“Magnetic dipole”的意思、由来-开放百科全书

词条

Magnetic dipole

释义

External magnetic field produced by a magnetic dipole moment
Internal magnetic field of a dipole
Forces between two magnetic dipoles
Dipolar fields from finite sources
Notes
References

{{multiple image
| left
| footer = The magnetic field and magnetic moment, due to natural magnetic dipoles (left), or an electric current (right). Either generates the same field profile.^[1]
| width1 = 190
| image1 = Magnetic field due to dipole moment.svg
| caption1 = Dipole moment m.
| width2 = 160
| image2 = Magnetic field due to current.svg
| caption2 = Electric current I.

A magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the dimensions{{clarify|reason=which dimensions?|date=March 2019}} of the source are reduced to zero while keeping the magnetic moment constant. It is a magnetic analogue of the electric dipole, but the analogy is not perfect. In particular, a magnetic monopole, the magnetic analogue of an electric charge, has never been observed. Moreover, one form of magnetic dipole moment is associated with a fundamental quantum property—the spin of elementary particles.

The magnetic field around any magnetic source looks increasingly like the field of a magnetic dipole as the distance from the source increases.

External magnetic field produced by a magnetic dipole moment

In classical physics, the magnetic field of a dipole is calculated as the limit of either a current loop or a pair of charges as the source shrinks to a point while keeping the magnetic moment {{math|m }} constant. For the current loop, this limit is most easily derived for the vector potential. Outside of the source region, this potential is (in SI units)^[2]

with {{math|4π r²}} being the surface of a sphere of radius {{math|r}};

and the magnetic flux density (strength of the B-field) in teslas is^[2]

Equivalently, if is the unit vector in the direction of ^[3]

In spherical coordinates with the magnetic moment aligned with the z-axis, if we use , then this relation can be expressed as

Alternatively one can obtain the scalar potential first from the magnetic pole limit,

and hence the magnetic field strength (or strength of the H-field) in ampere-turns per meter is

The magnetic field is symmetric under rotations about the axis of the magnetic moment.

Internal magnetic field of a dipole

The two models for a dipole (current loop and magnetic poles), give the same predictions for the magnetic field far from the source. However, inside the source region they give different predictions. The magnetic field between poles is in the opposite direction to the magnetic moment (which points from the negative charge to the positive charge), while inside a current loop it is in the same direction (see the figure to the right). Clearly, the limits of these fields must also be different as the sources shrink to zero size. This distinction only matters if the dipole limit is used to calculate fields inside a magnetic material.

If a magnetic dipole is formed by making a current loop smaller and smaller, but keeping the product of current and area constant, the limiting field is

where {{math|n {{=}} {{sfrac|x|{{abs|x}}}}}} is a unit vector, and {{math|δ(x)}} is the Dirac delta function in three dimensions. Unlike the expressions in the previous section, this limit is correct for the internal field of the dipole.

If a magnetic dipole is formed by taking a "north pole" and a "south pole", bringing them closer and closer together but keeping the product of magnetic pole-charge and distance constant, the limiting field is

These fields are related by {{math|B {{=}} μ₀(H + M)}}, where

is the magnetization.

Forces between two magnetic dipoles

{{See also|Force between magnets#Magnetic dipole-dipole interaction}}

The force {{math|F}} exerted by one dipole moment {{math|m₁}} on another {{math|m₂}} separated in space by a vector {{math|r}} can be calculated using:^[4]

or ^[5]^[6]

where {{math|r}} is the distance between dipoles. The force acting on {{math|m₁}} is in the opposite direction.

The torque can be obtained from the formula

Dipolar fields from finite sources

The magnetic scalar potential {{math|ψ}} produced by a finite source, but external to it, can be represented by a multipole expansion. Each term in the expansion is associated with a characteristic moment and a potential having a characteristic rate of decrease with distance {{math|r}} from the source. Monopole moments have a {{math|1/r}} rate of decrease, dipole moments have a {{math|1/r²}} rate, quadrupole moments have a {{math|1/r³}} rate, and so on. The higher the order, the faster the potential drops off. Since the lowest-order term observed in magnetic sources is the dipolar term, it dominates at large distances. Therefore, at large distances any magnetic source looks like a dipole of the same magnetic moment.

Notes

1. ^{{cite book|author=I.S. Grant, W.R. Phillips|title=Electromagnetism|edition=2nd|publisher=Manchester Physics, John Wiley & Sons|year=2008|isbn=978-0-471-92712-9}}
2. ^¹{{harvnb|Chow|2006|pages=146–150}}
3. ^{{harvnb|Jackson|1975|p=182}}
4. ^{{cite book|title=Introduction to Electrodynamics|edition=3rd |author=D.J. Griffiths|publisher=Pearson Education|page=276|year=2007|isbn=81-7758-293-3}}
5. ^{{harvnb|Furlani|2001|p=140}}
6. ^{{cite journal |year=1998 |title= An Analytic Solution for the Force between Two Magnetic Dipoles|author1=K.W. Yung |author2=P.B. Landecker |author3=D.D. Villani |url=http://downloads.hindawi.com/archive/1998/079537.pdf|format=PDF |accessdate=November 24, 2012 }}

References

{{cite book

|last=Chow
|first=Tai L.
|title=Introduction to electromagnetic theory: a modern perspective
|publisher = Jones & Bartlett Learning
|year=2006
|isbn=978-0-7637-3827-3
|ref=harv
}}

{{Cite book |last1=Jackson |first1=John D. | title=Classical Electrodynamics | edition=2nd | publisher=Wiley | year=1975 | isbn=0-471-43132-X |ref=harv}}
{{cite book

|last = Furlani
|first = Edward P.
|title = Permanent Magnet and Electromechanical Devices: Materials, Analysis, and Applications
|publisher = Academic Press
|year = 2001
|page =
|url = https://books.google.com/books?id=irsdLnC5SrsC&dq=permanent+magnet+and+electromechanical+devices&printsec=frontcover&q=3.130
|isbn = 0-12-269951-3
|ref=harv
}}

{{cite journal

| author = Schill, R. A.
| title = General relation for the vector magnetic field of a circular current loop: A closer look
| year = 2003
| journal = IEEE Transactions on Magnetics
| volume = 39
| issue = 2
| pages = 961–967
| doi = 10.1109/TMAG.2003.808597|bibcode = 2003ITM....39..961S }}{{Refend}}

3 : Magnetostatics|Magnetism|Electric and magnetic fields in matter

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。