\Delta m = 60 \, mg$ on the balance pan. Find the magnetic induction $B$ at the spot where the coil is located. (in $, T$)

$A$ uniform,constant magnetic field $\vec B$ is directed at an angle of $45^o$ to the $x-$ axis in the $xy-$ plane. $PQRS$ is a rigid square wire frame carrying a steady current $I_0,$ with its centre at the origin $O.$ At time $t = 0,$ the frame is at rest in the position shown in the figure,with its sides parallel to the $x$ and $y$ axis. Each side of the frame is of mass $M$ and length $L.$ Find the torque $\vec \tau$ acting on the frame.

$A$ circular coil of $20$ turns and radius $10\, cm$ is placed in a uniform magnetic field of $0.10\, T$ normal to the plane of the coil. If the current in the coil is $5\, A$,then the torque acting on the coil will be...... $Nm$.

$A$ square coil of side $10 \ cm$ having $200$ turns is placed in a uniform magnetic field of $2 \ T$ such that the plane of the coil is in the direction of the magnetic field. If the current through the coil is $3 \ mA$,then the torque acting on the coil is