$A$ 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

$A$ circular coil of $16$ turns and radius $10 \;cm$ carrying a current of $0.75 \;A$ rests with its plane normal to an external field of magnitude $5.0 \times 10^{-2} \;T$. The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released,it oscillates about its stable equilibrium with a frequency of $2.0 \;s^{-1}$. What is the moment of inertia of the coil about its axis of rotation?

The figure represents four positions of a current-carrying coil in a magnetic field directed towards the right. $\hat{n}$ represents the direction of the area vector of the coil. The correct order of potential energy is:

$A$ rectangular coil (dimension $5\,cm \times 2\,cm$) with $100\,turns$,carrying a current of $3\,A$ in the clockwise direction,is kept centered at the origin and in the $X-Z$ plane. $A$ magnetic field of $1\,T$ is applied along the $X$-axis. If the coil is tilted through $45^{\circ}$ about the $Z$-axis,then the torque on the coil is.....$Nm$.

$A$ square coil of side $10 \; cm$ consists of $20$ turns and carries a current of $12 \; A$. The coil is suspended vertically and the normal to the plane of the coil makes an angle of $30^{\circ}$ with the direction of a uniform horizontal magnetic field of magnitude $0.80 \; T$. What is the magnitude of torque (in $N \; m$) experienced by the coil?

$A$ square coil of side $10 \ cm$ having $200$ turns is placed in a uniform magnetic field of $2 \ T$ such that the plane of the coil is in the direction of the magnetic field. If the current through the coil is $3 \ mA$, then the torque acting on the coil is