$A$ 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...... $Nm$.

$A$ closely wound solenoid of $2000$ turns and area of cross-section $1.6 \times 10^{-4} \;m^{2},$ carrying a current of $4.0 \;A,$ is suspended through its centre allowing it to turn in a horizontal plane.
$(a)$ What is the magnetic moment associated with the solenoid?
$(b)$ What is the force and torque on the solenoid if a uniform horizontal magnetic field of $7.5 \times 10^{-2} \;T$ is set up at an angle of $30^{\circ}$ with the axis of the solenoid?

Current $I$ is carried in a wire of length $L$. If the wire is bent into a circular coil of single turn,the maximum torque in a given magnetic field $B$ 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,

The radius of a circular ring of wire is $R$ and it carries a current of $I \, A$. At its centre,a smaller ring of radius $r$ with current $i$ and $N$ turns is placed. Assuming that the planes of the two rings are perpendicular to each other and the magnetic induction produced at the centre of the bigger ring is constant,then the torque acting on the smaller ring will be:

$A$ current-carrying coil is subjected to a uniform magnetic field. The coil will orient itself so that its plane becomes