$A$ circular coil of radius $R$ and a current $I$,which can rotate about a fixed axis passing through its diameter,is initially placed such that its plane lies along the magnetic field $B$. The kinetic energy of the loop when it rotates through an angle $90^{\circ}$ is: (Assume that $I$ remains constant)

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?

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

Two similar wires of equal lengths are bent in the form of a square and a circular loop. They are suspended in a uniform magnetic field and the same current is passed through them. The torque experienced by:

$A$ current-carrying coil experiences a torque due to a magnetic field. The value of the torque is $80 \%$ of the maximum possible torque. The angle between the magnetic field and the normal to the plane of the coil is

$A$ 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 ..... .