A negatively charged particle is revolving in a circle of radius $r$ out of the following which one figure represents the correct direction of $\overrightarrow{\mathit{L}}$ and $\overrightarrow{M}$ ($L$ is the angular momentum of the particle and $\overrightarrow{M}$ is the magnetic moment of the particle):

The ratio of the magnetic field at the centre of a current-carrying circular coil to magnetic moment is $x$. If the current and the radius both are doubled. The new ratio will become

The rectangular coil of area $A$ is in a field $B.$ Find the torque about the $Z$-axis when the coil lies in the position shown and carries a current $I.$

A coil of $50$ turns carrying a current of $2\mathrm{A}$ in a magnetic field of $0.5\mathrm{T}$. The torque acting on the coil is

A $100$ turns coil shown in figure carries a current of $2 \mathrm{A}$ in a magnetic field $B=0.2 \mathrm{Wb} {\mathrm{m}}^{-2}.$ The torque acting on the coil is

The rectangular loop of dimensions $0.4 \mathrm{m}\times 0.2 \mathrm{m}$ shown in the figure consists of $50$ closely wrapped turns and is hinged along the $z$-axis. The plane of the loop makes an angle of $30°$ with the $y$-axis. The current in the windings is $0.5 \mathrm{A}$.

The torque exerted on the loop in this position by a magnetic field $\overrightarrow{B}=\hat{j}1.0 \mathrm{T}$

A rectangular loop of sides $10 \mathrm{cm}$ and $5 \mathrm{cm}$, carrying a current $I$ of $12 \mathrm{A}$, is placed in different orientations as shown in the figure below.
(a)  (b)

(c)  (d)

If there is a uniform magnetic field of $0.3 \mathrm{T}$ in the positive $z$ direction, in which orientations the loop would be in $\left(\mathrm{i}\right)$ stable equilibrium and $\left(\mathrm{ii}\right)$ unstable equilibrium?