Describing the magnetism of current carrying coils or microscopic particlesphysical quantity。The magnetic moment of plane current carrying coil is defined as m=iSe.Where, i is the current intensity;S is the coil area;E is formed with the current directionRight-hand spiralThe unit vector of the relationship.In a uniform external magnetic field, the resultant force on the plane current carrying coil is zero but the torque is not zero. This torque makes the magnetic moment m of the coil turn to the same direction as the direction of the external magnetic field B;In uniformradial distribution In the external magnetic field, the plane current carrying coil is deflected by torque.The working principle of many motors and electrical instruments is based on this.
magnetic momentIt is a physical property of magnet.be inExternal magnetic fieldThe magnet will feelmoment, forcing its magnetic moment along theMagnetic field lineDirection arrangement.The magnetic moment can be expressed as a vector.The direction of the magnetic moment of the magnet isGuide polepointRefers to the North PoleThe magnetic moment depends on the magnetism and quantity of the magnet.It is not just magnets that have magnetic moments,Current carrying circuit、Electronics、moleculeorplanetAnd so on, all have magnetic moments.
Scientists have yet to discover the existence ofMagnetic monopole。commonlyMagnetic materialThe magnetic field ofTaylor expansionOfMultipole expansion, due toMagnetic monopoleThe project is equal to zero. The first project isMagnetic dipoleItem, the second item isMagnetic quadrupole(quadrupole), and so on.The magnetic moment is also divided into magnetic dipole moment, magnetic quadrupole moment and so on.From the magnetic dipole moment and the magnetic quadrupole moment of the magnetic moment, the magnetic dipole item and the magnetic quadrupole item of the magnetic field can be calculated respectively.As the distance increases, the magnetic dipole moment becomes more important and becomes the main item. Therefore, the term magnetic moment is often used to refer to the magnetic dipole moment.In some textbooks, the definition of magnetic moment is the same as that of magnetic dipole moment.
Calculation formula
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The magnetic dipole moment of a current carrying cycle iselectric currentMultiply by loop area:
Among them,
Is the magnetic dipole moment,
Is the current,
Is the area vector.The direction of magnetic dipole moment and area vector is determined byRight-handed ruledecision.
Current carrying cycle in external magnetic field, the torque it receives and itspotential energyThe relationship with magnetic dipole moment is:
，
, where,
Is the moment,
Is the magnetic field,
Is the potential energy.
manyElementary particle, for exampleElectronics, both haveIntrinsic magnetic moment。This intrinsic magnetic moment is source of the many macroscopic magnetic forces, and many physical phenomena are also related to it.This magnetic moment is different from that of classical physics, but is different from that of particlesspinRelevant, must usequantum mechanicsTo explain.These intrinsic magnetic moments arequantizationThe smallest basic unit, often called“Magneton”（magneton）。For example, electronicspinMagnetic moment andBohr magnetonThe relationship of is:
, where, is the magnetic moment of the electron spin,Electron spin g factorIs a proportional constant, which isBohr magneton, electronicspin, YesReduced Planck constant。
Two magnetic sources
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In any physical system, there are two basic sources of magnetic moment:
chargeThe motion of, like an electric current, produces a magnetic moment.As long as we know all the current density distribution (or the position and speed of all the charges) in the physical system, we can theoretically calculate the magnetic moment.
Like electronicsprotonA class of elementary particles will produce magnetic moments due to spin.The magnitude of the intrinsic magnetic moment of each basic particle is a constant, which can be deduced theoretically, and the results obtained have also been verified to be highly accurate through experiments.For example, the measured value of the electronic magnetic moment is − 9.284764 × 10 joules/Tesla.The direction of the magnetic moment is completely determined by the spin direction of the particle (the measured value of the electronic magnetic moment is negative, which means that the magnetic moment of the electron is in the opposite direction to the spin).
The net magnetic moment of the whole physical system is the vector sum of all magnetic moments.For example,hydrogen atomThe magnetic field of is the vector sum of the following magnetic moments:
The spin of the electron.
The electrons move around the orbital region of the proton.
The spin of the proton.
As another example, the vector sum of the intrinsic magnetic moment of the unpaired electrons and the orbital magnetic moment of the material constituting the bar magnet is the magnetic moment of the bar magnet.
definition
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In an atom, electrons are wound byNucleusMotion with orbital magnetic moment;The electron hasSpin magnetic moment；Nucleus, protonneutronAnd other elementary particles also have their own spin magnetic moments.These studiesAtomic energy levelOffine structure , in magnetic fieldZeeman effectAnd magnetic resonance, which also shows that various basic particles have complex structures.
The magnetic moment of molecule is composed of the magnetic moment of electron orbit and the spin magnetic moment of electron and nucleus（μ=μs+μl=gsps+glpl)，Magnetic mediumThe magnetization of is the result of the external magnetic field acting on the molecular magnetic moment.
The variation of the magnetic moment of the ancient earth
Intrinsic attributes of particles.Each particle has a certain intrinsic magnetic moment.Spin sPoint particleThe magnetic moment μ of is given by μ=g (e/2m) p, where e and m are the charge and mass of the particle respectively, g is a numerical factor, and p is the spin angular momentum.Spin zeroParticle magnetic momentIs zero.For a particle with 1/2 spin, g=2; for a particle with 1 spin, g=1; for a particle with 3/2 spin, g=2/3. In theory, g=1/s is generally given.
The magnetic moment of particles can be measured by experiments.However, the experimental results do not agree with this, and the difference between them is called abnormal magnetic moment.For electrons, muonsprotonAnd neutrons, and accurately measure their g factors as
Electronic gl2=1.001159652193（10）
Muon gl2=1.001165923（8）
Proton gl2=2.792847386（63）
Neutron gl2=－1.91304275（45）
There are two sources of the anomalous magnetic moment of particles: one is the radiation correction of quantum electrodynamics, which is the case for electrons and muons. Even for point particles, the effect of the electromagnetic field generated by the particles on their own leads to a small change in the spin magnetic moment, which can be precisely calculated with quantum electrodynamics, and the results are in good agreement with the experimental measurements;On the other hand, due to the internal structure and strong interaction of particles, protons and neutrons belong to this situation. The abnormal magnetic moments of protons and neutrons are used to analyze their internal structures.
Various magnetic moments
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Magnetic moment of current carrying circuit
In a current carrying circuit, the magnetic moment is the current multiplied by the circuit area: u=I × S;
Where u is the magnetic moment, I is the current, and S is the area.
The direction of magnetic moment is the direction of current bypassRight-handed ruleThe direction determined.
Current carrying circuit in magnetic fieldmomentThe relationship between M and magnetic moment is:
manyElementary particle(For example, electrons) all have intrinsic magnetic moments, which are different from those of classical physics and must be usedquantum mechanicsTo explain it and thespinofThis intrinsic magnetic moment is the source of many magnetic forces at the macro levelphysical phenomenonIt is also related to this.These intrinsic magnetic moments arequantizationThat is, it has the smallest basic unit, often called“Magneton”(magneton) orMagnetic element, for exampleElectron spin magnetic momentThe absolute value of vector of is the sumBohr magnetonProportional relationship:
, usually measured inBohr magnetonorNucleon（nuclear magneton）。The magnetic moment relates to the spin of particles and/or the orbital motion of particles in the system.The following list shows the intrinsic magnetic moments of some particles:
Intrinsic magnetic moments and spins of some elementary particles
For more information on the physical relationship between magnetic moment and magnetization, see the entryMagnetization。
Current carrying circuit magnetic field
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Magnetic dipoleMagnetic field line。Viewed from the side, the magnetic dipole stands in the center of the drawing.
Current carrying circuits generate magnetic fields around them.This magnetic field includes dipole magnetic field and higher multipolar items.However, as the distance increases, these multipolar items will decrease more quickly. Therefore, only the dipole items are prominent items of the magnetic field at a distant location.
The Dirac δ function project of the dipole magnetic field creates the atomenergy levelSplit, thus formingHyperfine structure（hyperfine structure）。stayastronomyLi,hydrogen atomThe hyperfine structure of21cm spectral line, onelectromagnetic radiationOfradio wavesRange, except3K background radiationBesides, the universe is permeated with the broadest electromagnetic radiation.fromComposite era(recombination) toReionization eraAstronomical research can only rely on the observation of radio waves with 21 cm spectral lines.
Given several magnetic dipole momentssuperposition principle The total magnetic field is the total vector sum of each magnetic dipole moment.
Magnetic torque felt by magnetic dipole
Illustration
A square current carrying cycle in a uniform magnetic field.
As shown on the right, it is assumed that there is current
A square cycle of is in the external magnetic field
。The length of the four sides of a square loop is
, two of which are
The parallel side is perpendicular to the external magnetic field, and the angle arc between the other two sides and the magnetic field is
。
The magnetic torque felt by the two sides perpendicular to the external magnetic field is
The magnetic moments felt by the other two sides cancel each other.Note that the magnetic dipole moment of this cycle is
。Therefore, the magnetic torque felt in this cycle is
The area of current carrying cycle tends to zero and the current tends to infinity, while maintaining
If the current carrying cycle does not change, the current carrying cycle tends to an ideal magnetic dipole.Therefore, the magnetic torque felt by the magnetic dipole in the external magnetic field can also be expressed by the above equation.
When the magnetic dipole moment is perpendicular to the magnetic field, the magnitude of the magnetic torque is the maximum
；When the magnetic dipole moment is parallel to the magnetic field, the magnetic moment is equal to zero.
Magnetic moment of solenoid
A multi turn coil (orsolenoid）The magnetic moment of is the vector sum of the magnetic moments of each single turn coil.For identical turns (single-layer winding), the total magnetic moment can be obtained by multiplying the magnetic moment of a single turn coil by the number of turns.Then, the total magnetic moment can be used to calculate the magnetic field, torque, and stored energy in the same way as using a single turn coil.
