$A$ current-carrying loop is placed in a uniform magnetic field in four different orientations,$I$,$II$,$III$,and $IV$. Arrange them in the decreasing order of potential energy.

$A$ circular coil of $16$ turns and radius $10 \;cm$ carrying a current of $0.75 \;A$ rests with its plane normal to an external field of magnitude $5.0 \times 10^{-2} \;T$. The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released,it oscillates about its stable equilibrium with a frequency of $2.0 \;s^{-1}$. What is the moment of inertia of the coil about its axis of rotation?

$A$ circular coil having $200$ turns,$2.5 \times 10^{-4} \text{ m}^2$ area and carrying $100 \mu\text{A}$ current is placed in a uniform magnetic field of $1 \text{ T}$. Initially,the magnetic dipole moment $(\vec{M})$ was directed along $\vec{B}$. The amount of work required to rotate the coil through $90^{\circ}$ from its initial orientation such that $\vec{M}$ becomes perpendicular to $\vec{B}$ is . . . . $\mu\text{J}$.

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

$A$ 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?

$A$ circular loop of radius $R$ carries a current $I$. Another circular loop of radius $r (r \ll R)$ carries a current $i$ and is placed at the centre of the larger loop. The planes of the two circles are at right angles to each other. Find the torque acting on the smaller loop.