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Electromagnetism
Electricity · Magnetism
Magnetostatics
 · Ampère’s law · Electric current · Magnetic field · Magnetic flux · Biot–Savart law · Magnetic dipole moment · Gauss’s law for magnetism ·
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In physics, astronomy, chemistry, and electrical engineering, the term magnetic moment of a system (such as a loop of electric current, a bar magnet, an electron, a molecule, or a planet) usually refers to its magnetic dipole moment, and is a measure of the strength of the system's net magnetic source. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Magnetostatics is the study of static Magnetic fields In Electrostatics the charges are stationary whereas here the currents are stationary or dc(direct In Classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère, relates the integrated Magnetic field around a closed Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Magnetic flux, represented by the Greek letter Φ ( Phi) is a measure of quantity of Magnetism, taking into account the strength and the extent of a Magnetic The Biot–Savart Law is an equation in electromagnetism that describes the Magnetic field B generated by an Electric current. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties Electrical engineering, sometimes referred to as electrical and electronic engineering, is a field of Engineering that deals with the study and application of Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. A magnet (from Greek grc μαγνήτης λίθος " Magnesian stone" is a material or object that produces a Magnetic field. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Specifically, magnetic dipole moment quantifies the contribution of the system's internal magnetism to the external dipolar magnetic field produced by the system (i. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges e. the component of the external magnetic field that drops off with distance as the inverse cube). Any dipolar magnetic field pattern is symmetric with respect to rotations around a particular axis, therefore it is customary to describe the magnetic dipole moment that creates such a field as a vector with a direction along that axis. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a For quadrupolar, octupolar, and higher-order multipole magnetic moments, see Multipole expansion. A quadrupole or quadrapole is one of a sequence of configurations of — for example — electric charge or current or gravitational mass that can exist in ideal form but it Multipole moments are the Coefficients of a Series expansion of a Potential due to continuous or discrete sources (e Multipole moments are the Coefficients of a Series expansion of a Potential due to continuous or discrete sources (e A multipole expansion is a mathematical series representing a function that depends on angles — usually the two angles on a sphere.

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Two kinds of magnetic sources

Fundamentally, contributions to any system's magnetic moment may come from sources of two kinds: (1) motion of electric charges, such as electric currents and (2) the intrinsic magnetism of elementary particles, such as the electron. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin In Particle physics, an elementary particle or fundamental particle is a particle not known to have substructure that is it is not known to be made The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J

Contributions due to the sources of the first kind can be calculated from knowing the distribution of all the electric currents (or, alternatively, of all the electric charges and their velocities) inside the system, by using the formulas below. On the other hand, the magnitude of each elementary particle's intrinsic magnetic moment is a fixed number, often measured experimentally to a great precision. For example, any electron's magnetic moment is measured to be −9. 284764×10-24 J/T. [1] The direction of the magnetic moment of any elementary particle is entirely determined by the direction of its spin (the minus in front of the value above indicates that any electron's magnetic moment is antiparallel to its spin). In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin The plus and minus signs ( + and &minus) are Mathematical symbols used to represent the notions of positive and negative as well as the operations

Finally, the net magnetic moment of any system is a vector sum of contributions from one or both types of sources. For example, a hydrogen atom's magnetic moment is a vector sum of the following contributions: the intrinsic moment of the electron, the orbital motion of the electron around the proton, and the intrinsic moment of the proton.

Formulas and values for calculating magnetic moments

In the simplest case of a planar loop of electric current, its magnetic moment is defined as:

\vec{\mu}=I \mathbf{a}

where

\vec{\mu} is the magnetic moment, a vector measured in ampere–square meters, or equivalently in joules per tesla,
\mathbf{a} is the vector area of the current loop, measured in square meters (x, y, and z coordinates of this vector are the areas of projections of the loop onto the yz, zx, and xy planes), and
I is the current in the loop (assumed to be constant), a scalar measured in amperes. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. The ampere, in practice often shortened to amp, (symbol A is a unit of Electric current, or amount of Electric charge per second M^2 redirects here For other uses see M². CM2 redirects here The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity The tesla (symbol T) is the SI derived unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic In Geometry, for a finite planar surface of scalar Area S the vector area \mathbf{S} is defined as a vector M^2 redirects here For other uses see M². CM2 redirects here In Physics, a scalar is a simple Physical quantity that is not changed by Coordinate system rotations or translations (in Newtonian mechanics or The ampere, in practice often shortened to amp, (symbol A is a unit of Electric current, or amount of Electric charge per second

By convention, the direction of the vector area is given by the right hand rule (moving one's right hand in the direction of the current around the loop, when the palm of the hand is "touching" the loop's outer edge, and the straight thumb indicates the direction of the vector area and thus of the magnetic moment). For the related yet different principle relating to electromagnetic coils see Right hand grip rule.

