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

$A$ 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 . . . . . .

If $m$ is the magnetic moment and $B$ is the magnetic field,then the torque is given by

$A$ uniform magnetic field of $3000 \; G$ is established along the positive $z-$direction. $A$ rectangular loop of sides $10 \; cm$ and $5 \; cm$ carries a current of $12 \; A$. What is the torque on the loop in the different cases shown in Figure? What is the force on each case? Which case corresponds to stable equilibrium?

Four wires of equal length are bent in the form of four loops $P, Q, R$ and $S.$ These are suspended in a uniform magnetic field and the same current is passed through them. The maximum torque will act on:

The torque required to hold a small circular coil of $10$ turns, area $1 \,mm^{2}$ and carrying a current of $\left(\frac{21}{44}\right) \,A$ in the middle of a long solenoid of $10^{3} \,turns/m$ carrying a current of $2.5 \,A$, with its axis perpendicular to the axis of the solenoid is