$A$ uniform magnetic field is established along the positive $z-$direction. $A$ rectangular loop,carrying a current $I,$ is suspended in this magnetic field. Which case corresponds to stable equilibrium?

$A$ uniform magnetic field of $0.3 \text{ T}$ is established along the $+z$-direction. $A$ rectangular loop of sides $10 \text{ cm}$ and $5 \text{ cm}$ carries a current of $12 \text{ A}$ and is placed in the $xy$-plane as shown in the figure. The torque acting on the loop is $....... \text{ Nm}$.

$A$ current-carrying rectangular coil is placed in a uniform magnetic field. In which orientation will the coil not tend to rotate?

$A$ disc of radius $r$ carrying a positive charge $q$ is rotating with an angular speed $\omega$ in a uniform magnetic field $B$ about a fixed axis as shown in the figure,such that the angle made by the axis of the disc with the magnetic field is $\theta$. The torque applied by the axis on the disc 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.....$Nm$.

$A$ 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 $\,Nm$)