$A$ galvanometer coil has $500$ turns and each turn has an average area of $3 \times 10^{-4} \ m^{2}$. If a torque of $1.5 \ Nm$ is required to keep this coil parallel to the magnetic field when a current of $0.5 \ A$ is flowing through it,the strength of the magnetic field (in $T$) is:

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

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?

$A$ 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 ........ $J$.

$A$ 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 $B$ 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).