$A$ 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.

$A$ $250$-turn rectangular coil of length $2.1\, cm$ and width $1.25\, cm$ carries a current of $85\, \mu A$ and is subjected to a magnetic field of strength $0.85\, T.$ The work done to rotate the coil by $180^o$ against the torque is .............. $\mu J$.

$A$ circular coil of radius $10 \,cm$ with $100$ turns carrying a current of $0.5 \,A$ lies in a magnetic field of $2 \,T$ such that the normal drawn to the plane of the coil makes an angle $\theta$ with the direction of the field. Work done in rotating the coil to change the angle $\theta$ from $0^{\circ}$ to $180^{\circ}$ is

$A$ square loop of side $2a$ carrying current $I$ is kept in the $XZ$ plane with its centre at the origin. $A$ long wire carrying the same current $I$ is placed parallel to the $z$-axis and passes through the point $(0, b, 0)$,where $b >> a$. The magnitude of the torque on the loop about the $z$-axis is given by:

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

$A$ circular coil of radius $4\, cm$ has $50$ turns. In this coil,a current of $2\, A$ is flowing. It is placed in a magnetic field of $0.1\, Wb/m^2$. The amount of work done in rotating it through $180^\circ$ from its equilibrium position will be ........ $J$.