What happens when a magnet is cut in half?

Important Questions on Matter and Magnetism

MEDIUM

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

An insulating thin rod of length $l$ has a linear charge density $\rho \left(x\right)={\rho }_0\frac{x}{l}$ on it. The rod is rotated about an axis passing through the origin $\left(x=0\right)$ and perpendicular to the rod. If the rod makes $n$ rotations per second, then the time averaged magnetic moment of the rod is:

MEDIUM

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

A thin rod of length $L$ is magnetized and has magnetic moment $M$. The rod is then bent in a semicircular arc. The magnetic moment in the new shape is

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

A large magnet is broken into two pieces so that their lengths are in the ratio $1:2$. The ratio of their magnetic moments is 

HARD

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

What is magnetic dipole moment? Derive the expression for torque on a bar magnet placed in a uniform magnetic field.

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

A circular coil having $\mathrm{N}$ turns and radius $\mathrm{r}$ carries a current $\mathrm{I}.$ It is held in the $\mathrm{X}\mathrm{Z}$ plane in a magnetic field $\mathrm{B}\widehat{\mathrm{i}}$ . The torque on the coil due to the magnetic field is:

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

The magnetic moment of two bar magnets are $\overrightarrow{{\mathrm{M}}_1}$ and $\overrightarrow{{\mathrm{M}}_2}$. If angle between them is $\mathrm{\theta }$, then write the value of resultant magnetic moment.

HARD

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

A bar magnet of length $14 \mathrm{cm}$ is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of $18 \mathrm{cm}$ from the center of the magnet. If $B_H=0.4 \mathrm{G}$, the magnetic moment of the magnet is $\left(1 \mathrm{G}={10}^{-4} \mathrm{T}\right)$

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

What is the magnitude of the equatorial fields due to a bar magnet of length $5.0 \mathrm{cm}$ at a distance $75 \mathrm{cm}$ from its mid point? The magnetic moment of the bar magnet is $0.75 \mathrm{A} {\mathrm{m}}^2$.

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

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:

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

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?

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

Write SI unit of magnetic dipole moment..

HARD

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

Two short bar magnets of length $1cm$ each have magnetic moments $1.20 \mathrm{A} {\mathrm{m}}^2$ and $1.00 \mathrm{A} {\mathrm{m}}^2$ respectively. They are placed on a horizontal table parallel to each other with their $\text{N}$ poles pointing towards the south. They have a common magnetic equator and are separated by a distance of $20.0 \mathrm{cm}$. The value of the resultant horizontal magnetic induction at the mid-point $\text{O}$ of the line joining their centres is close to
( Horizontal component of earth's magnetic induction is $3.6\times {10}^{-5} \mathrm{Wb} {\mathrm{m}}^{-2}$ )

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

A straight steel wire of length $l$ has magnetic moment $m$. If the wire is bent in the form of a semicircle, what is the new value of the magnetic dipole moment?

MEDIUM

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

A long magnetic needle of length $2l$ magnetic moment $\mathit{M}$ and pole strength $m$ is broken into two pieces at the middle. The magnetic moment and pole strength of each piece will be

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

A bar magnet of magnetic moment $M$ is bent to form a semicircle. What is the magnetic moment of the bent magnet?

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

The pole strength of poles of a bar magnet of effective length $0.1\mathrm{m}$ is $40 \mathrm{A}-\mathrm{m}$. Calculate it's magnetic moment.

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

A magnet of pole strength $m$ and length $l$ is broken into two pieces. The pole strength of each piece is

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

The magnetic dipole moment of a short magnetic dipole at a distant point along the equator of magnet has a magnitude of $X$ in SI units. If the distance between point and the magnet is halved then the magnitude of dipole moment will be

HARD

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

The magnetic flux near the axis and inside the air-core solenoid of length $60 \mathrm{cm}$ carrying current $I$ is $1.57\times {10}^6\mathrm{ Wb}.$ Its magnetic moment will be (cross-sectional area of a solenoid is very small as compared to its length, ${\mu }_0=4\pi \times {10}^{-7}$ SI units)

HARD

Physics>Electricity and Magnetism>Matter and Magnetism>Change in Dipole Moment of a Bar Magnet After Being Cut

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are $T_h$ and $T_c$ respectively, then: