a dipple dap do ......it is This article is about the electromagnetic phenomenon. For the radio antenna, see dipole antenna. For the permanent magnet, see dipole magnet. For the graph, see dipole graph. For the loudspeaker enclosure, see dipole speaker.
The Earth's magnetic field, which is approximately a magnetic 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.
The Earth's magnetic field, which is approximately a magnetic 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.
In physics, there are two kinds of dipoles (Hellènic: di(s)- = two- and pòla = pivot, hinge). 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. A permanent electric dipole is called an electret. 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]
Diagram of a physical dipole, with equipotential surfaces and field lines indicated
Diagram of a physical dipole, with equipotential surfaces and field lines indicated
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.
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.
Contents
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* 1 Physical dipoles, point dipoles, and approximate dipoles
* 2 Molecular dipoles
* 3 Quantum mechanical dipole operator
* 4 Atomic dipoles
* 5 Field from a magnetic dipole
o 5.1 Magnitude
o 5.2 Vector form
o 5.3 Magnetic vector potential
o 5.4 Euler Parameters
* 6 Field from an electric dipole
* 7 Torque on a dipole
* 8 Dipole radiation
* 9 See also
* 10 References
* 11 External links
[edit] 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
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.
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 / 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.
[edit] Molecular dipoles
Many molecules have such dipole moments due to non-uniform distributions of positive and negative charges on the various atoms. For example:
Electric dipole field lines
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.
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 Ï (remember that a molecule has a charge distribution) is caused by an electric field external to Ï. This field may, for instance, originate from an ion or polar molecule in the vicinity of Ï 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 Ï.
Typical gas phase values of some chemical compounds in debye units:[3]
* 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.
[edit] 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 physical quantity (observable) dipole has the quantum mechanical operator:
\mathfrak{p} = \sum_{i=1}^N \, q_i \, \mathbf{r}_i .
[edit] 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. 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 =