$A$ square loop of side $2a$ carrying current $I$ is kept in the $xz$-plane with its centre at the origin. $A$ long wire carrying the same current $I$ is placed parallel to the $z$-axis and passes through the point $(0, b, 0)$,where $b \gg a$. The magnitude of the torque on the loop about the $z$-axis is:

$A$ circular coil of radius $R$ and $N$ turns has negligible resistance. As shown in the schematic figure,its two ends are connected to two wires and it is hanging by those wires with its plane being vertical. The wires are connected to a capacitor with charge $Q$ through a switch. The coil is in a horizontal uniform magnetic field $B_0$ parallel to the plane of the coil. When the switch is closed,the capacitor gets discharged through the coil in a very short time. By the time the capacitor is discharged fully,the magnitude of the angular momentum gained by the coil will be (assume that the discharge time is so short that the coil has hardly rotated during this time):

Four wires,each of length $2.0\,m$,are bent into four loops $P, Q, R$ and $S$ and then suspended in a uniform magnetic field. If the same current is passed in each,then the torque will be maximum on the loop:

$A$ 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?

$A$ current $i$ flows in a circular coil of radius $r$. If the coil is placed in a uniform magnetic field $B$ with its plane parallel to the field,the magnitude of the torque that acts on the coil is

$A$ circular coil of radius $4\, cm$ has $50$ turns. In this coil,a current of $2\, A$ is flowing. It is placed in a magnetic field of $0.1\, Wb/m^2$. The amount of work done in rotating it through $180^\circ$ from its equilibrium position will be ........ $J$.