$A$ 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

$A$ current-carrying loop is placed in a uniform magnetic field $B$ in different orientations $I$, $II$, $III$, and $IV$ as shown in the figure. The correct order of decreasing potential energy is ($\hat{n}$ is the unit vector normal to the plane of the loop).

$A$ 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 $b \gg a$. The magnitude of the torque on the loop about the $z$-axis is:

$A$ $250$-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 .............. $\mu J$.

$A$ uniform,constant magnetic field $\vec B$ is directed at an angle of $45^o$ to the $x-$ axis in the $xy-$ plane. $PQRS$ is a rigid square wire frame carrying a steady current $I_0,$ with its centre at the origin $O.$ At time $t = 0,$ the frame is at rest in the position shown in the figure,with its sides parallel to the $x$ and $y$ axis. Each side of the frame is of mass $M$ and length $L.$ Find the torque $\vec \tau$ acting on the frame.

$A$ closely wound solenoid of $2000$ turns and area of cross-section $1.5 \times 10^{-4} \, m^2$ carries a current of $2.0 \, A$. It is suspended through its centre and perpendicular to its length,allowing it to turn in a horizontal plane in a uniform magnetic field of $5 \times 10^{-2} \, T$ making an angle of $30^o$ with the axis of the solenoid. The torque on the solenoid will be: