$A$ thin wire of length $L$ made of an insulating material is bent to form a circular loop and a positive charge $q$ is given so that it is distributed uniformly around the circumference of the loop. The loop is then rotated with an angular speed $\omega$ about an axis passing through its centre. If a uniform magnetic field $B$ directed parallel to the plane of the loop is applied,then the magnitude of the magnetic torque on the loop is:

$A$ current-carrying loop is placed in a uniform magnetic field in four different orientations,$I$,$II$,$III$,and $IV$. Arrange them in the decreasing order of potential energy.

$A$ 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):

$A$ current-carrying loop is placed in a uniform magnetic field $B$ in different orientations $I$, $II$, $III$, and $IV$ as shown in the figure. The correct order of decreasing potential energy is ($\hat{n}$ is the unit vector normal to the plane of the loop).

$A$ small circular loop of conducting wire has radius $a$ and carries current $I$. It is placed in a uniform magnetic field $B$ perpendicular to its plane such that when rotated slightly about its diameter and released,it starts performing simple harmonic motion of time period $T$. If the mass of the loop is $m$,then find the expression for $T$.

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