In case of an arbitrary closed loop of constant current I, the magnetic moment is given by

\vec{\mu}=I\int d \mathbf{a}

where d \mathbf{a} is the element of the vector area of the current loop. In Geometry, for a finite planar surface of scalar Area S the vector area \mathbf{S} is defined as a vector

In the most general case of an arbitrary current distribution in space, the magnetic moment of such a distribution can be found from the following equation:

\vec{\mu}=\frac{1}{2}\int\mathbf{r}\times\mathbf{J}\,dV

where

dV = r^2 \sin \theta \,dr\, d \theta\,d\phi is the volume element, \mathbf{r} is the position vector pointing from the origin to the location of the volume element, and J is the current density vector at that location. Current density is a measure of the Density of flow of a conserved charge.

The above equation can be used for calculating a magnetic moment of any assembly of moving charges, such as a spinning charged solid, by substituting

\mathbf{J}=\rho \mathbf{v} where ρ is the electric charge density at a given point and \mathbf{v} is the instantaneous linear velocity of that point.

For example, the magnetic moment produced by an electric charge moving along a circular path is

\vec{\mu}=\frac{1}{2}\, q\, \mathbf{r}\times\mathbf{v},

where \mathbf{r} is the position of the charge q relative to the center of the circle and \mathbf{v} is the instantaneous velocity of the charge.

For a free point charge moving in an external magnetic field the magnetic moment is a measure of the magnetic flux set up by the gyration of the charge in the magnetic field. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Magnetic flux, represented by the Greek letter Φ ( Phi) is a measure of quantity of Magnetism, taking into account the strength and the extent of a Magnetic Gyration is another term for Rotation. A center of actual rotation as well as Rotational symmetry may be called gyration center gyration point or rotocenter The moment is opposite to the direction of magnetic field (i. e. it is diamagnetic) and is equal to the kinetic energy of the rotary motion divided by the magnetic field. Diamagnetism is the property of an object which causes it to create a magnetic field in opposition of an externally applied Magnetic field, thus causing a repulsive effect

For a spinning charged solid with a uniform charge density to mass density ratio, the ratio of its magnetic moment to its angular momentum, also known as gyromagnetic ratio, is equal to half the charge-to-mass ratio. In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position In Physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines of a particle or system is the Ratio of its The mass-to-charge ratio, is a Physical quantity that is widely used in the Electrodynamics of charged particles e This implies that a more massive assembly of charges spinning with the same angular momentum will have a proportionately weaker magnetic moment, compared to its lighter counterpart. In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position Even though atomic particles cannot be accurately described as spinning charge distributions of uniform charge-to-mass ratio, this general trend can be sometimes observed in the atomic world, where intrinsic angular momenta of most particles are fairly constant: a small half-integer (spin) times the reduced Planck constant \hbar. In Mathematics, a half-integer is a Number of the form n + 1/2 where n is an Integer. In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. This is the basis for defining the magnetic moment units of Bohr magneton (assuming charge-to-mass ratio of the electron) and nuclear magneton (assuming charge-to-mass ratio of the proton). UNIT ( U nited N ations I ntelligence T askforce later the UN ified I ntelligence T askforce is a fictional military In Atomic physics, the Bohr magneton (symbol \mu_\mathrm{B} is named after the Physicist Niels Bohr. The mass-to-charge ratio, is a Physical quantity that is widely used in the Electrodynamics of charged particles e The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J The nuclear magneton (symbol \mu_\mathrm{N}\! is a Physical constant of Magnetic moment, defined by \mu_\mathrm{N} = The mass-to-charge ratio, is a Physical quantity that is widely used in the Electrodynamics of charged particles e The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive

In atomic and nuclear physics, the symbol μ represents the magnitude of the magnetic moment, often measured in Bohr magnetons or nuclear magnetons, associated with the intrinsic spin of the particle and/or with the orbital motion of the particle in a system. In Atomic physics, the Bohr magneton (symbol \mu_\mathrm{B} is named after the Physicist Niels Bohr. The nuclear magneton (symbol \mu_\mathrm{N}\! is a Physical constant of Magnetic moment, defined by \mu_\mathrm{N} = Values of the intrinsic magnetic moments of some particles are given in the table below:

Intrinsic magnetic moments and spins of some elementary particles [2]
Particle Magnetic dipole moment in SI units, μ (10-27 J/T) Spin (dimensionless)
electron -9284. The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity The tesla (symbol T) is the SI derived unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J 764 1/2
proton +14. The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive 106067 1/2
neutron -9. This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron. 66236 1/2
muon -44. The muon (from the letter mu (μ--used to represent it is an Elementary particle with negative Electric charge and a spin of 1/2 904478 1/2
deuteron +4. Deuterium, also called heavy hydrogen, is a Stable isotope of Hydrogen with a Natural abundance in the Oceans of Earth 3307346 1
triton +15. Tritium (ˈtɹɪtiəm symbol or, also known as Hydrogen-3) is a radioactive Isotope of Hydrogen. 046094 1/2

For relation between the notions of magnetic moment and magnetization see magnetization. Magnetization is defined as the quantity of Magnetic moment per unit volume

Magnetic field produced by a magnetic moment

Any system possessing a net magnetic dipole moment \vec{\mu} will produce a dipolar magnetic field (described below) in the space surrounding the system. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a While the net magnetic field produced by the system can also have higher-order multipole components, those will drop off with distance more rapidly, so that only the dipolar component will dominate the magnetic field of the system at distances far away from it. Multipole moments are the Coefficients of a Series expansion of a Potential due to continuous or discrete sources (e

Chosing a frame of reference in which the system center is at the origin, and the z axis is pointing in the direction of the system's magnetic moment \vec{\mu} simplifies the description of the magnetic field. See also Inertial frame A frame of reference in Physics, may refer to a Coordinate system or set of axes within which to In such frame of reference, the components of the dipolar magnetic field produced by the system, at any point (x,y,z) in space, are (in teslas):

B_x(x,y,z)\,=\,\frac{\mu_0}{4 \pi}\,\, 3\mu\,\frac{x z}{(x^2+y^2+z^2)^{5/2}}
B_y(x,y,z)\,=\,\frac{\mu_0}{4 \pi}\,\, 3\mu\,\frac{y z}{(x^2+y^2+z^2)^{5/2}}
B_z(x,y,z)\,=\,\frac{\mu_0}{4 \pi}\,\, 3\mu\,\frac{\,z^2\!-\frac{1}{3}\,(x^2+ y^2+z^2)\,}{(x^2+y^2+z^2)^{5/2}}\,, as well as the 'transverse' component:
B_{\perp}(x,y,z)\,=\,\sqrt{B_x^2(x,y,z)+B_y^2(x,y,z)}\,=\,\frac{\mu_0}{4 \pi}\,\, 3\mu\,\frac{z \sqrt{x^2+y^2}}{(x^2+y^2+z^2)^{5/2}},\,
where μ0 is the magnetic constant, π is the number Pi, μ is the magnitude of \vec{\mu}, and x, y, and z are coordinates measured in metres. The vacuum permeability, referred to by international standards organizations as the magnetic constant, and denoted by the symbol μ 0 (also IMPORTANT NOTICE Please note that Wikipedia is not a database to store the millions of digits of π please refrain from adding those to Wikipedia as it could cause technical problems In Mathematics and its applications a coordinate system is a system for assigning an n - Tuple of Numbers or scalars to each point The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International

Effects of an external magnetic field on a magnetic moment

Equivalently, the magnetic moment of an object can be defined as a vector relating the aligning torque on the object from an externally applied magnetic field to the field vector itself. A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges The relationship is given by

\vec{\tau} = \vec{\mu} \times\mathbf{B}

where

\vec{\tau} is the torque, measured in newton-meters,
\vec{\mu} is the magnetic moment, measured in ampere meters-squared, and
\mathbf{B} is the magnetic field, measured in teslas or, equivalently in newtons per (ampere-meter). Newton metre is the unit of moment ( Torque) in the SI system

A magnetic moment in an externally-produced magnetic field has a potential energy U:

U=-\vec{\mu}\cdot\mathbf{B}

In a case when the external magnetic field is non-uniform, there will be a force, proportional to the magnetic field gradient, acting on the magnetic moment itself. In Vector calculus, the gradient of a Scalar field is a Vector field which points in the direction of the greatest rate of increase of the scalar

