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

In Bohr's hydrogen like atom magnetic dipole moment in ${\mathrm{n}}^{\mathrm{th}}$ orbit is expressed as.

When charged particle moves in circle then vectorial representation of magnetic dipole moment is ( if $\overrightarrow{\mathrm{L}}$ is angular momentum)

An electron revolves around the nucleus of hydrogen like atom then magnetic moment of electron is

A bar magnet is placed in the position of stable equilibrium in a uniform magnetic field of induction B. If it is rotated through an angle $180°$
 , then the work is (M= magnetic dipole moment of bar magnet).

In which orientation,a dipole placed in a uniform electric field is in (i) stable equilibrium (ii) unstable equilibrium?

Calculate the spin only magnetic moment of $F{e}^{+2}$ (.Atomic no.=$26$.)

Define spin magnetic moment?

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.

Which of the following is the correct orientation 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

What is Bohr magneton ?

The value of Bohr magneton (${\mu }_B$​) is $9.3\times {10}^y{\mathrm{Am}}^2$. The value of $y$ 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.