NationMaster - Encyclopedia: Dipole

The Earth's magnetic field, which is approximately a dipole. 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.

Bar magnet dipole moment.

In physics, there are two kinds of dipoles (Greek: di(s) = double and polos = pivot). 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. By contrast, a magnetic dipole is a closed circulation of electric current. A simple example of this is a single loop of wire with some constant current flowing through it. ^[1] ^[2] Dipole field from NASA. Copied from http://geomag. ... Dipole field from NASA. Copied from http://geomag. ... The magnetosphere shields the surface of the Earth from the charged particles of the solar wind. ... Image File history File links Magnetic_dipole_moment. ... Image File history File links Magnetic_dipole_moment. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Electric current is by definition the flow of electric charge. ...

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 rule), with a magnitude equal to the current in the loop times the area of the loop. This article is about the electromagnetic phenomenon. ... In physics, the magnetic moment of an object is a vector relating the aligning torque in a magnetic field experienced by the object to the field vector itself. ... The right hand rule is also an algorithm used to solve Mazes In mathematics and physics, the right-hand rule is a convention for determining relative directions of certain vectors. ...

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.) e- redirects here. ... In particle physics, an elementary particle is a particle of which other, larger particles are composed. ... For other senses of this term, see magnetic field (disambiguation). ... Intrinsic is used to describe a characteristic or property of some thing or action which is specific to that thing or action, and which is wholly independent of any other object, action or consequence. ... There are very few or no other articles that link to this one. ...

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. In physics, a magnetic monopole is a hypothetical particle that may be loosely described as a magnet with only one pole (see electromagnetic theory for more on magnetic poles). ... Amundsen-Scott South Pole Station. ... North Pole Scenery When not otherwise qualified, the term North Pole usually refers to the Geographic North Pole â€“ the northernmost point on the surface of the Earth, where the Earths axis of rotation intersects the Earths surface. ...

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 physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... In physics, a magnetic monopole is a hypothetical particle that may be loosely described as a magnet with only one pole (see electromagnetic theory for more on magnetic poles). ...

1 Electric dipole moment
2 Torque on a dipole
3 Physical dipoles, point dipoles, and approximate dipoles
4 Molecular dipoles
5 Quantum mechanical dipole operator
6 Atomic dipoles
7 Field from a magnetic dipole
8 Field from an electric dipole
9 Dipole radiation
10 See also
11 References
12 External links

Electric dipole moment

It is often convenient to be able to treat complex configurations of charge by their dipole-like qualities. To that end, we define an electric dipole moment.

For an electric dipole having a certain length given by r, the end of which is at position r and having opposite charges at opposite ends, the electric dipole moment p is defined by

$mathbf{p} = q , mathbf{r}.$

Note that since r is a vector with a certain direction, so is p. Simplistically, it points from negative charge to positive charge.

Of course, this easily generalizes to cases where one wishes to find the electric dipole moment of some configuration of N discrete charges by

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

which can be carried over to an integral in the case of a continuous distribution of charges

$mathbf{p} = intrho(mathbf{r'}), mathbf{r'} d tau'$

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: It has been suggested that optical field be merged into this article or section. ... For other senses of this term, see magnetic field (disambiguation). ... In physics, the force experienced by a body is defined as the rate of change of momentum with time. ... It has been suggested that this article or section be merged with Moment (physics). ...

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

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 magnetic moment of an object is a vector relating the aligning torque in a magnetic field experienced by the object to the field vector itself. ...

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

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

Physical dipoles, point dipoles, and approximate dipoles

Diagram of a physical dipole, with equipotential surfaces and field lines indicated

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. Image File history File links Download high resolution version (1013x1100, 1904 KB) Summary A physical dipole with charge, equipotentials and electric fields indicated. ... Image File history File links Download high resolution version (1013x1100, 1904 KB) Summary A physical dipole with charge, equipotentials and electric fields indicated. ... This article is in need of attention from an expert on the subject. ...

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. In physics, a magnetic monopole is a hypothetical particle that may be loosely described as a magnet with only one pole (see electromagnetic theory for more on magnetic poles). ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... e- redirects here. ...

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. This article is in need of attention from an expert on the subject. ...

Molecular dipoles

Many molecules have such dipole moments due to non-uniform distributions of positive and negative charges on the various atoms. For example: In science, a molecule is a group of atoms in a definite arrangement held together by chemical bonds. ...

(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. Petrus Josephus Wilhelmus Debije (March 24, 1884 â€“ November 2, 1966) was a Dutch physical chemist. ... The debye (symbol: D) is a non-SI and non-CGS unit of electrical dipole moment. ...

