$A$ coil in the shape of an equilateral triangle of side $10 \, cm$ lies in a vertical plane between the pole pieces of a permanent magnet producing a horizontal magnetic field of $20 \, mT$. The torque acting on the coil when a current of $0.2 \, A$ is passed through it and its plane becomes parallel to the magnetic field will be $\sqrt{x} \times 10^{-5} \, Nm$. The value of $x$ is ..... .

$A$ coil having $10 \text{ A m}^2$ magnetic moment is placed in a vertical plane and is free to rotate about its horizontal axis, which coincides with its diameter. $A$ uniform magnetic field of $2 \text{ T}$ in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of $90^{\circ}$ under the influence of the magnetic field. The moment of inertia of the coil is $0.1 \text{ kg m}^2$. What will be its angular speed (in $\text{ rad/s}$)?

$A$ circular coil has a moment of inertia of $0.8 \, kg \cdot m^2$ around any diameter and is carrying a current to produce a magnetic moment of $20 \, A \cdot m^2$. The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of $4 \, T$ is applied along the vertical,it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by $60^{\circ}$ will be:

$A$ closely wound solenoid of $2000$ turns and area of cross-section $1.6 \times 10^{-4} \;m^{2},$ carrying a current of $4.0 \;A,$ is suspended through its centre allowing it to turn in a horizontal plane.
$(a)$ What is the magnetic moment associated with the solenoid?
$(b)$ What is the force and torque on the solenoid if a uniform horizontal magnetic field of $7.5 \times 10^{-2} \;T$ is set up at an angle of $30^{\circ}$ with the axis of the solenoid?

Current $i$ is carried in a wire of length $L$. If the wire is turned into a circular coil,the maximum magnitude of torque in a given magnetic field $B$ will be

$A$ uniform magnetic field is established along the positive $z-$direction. $A$ rectangular loop,carrying a current $I,$ is suspended in this magnetic field. Which case corresponds to stable equilibrium?