$A$ square coil of side $10 \; cm$ consists of $20$ turns and carries a current of $12 \; A$. The coil is suspended vertically and the normal to the plane of the coil makes an angle of $30^{\circ}$ with the direction of a uniform horizontal magnetic field of magnitude $0.80 \; T$. What is the magnitude of torque (in $N \; m$) experienced by the coil?

$A$ 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 $, T$)

$A$ small coil of $N$ turns has an effective area $A$ and carries a current $I$. It is suspended in a horizontal magnetic field $\overrightarrow{B}$ such that its plane is perpendicular to $\overrightarrow{B}$. The work done in rotating it by $180^\circ$ about the vertical axis 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.

$A$ rectangular loop carrying a current $i$ is placed in a uniform magnetic field $B$. The area enclosed by the loop is $A$. If there are $n$ turns in the loop,the torque acting on the loop is given by

$A$ current-carrying loop is placed in a uniform magnetic field. The torque acting on it does not depend upon