With respect to molecules there are three types of dipoles:

Permanent dipoles: These occur when 2 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 attraction.
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 $ρ$ (remember that a molecule is 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). The size of the induced dipole is equal to the product of the strength of the external field and the dipole polarizability of $ρ$ . Electronegativity is a measure of the ability of an atom or molecule to attract electrons in the context of a chemical bond. ... Intermolecular forces are electromagnetic forces which act between molecules or between widely separated regions of a macromolecule. ... e- redirects here. ... In science, a molecule is a group of atoms in a definite arrangement held together by chemical bonds. ... Intermolecular forces are electromagnetic forces which act between molecules or between widely separated regions of a macromolecule. ... Intermolecular forces are electromagnetic forces which act between molecules or between widely separated regions of a macromolecule. ... Capacitors: SMD ceramic at top left; SMD tantalum at bottom left; through-hole tantalum at top right; through-hole electrolytic at bottom right. ... Polarizability is the relative tendency of the electron cloud of an atom to be distorted from its normal shape by the presence of a nearby ion or dipole--that is, by an external electric field. ...

Typical gas phase values of some chemical compounds in debye units ^[3]: The debye (symbol: D) is a non-SI and non-CGS unit of electrical dipole moment. ...

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. Carbon dioxide is a chemical compound composed of one carbon and two oxygen atoms. ... Carbon monoxide, with the chemical formula CO, is a colorless, odorless, and tasteless gas. ... For other uses, see Ozone (disambiguation). ... Phosgene (also known as carbonyl chloride, COCl2) is a highly toxic gas or refrigerated liquid that was used as a chemical weapon in World War I. It has no color, but is detectable in air by its odor, which resembles moldy hay. ... It has been suggested that multiple sections of steam be merged into this article or section. ... Hydrogen cyanide is a chemical compound with chemical formula HCN. A solution of hydrogen cyanide in water is called hydrocyanic acid. ... Cyanamide (CN2H2) is an amide of cyanogen, a white, crystalline compound. ... Potassium bromide (KBr) is a salt, used as an anticonvulsant and a sedative in the 1800s. ... The relative dielectric constant of a material under given conditions is a measure of the extent to which it concentrates electrostatic lines of flux. ... Geometry of the water molecule Molecular geometry or molecular structure is the three dimensional arrangement of the atoms that constitute a molecule, inferred from the spectroscopic studies of the compound. ...

Quantum mechanical dipole operator

Consider a collection of N particles with charges $q i$ 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 $e Z i$ , where $Z i$ is the atomic number of the i ^th nucleus. The physical quantity (observable) dipole has the quantum mechanical operator: Properties The electron (also called negatron, commonly represented as e−) is a subatomic particle. ... It has been suggested that List of elements by atomic number be merged into this article or section. ...

$mathbf{M} = sum_{i=1}^N , q_i , mathbf{r}_i .$

Atomic dipoles

A non-degenerate (S-state) atom can only have 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, 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 line segment with endpoints X and X*. In other words, the vector from X to P is the same as the vector from...

$I ;mathbf{M}; I^{-1} = - mathbf{M},$

where $mathbf{M}$ is the dipole operator and $I,$ is the inversion operator. 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, The energy levels of two or more physical states are said to be degenerate when they have the same value. ...

$langle mathbf{M} rangle = langle, S, | mathbf{M} |, S ,rangle,$

where $|, S, rangle$ is an S-state, non-degenerate, wavefunction, which is symmetric or antisymmetric under inversion: $I,|, S, rangle= pm |, S, rangle$ . Since the product of the wavefunction (in the ket) and its complex conjugate (in the bra) is always symmetric under inversion and its inverse,

$langle mathbf{M} rangle = langle, I^{-1}, S, | mathbf{M} |,I^{-1}, S ,rangle = langle, S, | I, mathbf{M} ,I^{-1}| , S ,rangle = -langle mathbf{M} rangle$

it follows that the expectation value changes sign under inversion. We used here the fact that $I,$ , being a symmetry operator, is unitary: $I^{-1} = I^{*},$ and by definition the Hermitian adjoint $I^*,$ may be moved from bra to ket and then becomes $I^{**} = I,$ . Since the only quantity that is equal to minus itself is the zero, the expectation value vanishes, In functional analysis, a unitary operator is a bounded linear operator U on a Hilbert space satisfying U*U=UU*=I where I is the identity operator. ... In mathematics, specifically in functional analysis, each linear operator on a Hilbert space has a corresponding adjoint operator. ...

$langle mathbf{M}rangle = 0.$

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). The Stark effect is the splitting of a spectral line into several components in the presence of an electric field. ... In physics, a parity transformation (also called parity inversion) is the simultaneous flip in the sign of all spatial coordinates: A 3Ã—3 matrix representation of P would have determinant equal to â€“1, and hence cannot reduce to a rotation. ... In classical mechanics, for a central force with potential, the Laplace-Runge-Lenz vector is a conserved vector of motion. ...

