The Earth's magnetic field, which is approximately a magnetic dipole. Earth 's magnetic field (and the surface magnetic field) is approximately a Magnetic dipole, with one pole near the North pole (see However, the "N" and "S" (north and south) poles are labeled here geographically, which is the opposite of the convention for labeling the poles of a magnetic dipole moment.

In physics, there are two kinds of dipoles (Hellènic: di(s)- = two- and pòla = pivot, hinge). The Ancient Greek language is the historical stage in the development of the Hellenic language family spanning the Archaic (c An electric dipole is a separation of positive and negative charge. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some, usually small, distance. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. A permanent electric dipole is called an electret. Electret (formed of elektr- from " Electricity " and -et from " Magnet " is a Dielectric material that has a quasi-permanent By contrast, a magnetic dipole is a closed circulation of electric current. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. A simple example of this is a single loop of wire with some constant current flowing through it. [1][2]

Contour plot of an electrical dipole, with equipotential surfaces indicated. Equipotential surfaces are Surfaces of constant Scalar potential.

Dipoles can be characterized by their dipole moment, a vector quantity. For the simple electric dipole given above, the electric dipole moment would point from the negative charge towards the positive charge, and have a magnitude equal to the strength of each charge times the separation between the charges. In Physics, the electric dipole moment (or electric dipole for short is a measure of the polarity of a system of Electric charges. For the current loop, the magnetic dipole moment would point through the loop (according to the right hand grip rule), with a magnitude equal to the current in the loop times the area of the loop. In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current For the related yet different principle relating to electromagnetic coils see Right-hand rule.

In addition to current loops, the electron, among other fundamental particles, is said to have a magnetic dipole moment. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J 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 This is because it generates a magnetic field which is identical to that generated by a very small current loop. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges However, to the best of our knowledge, the electron's magnetic moment is not due to a current loop, but is instead an intrinsic property of the electron. The term intrinsic denotes a characteristic or property of some thing or action which is essential and specific to that thing or action and which is wholly independent It is also possible that the electron has an electric dipole moment, although this has not yet been observed (see electron electric dipole moment for more information. The electron Electric dipole moment (EDM d_e is roughly speaking a measure of the charge distribution within an Electron. )

A permanent magnet, such as a bar magnet, owes its magnetism to the intrinsic magnetic dipole moment of the electron. The two ends of a bar magnet are referred to as poles (not to be confused with monopoles), and are labeled "north" and "south. In Physics, a magnetic monopole is a hypothetical particle that is a Magnet with only one pole (see Maxwell's equations for more on magnetic " The dipole moment of the bar magnet points from its magnetic south to its magnetic north pole—confusingly, the "north" and "south" convention for magnetic dipoles is the opposite of that used to describe the Earth's geographic and magnetic poles, so that the Earth's geomagnetic north pole is the south pole of its dipole moment. The South Pole, also known as the Geographic South Pole or Terrestrial South Pole, is the southernmost point on the surface of the Earth. The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is subject to the caveats explained below defined as the point in the northern (This should not be difficult to remember; it simply means that the north pole of a bar magnet is the one which points north if used as a compass. A compass, magnetic compass or mariner's compass is a navigational instrument for determining direction relative to the earth's Magnetic poles It consists )

The only known mechanisms for the creation of magnetic dipoles are by current loops or quantum-mechanical spin since the existence of magnetic monopoles has never been experimentally demonstrated. In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin In Physics, a magnetic monopole is a hypothetical particle that is a Magnet with only one pole (see Maxwell's equations for more on magnetic

## Physical dipoles, point dipoles, and approximate dipoles

Real-time evolution of the electric field of an oscillating electric dipole. The dipole is located at (60,60) in the graph, oscillating at 1 rad/s (~. 16Hz) in the vertical direction

A physical dipole consists of two equal and opposite point charges: literally, two poles. Its field at large distances (i. e. , distances large in comparison to the separation of the poles) depends almost entirely on the dipole moment as defined above. A point (electric) dipole is the limit obtained by letting the separation tend to 0 while keeping the dipole moment fixed. The field of a point dipole has a particularly simple form, and the order-1 term in the multipole expansion is precisely the point dipole field. A multipole expansion is a mathematical series representing a function that depends on angles — usually the two angles on a sphere.

Although there are no known magnetic monopoles in nature, there are magnetic dipoles in the form of the quantum-mechanical spin associated with particles such as electrons (although the accurate description of such effects falls outside of classical electromagnetism). In Physics, a magnetic monopole is a hypothetical particle that is a Magnet with only one pole (see Maxwell's equations for more on magnetic In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J A theoretical magnetic point dipole has a magnetic field of the exact same form as the electric field of an electric point dipole. A very small current-carrying loop is approximately a magnetic point dipole; the magnetic dipole moment of such a loop is the product of the current flowing in the loop and the (vector) area of the loop.

Any configuration of charges or currents has a 'dipole moment', which describes the dipole whose field is the best approximation, at large distances, to that of the given configuration. This is simply one term in the multipole expansion; when the charge ("monopole moment") is 0 — as it always is for the magnetic case, since there are no magnetic monopoles — the dipole term is the dominant one at large distances: its field falls off in proportion to 1 / r3, as compared to 1 / r4 for the next (quadrupole) term and higher powers of 1 / r for higher terms, or 1 / r2 for the monopole term. A multipole expansion is a mathematical series representing a function that depends on angles — usually the two angles on a sphere.

## Molecular dipoles

Many molecules have such dipole moments due to non-uniform distributions of positive and negative charges on the various atoms. 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 For example:

Electric dipole field lines
(positive) H-Cl (negative)

A molecule with a permanent dipole moment is called a polar molecule. A molecule is polarized when it carries an induced dipole. The physical chemist Peter J. W. Debye was the first scientist to study molecular dipoles extensively, and dipole moments are consequently measured in units named debye in his honor. Peter Joseph William Debye ( March 24 1884 &ndash November 2 1966) was a Dutch physicist and physical chemist The debye (symbol D) is a non- SI, CGS unit of electrical dipole moment.

With respect to molecules there are three types of dipoles:

• Permanent dipoles: These occur when two atoms in a molecule have substantially different electronegativity—one atom attracts electrons more than another becoming more negative, while the other atom becomes more positive. " Electronegativity " is the opposite of " Electropositivity," which describes an element's ability to donate electrons See dipole-dipole attractions. In Physics, Chemistry, and Biology, intermolecular forces are forces that act between stable Molecules or between functional groups of
• Instantaneous dipoles: These occur due to chance when electrons happen to be more concentrated in one place than another in a molecule, creating a temporary dipole. 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 See instantaneous dipole. In Physics, Chemistry, and Biology, intermolecular forces are forces that act between stable Molecules or between functional groups of
• Induced dipoles These occur when one molecule with a permanent dipole repels another molecule's electrons, "inducing" a dipole moment in that molecule. See induced-dipole attraction. In Physics, Chemistry, and Biology, intermolecular forces are forces that act between stable Molecules or between functional groups of

The definition of an induced dipole given in the previous sentence is too restrictive and misleading. An induced dipole of any polarizable charge distribution ρ (remember that a molecule has a charge distribution) is caused by an electric field external to ρ. This field may, for instance, originate from an ion or polar molecule in the vicinity of ρ or may be macroscopic (e. g. , a molecule between the plates of a charged capacitor). A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors The size of the induced dipole is equal to the product of the strength of the external field and the dipole polarizability of ρ. Polarizability is the relative tendency of a charge distribution like the Electron cloud of an Atom or Molecule, to be distorted from its normal shape

Typical gas phase values of some chemical compounds in debye units:[3]

• carbon dioxide: 0
• carbon monoxide: 0. The debye (symbol D) is a non- SI, CGS unit of electrical dipole moment. Carbon dioxide ( Chemical formula:) is a Chemical compound composed of two Oxygen Atoms covalently bonded to a single Carbon monoxide, with the chemical formula CO is a colorless odorless tasteless yet highly toxic Gas. 112
• ozone: 0. OZONE is an object oriented Operating system written in the C programming language. 53
• phosgene: 1. Phosgene is the Chemical compound with the formula COCl2 This colorless gas gained infamy as a Chemical weapon during World War I 17
• water vapor: 1. General properties of water vapor Evaporation/sublimation Whenever a water molecule leaves a surface it is said to have evaporated 85
• hydrogen cyanide: 2. Hydrogen cyanide is a Chemical compound with Chemical formula HCN 98
• cyanamide: 4. Cyanamide ( C[[Nitrogen N]]2 H 2 is an Amide of Cyanogen, a white crystalline compound 27
• potassium bromide: 10. Potassium bromide ( K[[Bromine Br]] is a salt, widely used as an Anticonvulsant and a Sedative in the late 19th and early 20th centuries 41

These values can be obtained from measurement of the dielectric constant. Measurement The relative static permittivity εr can be measured for static Electric fields as follows first the Capacitance of a test When the symmetry of a molecule cancels out a net dipole moment, the value is set at 0. The highest dipole moments are in the range of 10 to 11. From the dipole moment information can be deduced about the molecular geometry of the molecule. Molecular geometry or molecular structure is the three- Dimensional arrangement of the Atoms that constitute a Molecule. For example the data illustrate that carbon dioxide is a linear molecule but ozone is not.

## Quantum mechanical dipole operator

Consider a collection of N particles with charges qi and position vectors $\mathbf{r}_i$. For instance, this collection may be a molecule consisting of electrons, all with charge -e, and nuclei with charge eZi, where Zi is the atomic number of the i th nucleus. The elementary charge, usually denoted e, is the Electric charge carried by a single Proton, or equivalently the negative of the electric charge carried See also List of elements by atomic number In Chemistry and Physics, the atomic number (also known as the proton The physical quantity (observable) dipole has the quantum mechanical operator:

$\mathfrak{p} = \sum_{i=1}^N \, q_i \, \mathbf{r}_i .$

## Atomic dipoles

A non-degenerate (S-state) atom can have only a zero permanent dipole. This fact follows quantum mechanically from the inversion symmetry of atoms. All 3 components of the dipole operator are antisymmetric under inversion with respect to the nucleus,

$\mathfrak{I} \;\mathfrak{p}\; \mathfrak{I}^{-1} = - \mathfrak{p},$

where $\stackrel{\mathfrak{p}}{}$ is the dipole operator and $\stackrel{\mathfrak{I}}{}\,$ is the inversion operator. In Euclidean geometry, the inversion of a point X in respect to a point P is a point X * such that P is the midpoint of The permanent dipole moment of an atom in a non-degenerate state (see degenerate energy level) is given as the expectation (average) value of the dipole operator,

$\langle \mathfrak{p} \rangle = \langle\, S\, | \mathfrak{p} |\, S \,\rangle,$

where $|\, S\, \rangle$ is an S-state, non-degenerate, wavefunction, which is symmetric or antisymmetric under inversion: $\mathfrak{I}\,|\, S\, \rangle= \pm |\, S\, \rangle$. This article refers to physical states having the same energy Since the product of the wavefunction (in the ket) and its complex conjugate (in the bra) is always symmetric under inversion and its inverse,

$\langle \mathfrak{p} \rangle = \langle\, \mathfrak{I}^{-1}\, S\, | \mathfrak{p} |\, \mathfrak{I}^{-1}\, S \,\rangle = \langle\, S\, | \mathfrak{I}\, \mathfrak{p} \, \mathfrak{I}^{-1}| \, S \,\rangle = -\langle \mathfrak{p} \rangle$

it follows that the expectation value changes sign under inversion. We used here the fact that $\mathfrak{I}\,$, being a symmetry operator, is unitary: $\mathfrak{I}^{-1} = \mathfrak{I}^{*}\,$ and by definition the Hermitian adjoint $\mathfrak{I}^*\,$ may be moved from bra to ket and then becomes $\mathfrak{I}^{**} = \mathfrak{I}\,$. In Functional analysis, a branch of Mathematics, a unitary operator is a Bounded linear operator U    H  →  In Mathematics, specifically in Functional analysis, each Linear operator on a Hilbert space has a corresponding adjoint operator. Since the only quantity that is equal to minus itself is the zero, the expectation value vanishes,

