Torque on Current Loop, Magnetic Dipole

A rectangular coil PQ has $2n$ turns, an area $2a$ and carries a current $2I$, (refer figure). The plane of the coil is at $60^{\text{o}}$ to a horizontal uniform magnetic field of flux density $B$. The torque on the coil due to magnetic force is

A cone made of insulating material has a total charge $\mathit{Q}$ spread uniformly over its sloping surface having a slant length $\mathit{L}$. The energy required to take a test charge $\mathit{q}$ from infinity to apex $\mathrm{A}$ of the cone will be
 

A wire loop carrying current $i$ is placed in the $x-y$ plane as shown in the figure. If an external uniform magnetic field $\overrightarrow{B}=B\hat{\text{i}}$ is switched on, then the torque acting on the loop is

$Q$ charge is uniformly distributed over the curve surface of a right circular cone of semi-vertical angle $\theta$ and height $h$. The cone is uniformly rotated about its axis at angular velocity $\omega$. Calculate associated magnetic dipole moment. $(h>R)$

A magnetic needle suspended parallel to a magnetic field requires $\sqrt{3} \mathrm{J}$ of work to turn it through $60°$. The torque needed to maintain the needle in this position will be

When magnetic moment$\left(\overrightarrow{\mathrm{M}}\right)$ and magnetic field $\left(\overrightarrow{\mathrm{B}}\right)$ are antiparallel to each other, then current carrying loop in magnetic field is in _____ equilibrium?

The given orientation is of unstable equilibrium.

What is the necessary condition for unstable equilibrium fo current carrying loop placed in uniform magnetic field?

When a current carrying loop is placed in a uniform magnetic field with its magnetic moment directed anti-parallel to the field then equilibrium is

A magnetic wire of dipole moment $4\mathrm{\pi } \mathrm{A} {\mathrm{m}}^2$ is bent in the form of semicircle. The new magnetic moment is

The magnetic dipole moment of current loop is independent of

A circular loop and a square loop are formed from two wires of same length and cross-section. Same current is passed through them. Then the ratio of their dipole moments is

A square loop is carrying a steady current $\mathrm{I}\mathrm{ }$ and the magnitude of its magnetic dipole moment is $\mathrm{m}$ . If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be:

Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole $\overrightarrow{m}.$ Which configuration has highest net magnetic dipole moment?

A wire of length $L$ metre carrying a current of $I$ ampere is bent in the form of a circle. Its magnitude of the magnetic moment will be:

A circular coil of $300$ turns and diameter $14 \mathrm{cm}$ carries a current of $15 \mathrm{A}$. Magnitude of the magnetic dipole moment associated with the coil is 

Gyromagnetic ratio is the ratio of magnetic moment $\mu$ to the orbital angular momentum $\left(l\right)$. Its numerical value for an electron is given by.

What is gyromagnetic ratio?

A circular coil of $300$ turns and diameter $14 \mathrm{cm}$ carries a current of $15 \mathrm{A}$. Magnitude of the magnetic dipole moment associated with the coil is 

Magnetic moment associated with the solenoid-