$A$ current $i$ flows in a circular coil of radius $r$. If the coil is placed in a uniform magnetic field $B$ with its plane parallel to the field,the magnitude of the torque that acts on the coil 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

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:

$A$ uniform magnetic field of $0.3 \; T$ is established along the positive $Z$-direction. $A$ rectangular loop in the $XY$-plane with sides $10 \; cm$ and $5 \; cm$ carries a current of $I = 12 \; A$ as shown. The torque on the loop is

$A$ uniform,constant magnetic field $\vec B$ is directed at an angle of $45^o$ to the $x-$ axis in the $xy-$ plane. $PQRS$ is a rigid square wire frame carrying a steady current $I_0,$ with its centre at the origin $O.$ At time $t = 0,$ the frame is at rest in the position shown in the figure,with its sides parallel to the $x$ and $y$ axis. Each side of the frame is of mass $M$ and length $L.$ Find the torque $\vec \tau$ acting on the frame.

$A$ current carrying circular loop of radius $2 \text{ cm}$ with unit normal $\hat{n} = \frac{\hat{i} + \hat{j}}{\sqrt{2}}$ is placed in a magnetic field $\vec{B} = B_0(3\hat{i} + 2\hat{k})$. If $B_0 = 4 \times 10^{-3} \text{ T}$ and current $I = 100\sqrt{2} \text{ A}$, the torque experienced by the loop is . . . . . . $\text{N}\cdot\text{m}$. $(\pi = 3.14)$