$\langle \mathfrak{p}\rangle = 0.$

In the case of open-shell atoms with degenerate energy levels, one could define a dipole moment by the aid of the first-order Stark effect. The Stark effect is the shifting and splitting of Spectral lines of atoms and molecules due to the presence of an external static Electric field. This only gives a non-vanishing dipole (by definition proportional to a non-vanishing first-order Stark shift) if some of the wavefunctions belonging to the degenerate energies have opposite parity; i. In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate. e. , have different behavior under inversion. This is a rare occurrence, but happens for the excited H-atom, where 2s and 2p states are "accidentally" degenerate (see this article for the origin of this degeneracy) and have opposite parity (2s is even and 2p is odd).

## Field from a magnetic dipole

### Magnitude

The far-field strength, B, of a dipole magnetic field is given by

$B(m, r, \lambda) = \frac {\mu_0} {4\pi} \frac {m} {r^3} \sqrt {1+3\sin^2\lambda}$

where

B is the strength of the field, measured in teslas;
r is the distance from the center, measured in metres;
λ is the magnetic latitude (90°-θ) where θ = magnetic colatitude, measured in radians or degrees from the dipole axis (Magnetic colatitude is 0 along the dipole's axis and 90° in the plane perpendicular to its axis. The tesla (symbol T) is the SI derived unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 This article describes the unit of angle For other meanings see Degree. );
m is the dipole moment, measured in ampere square-metres (A•m2), which equals joules per tesla;
μ0 is the permeability of free space, measured in henrys per metre. The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. The henry (symbol H is the SI unit of Inductance. It is named after Joseph Henry (1797-1878 the American scientist who discovered electromagnetic

### Vector form

The field itself is a vector quantity:

$\mathbf{B}(\mathbf{m}, \mathbf{r}) = \frac {\mu_0} {4\pi r^3} \left(3(\mathbf{m}\cdot\hat{\mathbf{r}})\hat{\mathbf{r}}-\mathbf{m}\right) + \frac{2\mu_0}{3}\mathbf{m}\delta^3(\mathbf{r})$

where

B is the field;
r is the vector from the position of the dipole to the position where the field is being measured;
r is the absolute value of r: the distance from the dipole;
$\hat{\mathbf{r}} = \mathbf{r}/r$ is the unit vector parallel to r;
m is the (vector) dipole moment;
μ0 is the permeability of free space;
δ3 is the three-dimensional delta function. The Dirac delta or Dirac's delta is a mathematical construct introduced by the British theoretical physicist Paul Dirac. ($\delta^3(\mathbf{r})$ = 0 except at r = (0,0,0), so this term is ignored in multipole expansion. )

This is exactly the field of a point dipole, exactly the dipole term in the multipole expansion of an arbitrary field, and approximately the field of any dipole-like configuration at large distances.

### Magnetic vector potential

The vector potential A of a magnetic dipole is

$\mathbf{A}(\mathbf{r}) = \frac {\mu_0} {4\pi r^2} (\mathbf{m}\times\hat{\mathbf{r}})$

with the same definitions as above. In Vector calculus, a vector potential is a Vector field whose curl is a given vector field

### Euler Parameters

A possible parametrisation of a magnetic dipole parallel to the z axis by the Euler Potentials α,β in spherical coordinates is

$\alpha = \frac{m_{z}}{4 \pi r} \sin^{2}\theta \exp(\cot \theta) \qquad \beta = - \cos \phi \exp(-\cot \theta).$

## Field from an electric dipole

The electrostatic potential at position $\mathbf{r}$ due to an electric dipole at the origin is given by:

$\Phi(\mathbf{r}) = \frac{1}{4\pi\epsilon_0}\,\frac{\mathbf{p}\cdot\hat{\mathbf{r}}}{r^2}$

where

$\hat{\mathbf{r}}$ is a unit vector in the direction of $\mathbf{r}$;
p is the (vector) dipole moment;
ε0 is the permittivity of free space. At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical

