$A$ uniform magnetic field of $0.3 \; T$ is established along the positive $Z$-direction. $A$ rectangular loop in the $XY$-plane with sides $10 \; cm$ and $5 \; cm$ carries a current of $I = 12 \; A$ as shown. The torque on the loop is

$A$ circular coil of radius $9 \, cm$ carrying a current of $2 \, A$ is free to rotate about an axis in its plane perpendicular to an external magnetic field of $\pi \times 10^{-2} \, T$. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a time period of $\frac{1}{3} \, s$. If the moment of inertia of the coil about its axis of rotation is $9 \times 10^{-5} \, kg \cdot m^2$, the number of turns of the coil is . . . . . .

$A$ circular coil having $N$ turns and radius $R$ carrying current $I$ is held in the $z-x$ plane in a magnetic field $B\hat{k}$. The torque on the coil due to the magnetic field in $N-m$ is:

$A$ disc of radius $r$ carrying a positive charge $q$ is rotating with an angular speed $\omega$ in a uniform magnetic field $B$ about a fixed axis as shown in the figure,such that the angle made by the axis of the disc with the magnetic field is $\theta$. The torque applied by the axis on the disc is:

$A$ rectangular conducting loop consists of two wires on two opposite sides of length $l$ joined together by rods of length $d$. The wires are each of the same material but with cross-sections differing by a factor of $2$. The thicker wire has a resistance $R$ and the rods are of low resistance,which in turn are connected to a constant voltage source $V_{0}$. The loop is placed in a uniform magnetic field $\vec{B}$ at $45^{\circ}$ to its plane. Find the torque exerted by the magnetic field on the loop about an axis through the centers of the rods.

$A$ 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