$A$ circular coil of radius $2 \text{ cm}$ and $125 \text{ turns}$ carries a current of $1 \text{ A}$. The coil is placed in a uniform magnetic field of magnitude $0.4 \text{ T}$. The axis of the coil makes an angle of $30^{\circ}$ with the direction of the magnetic field. The torque acting on the coil is $\alpha \times 10^{-4} \text{ N.m}$. The value of $\alpha$ is . . . . . . .

$A$ 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.

$A$ conducting ring of mass $2 \ kg$ and radius $0.5 \ m$ is placed on a smooth horizontal plane. The ring carries a current $i = 4 \ A$. $A$ horizontal magnetic field $B = 10 \ T$ is switched on at time $t = 0$ as shown in the figure. The initial angular acceleration of the ring will be:

$A$ circular coil has a moment of inertia of $0.8 \, kg \cdot m^2$ around any diameter and is carrying a current to produce a magnetic moment of $20 \, A \cdot m^2$. The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of $4 \, T$ is applied along the vertical,it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by $60^{\circ}$ will be:

$A$ metal wire of length '$L$' is bent to form a circular coil of number of turns '$n$'. The coil is placed in a magnetic field '$B$' and a current '$I$' is passed through the coil. The maximum torque acting on the coil is:

$A$ circular coil of $30$ turns and radius $8 \,cm$ carrying a current of $6 \,A$ is suspended vertically in a uniform horizontal magnetic field of magnitude $1.0 \,T$. The field lines make an angle of $20^{\circ}$ with the normal of the coil. The magnitude of the counter torque that must be applied to prevent the coil from turning is (in $\,Nm$)