This term appears as the second term in the multipole expansion of an arbitrary electrostatic potential Φ(r). A multipole expansion is a mathematical series representing a function that depends on angles — usually the two angles on a sphere. If the source of Φ(r) is a dipole, as it is assumed here, this term is the only non-vanishing term in the multipole expansion of Φ(r). The electric field from a dipole can be found from the gradient of this potential:

$\mathbf{E} = - \nabla \Phi =\frac {1} {4\pi\epsilon_0} \left(\frac{3(\mathbf{p}\cdot\hat{\mathbf{r}})\hat{\mathbf{r}}-\mathbf{p}}{r^3}\right) - \frac{1}{3\epsilon_0}\mathbf{p}\delta^3(\mathbf{r})$

where E is the electric field and δ3 is the 3-dimensional delta function. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can 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 The Dirac delta or Dirac's delta is a mathematical construct introduced by the British theoretical physicist Paul Dirac. ($\delta^3(\mathbf{r})$ = 0 except at r = (0,0,0), so this term is ignored in multipole expansion. ) Notice that this is formally identical to the magnetic field of a point magnetic dipole; only a few names have changed.

## Torque on a dipole

Since the direction of an electric field is defined as the direction of the force on a positive charge, electric field lines point away from a positive charge and toward a negative charge. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can

When placed in an electric or magnetic field, equal but opposite forces arise on each side of the dipole creating a torque τ:

$\boldsymbol{\tau} = \mathbf{p} \times \mathbf{E}$

for an electric dipole moment p (in coulomb-meters), or

$\boldsymbol{\tau} = \mathbf{m} \times \mathbf{B}$

for a magnetic dipole moment m (in ampere-square meters). In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges In Physics, a force is whatever can cause an object with Mass to Accelerate. 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, the electric dipole moment (or electric dipole for short is a measure of the polarity of a system of Electric charges. In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current

The resulting torque will tend to align the dipole with the applied field, which in the case of an electric dipole, yields a potential energy of

$U = -\mathbf{p} \cdot \mathbf{E}$.

The energy of a magnetic dipole is similarly

$U = -\mathbf{m} \cdot \mathbf{B}$.

In addition to dipoles in electrostatics, it is also common to consider an electric or magnetic dipole that is oscillating in time.

In particular, a harmonically oscillating electric dipole is described by a dipole moment of the form $\mathbf{p}=\mathbf{p'(\mathbf r)}e^{-i\omega t}$ where ω is the angular frequency. Do not confuse with Angular velocity In Physics (specifically Mechanics and Electrical engineering) angular frequency In vacuum, this produces fields:

$\mathbf{E} = \frac{1}{4\pi\varepsilon_0} \left\{ \frac{\omega^2}{c^2 r} \hat{\mathbf{r}} \times \mathbf{p} \times \hat{\mathbf{r}} + \left( \frac{1}{r^3} - \frac{i\omega}{cr^2} \right) \left[ 3 \hat{\mathbf{r}} (\hat{\mathbf{r}} \cdot \mathbf{p}) - \mathbf{p} \right] \right\} e^{i\omega r/c}$
$\mathbf{B} = \frac{\omega^2}{4\pi\varepsilon_0 c^3} \hat{\mathbf{r}} \times \mathbf{p} \left( 1 - \frac{c}{i\omega r} \right) \frac{e^{i\omega r/c}}{r}.$

Far away (for $r\omega/c \gg 1$), the fields approach the limiting form of a radiating spherical wave:

$\mathbf{B} = \frac{\omega^2}{4\pi\varepsilon_0 c^3} (\hat{\mathbf{r}} \times \mathbf{p}) \frac{e^{i\omega r/c}}{r}$
$\mathbf{E} = \frac{1}{c} \mathbf{B} \times \hat{\mathbf{r}}$

which produces a total time-average radiated power P given by

$P = \frac{\omega^4}{12\pi\varepsilon_0 c} |\mathbf{p}|^2.$

This power is not distributed isotropically, but is rather concentrated around the directions lying perpendicular to the dipole moment. Usually such equations are described by spherical harmonics, but they look very different. In Mathematics, the spherical harmonics are the angular portion of an Orthogonal set of solutions to Laplace's equation represented in a system of A circular polarized dipole is described as a superposition of two linear dipoles.