The $(\tau - \theta)$ graph for a current-carrying coil in a magnetic field is:

$A$ circular coil of radius $9 \, cm$ carrying a current of $2 \, A$ is free to rotate about an axis in its plane perpendicular to an external magnetic field of $\pi \times 10^{-2} \, T$. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a time period of $\frac{1}{3} \, s$. If the moment of inertia of the coil about its axis of rotation is $9 \times 10^{-5} \, kg \cdot m^2$, the number of turns of the coil 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?

In the figure shown,a coil of single turn is wound on a sphere of radius $R$ and mass $m$. The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. The current in the coil is $i$. If the sphere is in equilibrium,the value of the magnetic field $B$ is:

An electron in the ground state of a hydrogen atom is revolving in an anticlockwise direction in a circular orbit of radius $r$. The atom is placed in a uniform magnetic field $B$ in such a way that the magnetic moment of the orbital electron makes an angle of $30^{\circ}$ with the magnetic field. The torque experienced by the orbital electron is

$A$ circular current loop of magnetic moment $M$ is in an arbitrary orientation in an external uniform magnetic field $\vec{B}$. The work done to rotate the loop by $30^{\circ}$ about an axis perpendicular to its plane is