$A$ wire of length $10 \ m$ carrying a current of $1 \ A$ is bent into a circular loop. If a magnetic field of $2 \pi \times 10^{-4} \ T$ is applied on the loop,then the maximum torque acting on it is

$A$ 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?

$A$ coil carrying electric current is placed in a uniform magnetic field,then

$A$ uniform current-carrying ring of mass $m$ and radius $R$ is suspended by a massless string as shown. $A$ uniform magnetic field $B_0$ exists in the region to keep the ring in a horizontal position. Determine the current $I$ in the ring.

Derive an expression for the torque acting on a current-carrying loop which subtends an angle $\theta$ with a uniform magnetic field.

$A$ thin magnetic needle is placed in a magnetic field of $200 \ G$ with its axis at $30^{\circ}$ to the direction of the field. Find the magnetic moment of the needle if it experiences a torque of $0.012 \ Nm$ in this field. (in $Am^2$)