Field from a magnetic dipole

Magnitude

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

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

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, which equals joules per tesla.

μ₀ is the permeability of free space, measured in henrys per metre.

SI unit. ... The metre, or meter (U.S.), is a measure of length. ... Some common angles, measured in radians. ... A degree (in full, a degree of arc, arc degree, or arcdegree), usually symbolized Â°, is a measurement of plane angle, representing 1ï¼360 of a full rotation. ... The joule (IPA pronunciation: or ) (symbol: J) is the SI unit of energy. ... Tesla may refer to: // Nikola Tesla, a Serbian-American physicist, inventor, and electrical engineer. ... In electromagnetism, permeability is the degree of magnetization of a material that responds linearly to an applied magnetic field. ... An inductor. ...

Vector form

The field itself is a vector quantity:

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

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

$δ 3$ is the three dimensional delta function.

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. The Dirac delta function, introduced by Paul Dirac, can be informally thought of as a function δ(x) that has the value of infinity for x = 0, the value zero elsewhere, and a total integral of one. ...

Magnetic vector potential

The vector potential A of a magnetic dipole is In vector calculus, a vector potential is a vector field whose curl is a given vector field. ...

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

with the same definitions as above.

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 of an electric dipole is Electric potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. ...

$Phi (mathbf{r}) = frac {1} {4piepsilon_0 r^2} (mathbf{p}cdothat{mathbf{r}}).$

And the electric field from a dipole can be found from the gradient of this potential: It has been suggested that optical field be merged into this article or section. ... For other uses, see Gradient (disambiguation). ...

$mathbf{E} ,$	$= - nabla Phi ,$
	$=frac {1} {4piepsilon_0 r^3} left(3(mathbf{p}cdothat{mathbf{r}})hat{mathbf{r}}-mathbf{p}right) + frac{1}{3epsilon_0}mathbf{p}delta^3(mathbf{r})$

where

E is the electric field

r, r, $hat{mathbf{r}}$ are as above

p is the (vector) dipole moment

ε₀ is the permittivity of free space.

$δ 3$ is the 3-dimensional delta function.

Notice that this is formally identical to the magnetic field of a point magnetic dipole; only a few names have changed. This article is in need of attention. ... The Dirac delta function, introduced by Paul Dirac, can be informally thought of as a function δ(x) that has the value of infinity for x = 0, the value zero elsewhere, and a total integral of one. ...

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 $mathbf{p}=mathbf{p'(mathbf r)}e^{-iomega t}$ where ω is the angular frequency. In vacuum, this produces fields: It has been suggested that this article or section be merged into Angular velocity. ...

$mathbf{E} = frac{1}{4pivarepsilon_0} left{ frac{omega^2}{c^2 r} hat{mathbf{r}} times mathbf{p} times hat{mathbf{r}} + left( frac{1}{r^3} - frac{iomega}{cr^2} right) left[ 3 hat{mathbf{r}} (hat{mathbf{r}} cdot mathbf{p}) - mathbf{p} right] right} e^{iomega r/c}$

$mathbf{H} = frac{omega^2}{4pi c} hat{mathbf{r}} times mathbf{p} left( 1 - frac{c}{iomega r} right) frac{e^{iomega r/c}}{r}$

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

$mathbf{H} = frac{omega^2}{4pi c} (hat{mathbf{r}} times mathbf{p}) frac{e^{iomega r/c}}{r}$

$mathbf{E} = sqrt{frac{mu_0}{epsilon_0}} mathbf{H} times hat{mathbf{r}}$

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

$P = sqrt{frac{mu_0}{epsilon_0}} frac{omega^4}{12pi c^2} |mathbf{p}|^2$

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. A circular polarized dipole is described as a superposition of two linear dipoles. In mathematics, the spherical harmonics are the angular portion of an orthogonal set of solutions to Laplaces equation represented in a system of spherical coordinates. ...

References

^ Brau, Charles A. (2004). Modern Problems in Classical Electrodynamics. Oxford University Press. ISBN 0-19-514665-4.
^ Griffiths, David J. (1999). Introduction to Electrodynamics, 3rd ed., Prentice Hall. ISBN 0-13-805326-X.
^ Weast, Robert C. (1984). CRC Handbook of Chemistry and Physics, 65rd ed., CRC Press. ISBN 0-8493-0465-2.

External links

USGS Geomagnetism Program
Fields of Force - a chapter from an online textbook
Electric Dipoles on Project PHYSNET

Categories: Electromagnetism | Chemical properties | Fundamental physics concepts

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