Magnetic Moment of a Current Loop

A current carrying loop is placed in magnetic field as shown in figure. Find time period of small oscillation around as axis passing through diameter of coil. Mass of coil is $\mathrm{m},$ radius is $\mathrm{R}.$

A magnetic dipole is placed as shown in figure. Find work done by external agent in rotating it by $90°$ anticlockwise and clockwise.

Magnetic field in a region is given by $\overrightarrow{\mathrm{B}}={\mathrm{B}}_0\hat{\mathrm{i}}+2{\mathrm{B}}_0 \hat{\mathrm{j}}.$ Find torque on the loop shown in figure.

A disk of radius $\mathrm{R}$ is rotated about an axis perpendicular to its plane and passing through its centre. If surface charge density $\mathrm{\sigma },$ at distance $\mathrm{r}$ from centre is given by $\mathrm{\sigma }=\mathrm{\alpha r}.$ Find magnetic dipole moment associated with disk. Assume angular speed to be $\mathrm{\omega }.$

A disk of radius $\mathrm{R}$ with charge $\mathrm{q}$ uniformly distributed over it is rotated with angular speed $\mathrm{\omega }.$ Find magnetic moment associated with it.

A ring of radius $\mathrm{R}$ with charge $\mathrm{q}$ uniformly distributed over it is rotated with angular speed $\mathrm{\omega }$ around its axis. Find magnetic moment of the ring.

A charge $\mathrm{q},$ mass $\mathrm{m}$ is moving in uniform circular motion under action of a magnetic field $\mathrm{B}.$ Find magnetic moment associated with the charge. Radius of circle is$\text{'}\mathrm{R}\text{'}.$

A ring carrying current $I$ lies in $x-z$ plane as shown. A short magnetic dipole with dipole moment directed along $x$-axis is fixed at origin. If the ring is free to move anywhere, then it will

Calculate the torque acting upon the following structure carrying current $/$ due to the magnetic field $B.$ Both the magnetic field and the structure are in the plane of paper as shown.

In the plane of coil a uniform magnetic field $B$ exists. Torque on the current carrying coil of radius $R$ is

A straight wire carrying current $i$ is turned into a circular loop. If the magnitude of magnetic moment associated with it in $M.K.S.$ unit is $M,$ the length of wire will be

Two particles, each of mass $m$ and charge $q$ are attached to the two ends of a light rigid rod of length $2R$. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is

Magnetic moment of revolving electron of charge $e$ and mass $m$ in terms of angular momentum $L$ of electron is

In a permanent magnet at room temperature

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 magnetic moment of an electron orbiting in a circular orbit of radius $r$ with a speed $v$ is equal to

A proton is revolving on a circular path of radius $2 \mathrm{mm}$ with frequency $10 \mathrm{Hz}$. Magnetic dipole moment associated with proton is

The ratio of angular momentum $L$ to the atomic dipole moment ${\mu }_i$ for hydrogen like atoms and ions is

An iron rod of volume ${10}^{-3} {\mathrm{m}}^3$ and relative permeability $1000$ is placed as core in a solenoid with$10 \mathrm{turns} {\mathrm{cm}}^{-1}$ . If a current of $0.5 \mathrm{A}$ is passed through the solenoid, then the magnetic moment of the rod will be :

A wire of length $l$, carrying current $i$, is bent in circle of radius $r$, then magnetic moment at centre of loop is