$A$ 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).

The figure below shows the north and south poles of a permanent magnet in which an $n$-turn coil of cross-sectional area $A$ is placed. When a current $i$ is passed through the coil,the plane of the coil makes an angle $\theta$ with respect to the direction of the magnetic field $B$. The torque on the coil is:

Four wires each of length $2.0 \, m$ are bent into four loops $P$,$Q$,$R$ (labeled as $P$ in the image,but distinct),and $S$ and then suspended in a uniform magnetic field. The same current is passed through each loop. Which statement is correct?

$A$ 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 ..... .

Two identical conducting wires $A$ and $B$ of same dimensions and same material are bent in the form of circular coils. Wire $A$ consists of a single turn,whereas wire $B$ consists of $2$ turns. Both these wires are then suspended in a uniform magnetic field with their planes parallel to one another,and the same current is passed through them. Which statement is correct?

$A$ rectangular coil $20\,cm \times 20\,cm$ has $100$ turns and carries a current of $1\,A$. It is placed in a uniform magnetic field $B = 0.5\,T$ with the direction of the magnetic field parallel to the plane of the coil. The magnitude of the torque required to hold this coil in this position is ........ $N-m$.