Assume that the number of turns of solenoid is
, the coil area of each turn is
, the passing current is
, the magnetic moment is
Magnetic moment of electron
Electrons and many other kinds of particles have intrinsic magnetic moments.This is a kind ofquantumProperties, involvingquantum mechanics。For details, see the entryElectron magnetic dipole moment（electron magnetic dipole moment）。The microscopic intrinsic magnetic moments are gathered to form the giant magnetic effect and other physical phenomena, such aselectron spin resonance。
according tofrontClassical results of calculation,
；But, inDirac mechanicsLi,
；More accurately, due to the quantum electrodynamics effect, its practical value is slightly larger,
。
Note that because of the negative sign in this equation, the magnetic moment of the electron is opposite to the spin.For this physical behavior,Classical electromagnetismIt is assumed that the spin angular momentum is generated by the electrons around a certain axis of rotation.Because the electron is negatively charged, the current generated by this rotation is in the opposite direction, and the magnetic moment generated by this current carrying circuit is in the opposite direction to the spin.The same reasoning, positively chargedPositron(ElectronicAntiparticle）Its magnetic moment is in the same direction as the spin.
Atomic magnetic moment
Inside an atom, there may be many electrons.To calculate the total angular momentum of a multi electron atom, we must first sum the spin of each electron to get the total spin, and thenOrbital angular momentumSum up, get the total orbital angular momentum, and finally useangular momentum coupling (angular momentum coupling) The total angular momentum of an atom can be obtained by summing the total spin and the total orbital angular momentum.Atomic magnetic moment
Component of magnetic moment to magnetic field direction
yes
Among them,
Is the component of the total angular momentum to the direction of the magnetic field,
yesMagnetic quantum number, you can take 2J+1 integer value, - J, - J+1,..., J-1, J, any integer value.
Because the electron has a negative charge
Is a negative value.
Magnetic dipole in magnetic fielddynamics, different from inelectric fieldOfElectric dipoleDynamics of.The magnetic field will exert torque on the magnetic dipole, forcing it to followMagnetic field lineArrange.However, torque is the derivative of angular momentum with respect to time.Therefore, there will be spinPrecessionThat is, the spin direction will change.The physical behavior is expressed as
Among them,
yesRotating magnetic ratio（gyromagnetic ratio） ，
Is a magnetic field.
Note that the left-hand item of the equation is the derivative of angular momentum with respect to time, while the right-hand item is the moment.The magnetic field can be divided into two parts:
Among them,
Is the effective magnetic field (external magnetic field plus any self
In this way, we can getLandau Livriz Gilbert equation（Landau–Lifshitz–Gilbert equation）：
The first item on the right side of the equation describes the precession of the magnetic dipole around the effective magnetic field, and the second item is the damping item, which will make the precession gradually weaken and finally disappear.Landau Livriz Gilbert equation is one of the most basic equations for studying magnetization dynamics.
Magnetic moment of atomic nucleus
The nuclear system is anucleon（protonandneutron）It is a precise physical system.Spin is one of the quantum properties of nucleons.becauseNucleusThese quantum properties can be studied from the measured data of nuclear magnetic moment and more specifically from the measured data of nuclear magnetic dipole moment.
Although some isotopesexcited stateOfDecay periodThe natural existence state of most common atomic nuclei isground state。Of each isotope nucleusEnergy stateThere is a unique and obvious nuclear magnetic dipole moment, and its size is a constant. Through carefully designed experiments, it can be measured to a very high accuracy.This value is very sensitive to the individual contribution of each nucleon in the nucleus.If this value can be measured or predicted, it can reveal the nucleonwave functionThe connotation of.Nowadays, there are many theoretical models that can predict the value of nuclear magnetic dipole moment, and there are also many experimental techniques that can be used for nuclear testing.
Magnetic moment of molecule
Any molecule has a definite magnetic moment.This magnetic moment may be related to the energy state of the molecule.Generally speaking, the magnetic moment of a molecule is the sum of the following contributions, which are listed from large to small according to the typical intensity:
If there are unpaired electrons, it is the magnetic moment generated by their spin（ParamagnetismContribution)
The orbital motion of the electron, when in the ground state, produces a magnetic moment that is often proportional to the external magnetic field（DiamagnetismContribution)
According to the nuclear spin configuration,Nuclear spinThe total magnetic moment generated.
Example of molecular magnetism
oxygenMolecule, OtwoBecause of the spin of the outermost two unpaired electrons, it has strong paramagnetism.
carbon dioxideMolecule, COtwo, a very weak magnetic moment generated by the movement of the electron orbit, which is proportional to the external magnetic field.In some rare cases, if the molecule is composed of magnetic isotopes, such as C or O, the isotope nucleus will also contribute its nuclear magnetism to the magnetic moment of the molecule.
hydrogenMolecule, HtwoIf it is in a weak magnetic field (or zero magnetic field), it will show nuclear magnetism.Two Spins of Hydrogen MoleculeIsomer，OrthohydrogenorSecondary hydrogen, have this physical property[1]。