Magnetic poles, analogy with the electric dipole moment

Magnetic moment can be visualized as a bar magnet which has magnetic poles of equal magnitude but opposite polarity. Each pole is the source of magnetic force which weakens with distance. Since magnetic poles always come in pairs, their forces partially cancel each other because while one pole pulls, the other repels. This cancellation is greatest when the poles are close to each other i. e. when the bar magnet is short. The magnetic force produced by a bar magnet, at a given point in space, therefore depends on two factors: on both the strength p of its poles, and on the distance d separating them. The force is proportional to the product \vec{\mu}=\mathbf{p}\mathbf{d}, where \vec{\mu} describes the "magnetic moment" or "dipole moment" of the magnet along a distance R and its direction as the angle between R and the axis of the bar magnet. These equations are completely analogous to the case of electric dipole moment. In Physics, the electric dipole moment (or electric dipole for short is a measure of the polarity of a system of Electric charges.

Magnetic moment of electrons

Electrons and many nuclei also have intrinsic magnetic moments, an explanation of which requires a quantum mechanical treatment and relates to the intrinsic angular momentum of the particles as discussed in the article electron magnetic dipole moment. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J In Atomic physics, the magnetic dipole moment of an Electron is caused by its intrinsic property of spin within a magnetic field In Atomic physics, the magnetic dipole moment of an Electron is caused by its intrinsic property of spin within a magnetic field It is these intrinsic magnetic moments that give rise to the macroscopic effects of magnetism, and other phenomena, such as nuclear magnetic resonance. In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials.

The magnetic moment of the electron is

\boldsymbol{\mu}_S=-g_S \mu_B (\boldsymbol{s}/\hbar)

where

\mu_B\, is the Bohr Magneton,

and

g_s = 2\,\! in Dirac mechanics, but is slightly larger due to quantum electrodynamics effects. In Atomic physics, the Bohr magneton (symbol \mu_\mathrm{B} is named after the Physicist Niels Bohr. Quantum electrodynamics ( QED) is a relativistic Quantum field theory of Electrodynamics.

Again it is important to notice that \vec{\mu} is a negative constant multiplied by the spin, so the magnetic moment is antiparallel to the spin angular momentum. In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin This can be understood with the following classical picture: if we imagine that the spin angular momentum is created by the electron mass spinning around some axis, the electric current that this rotation creates spins in the opposite direction, because of the negative charge of the electron; such current loops produce a magnetic moment which is antiparallel to the spin angular momentum.

Magnetic moments of nuclei

Also see nuclear magnetic moment. The nuclear magnetic moment is the Magnetic moment of an Atomic nucleus and arises from the spin of the Protons and Neutrons It is mainly a magnetic

The nuclear system is a complex physical system consisting of nucleons, i. e. , protons and neutrons. The quantum mechanical properties of the nucleons include the spin among others. Since the electromagnetic moments of the nucleus depends on the spin of the individual nucleons, one can look at these properties with measurements of nuclear moments, and more specifically the nuclear magnetic dipole moment.

The nuclear magnetic moment is very sensitive to the individual contributions from nucleons and a measurement or prediction of its value can reveal important information about the content of the nuclear wavefunction. There are several theoretical models that predict the value of the magnetic dipole moment and a number of experimental techniques aiming to carry out measurements in nuclei along the nuclear chart.

Magnetic moments of molecules

Any molecule has a well-defined magnitude of magnetic moment, which may depend on the molecule's energy state. A quantum mechanical system or particle that is bound, confined spacially can only take on certain discrete values of energy as opposed to classical particles which Typically, the overall magnetic moment of a molecule is a combination of the following contributions, in the order of their typical strength:

Examples of molecular magnetism

See also

Notes

  1. ^ NIST μe
  2. ^ See NIST's Fundamental Physical Constants website http://physics.nist.gov/cgi-bin/cuu/Results?search_for=+magnetic+moment
In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a In Physics, the electric dipole moment (or electric dipole for short is a measure of the polarity of a system of Electric charges. Magnetization is defined as the quantity of Magnetic moment per unit volume Magnetic dipole-dipole interaction, also called dipolar coupling, refers to the direct interaction between two Magnetic dipoles The Energy of the interaction

Dictionary

magnetic moment

-noun

  1. (physics) The torque exerted on a magnet within a magnetic field; a vector, being the product of the strength of the magnet and the distance between its poles.
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