# Dictionary Definition

dipole

### Noun

1 a pair of equal and opposite electric charges
or magnetic poles separated by a small distance

2 an aerial half a wavelength long consisting of
two rods connected to a transmission line at the center [syn:
dipole
antenna]

# User Contributed Dictionary

## English

### Noun

# Extensive Definition

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. 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 addition to current loops, the electron, among other fundamental
particles, is said to have a magnetic dipole moment. This is
because it generates a magnetic
field which is identical to that generated by a very small
current loop. 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. 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.)

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." 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.
(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.)

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.

## Physical dipoles, point dipoles, and approximate dipoles

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.

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). 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/r^3, as compared to 1/r^4
for the next (quadrupole) term and higher powers of 1/r for higher
terms, or 1/r^2 for the monopole term.

## Molecular dipoles

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

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. See dipole-dipole attractions.
- 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. See instantaneous dipole.
- 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.

The definition of an induced dipole given in the
previous sentence is too restrictive and misleading. An induced
dipole of any polarizable charge distribution \rho (remember that a
molecule has a charge distribution) is caused by an electric field
external to \rho. This field may, for instance, originate from an
ion or polar molecule in the vicinity of \rho or may be macroscopic
(e.g., a molecule between the plates of a charged capacitor). The size of the
induced dipole is equal to the product of the strength of the
external field and the dipole polarizability of
\rho.

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

- carbon dioxide: 0
- carbon monoxide: 0.112
- ozone: 0.53
- phosgene: 1.17
- water vapor: 1.85
- hydrogen cyanide: 2.98
- cyanamide: 4.27
- potassium bromide: 10.41

These values can be obtained from measurement of
the dielectric
constant. 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. 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 q_i and position vectors \mathbf_i. For instance, this collection may be a molecule consisting of electrons, all with charge -e, and nuclei with charge e Z_i , where Z_i is the atomic number of the i th nucleus. The physical quantity (observable) dipole has the quantum mechanical operator: \mathfrak = \sum_^N \, q_i \, \mathbf_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 \;\mathfrak\; \mathfrak^ = - \mathfrak,

where |\, S\, \rangle is an S-state,
non-degenerate, wavefunction, which is symmetric or antisymmetric
under inversion: \mathfrak\,|\, S\, \rangle= \pm |\, S\, \rangle.
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 \rangle = \langle\, \mathfrak^\, S\, |
\mathfrak |\, \mathfrak^\, S \,\rangle = \langle\, S\, |
\mathfrak\, \mathfrak \, \mathfrak^| \, S \,\rangle = -\langle
\mathfrak \rangle

it follows that the expectation value changes
sign under inversion. We used here the fact that \mathfrak\,, being
a symmetry operator, is unitary:
\mathfrak^ = \mathfrak^\, and
by definition the Hermitian adjoint \mathfrak^*\, may be moved
from bra to ket and then becomes \mathfrak^ = \mathfrak\,. Since
the only quantity that is equal to minus itself is the zero, the
expectation value vanishes, \langle \mathfrak\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. 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.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 \frac \sqrt

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.);
- 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.

### Vector form

The field itself is a vector quantity:- \mathbf(\mathbf, \mathbf) = \frac \left(3(\mathbf\cdot\hat)\hat-\mathbf\right) + \frac\mathbf\delta^3(\mathbf)

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 is the unit vector parallel to r;
- m is the (vector) dipole moment;
- μ0 is the permeability of free space;
- \delta^3 is the three-dimensional delta function. (\delta^3(\mathbf) = 0 except at r = (0,0,0), so this term is ignored in multipole expansion.)

### Magnetic vector potential

The vector potential A of a magnetic dipole is- \mathbf(\mathbf) = \frac (\mathbf\times\hat)

with the same definitions as above.

### Euler Parameters

A possible parametrisation of a magnetic dipole parallel to the z axis by the Euler Potentials \alpha , \beta in spherical coordinates is- \alpha = \frac \sin^\theta \exp(\cot \theta) \qquad \beta = - \cos \phi \exp(-\cot \theta).

## Field from an electric dipole

The electrostatic potential at position \mathbf due to an electric dipole at the origin is given by:- \Phi(\mathbf) = \frac\,\frac

where

- \hat is a unit vector in the direction of \mathbf;
- p is the (vector) dipole moment;
- ε0 is the permittivity of free space.

This term appears as the second term in the
multipole expansion of an arbitrary electrostatic potential
Φ(r). 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 = - \nabla \Phi =\frac \left(\frac\right) - \frac\mathbf\delta^3(\mathbf)

where E is the electric field and \delta^3 is the
3-dimensional delta
function. (\delta^3(\mathbf) = 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.

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

- \boldsymbol = \mathbf \times \mathbf

- \boldsymbol = \mathbf \times \mathbf

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 \cdot \mathbf.

The energy of a magnetic dipole is
similarly

- U = -\mathbf \cdot \mathbf.

## Dipole radiation

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=\mathbfe^ where ω is the angular
frequency. In vacuum, this produces fields:

- \mathbf = \frac \left\ e^
- \mathbf = \frac \hat \times \mathbf \left( 1 - \frac \right) \frac.

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

- \mathbf = \frac (\hat \times \mathbf) \frac
- \mathbf = \frac \mathbf \times \hat

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

- P = \frac |\mathbf|^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. A circular polarized
dipole is described as a superposition of two linear dipoles.

## See also

## References

## External links

- USGS Geomagnetism Program
- Fields of Force: a chapter from an online textbook
- Electric Dipoles on Project PHYSNET
- Electric Dipole Potential by Stephen Wolfram and Energy Density of a Magnetic Dipole by Franz Krafft. The Wolfram Demonstrations Project.

dipole in Bulgarian: Дипол

dipole in Czech: Elektrický dipól

dipole in German: Dipol

dipole in Spanish: Dipolo eléctrico

dipole in Italian: Dipolo elettrico

dipole in Hebrew: דיפול

dipole in Dutch: Dipool

dipole in Japanese: 双極子

dipole in Norwegian Nynorsk: Dipol

dipole in Russian: Диполь

dipole in Slovenian: Električni dipol

dipole in Serbian: Дипол

dipole in Chinese: 偶極子