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Encyclopedia > Electric dipole
The Earth's magnetic field, which is approximately a dipole
The Earth's magnetic field, which is approximately a dipole

A dipole (Greek: dyo = two and polos = pivot) is a pair of electric charges or magnetic poles of equal magnitude but opposite polarity (opposite electronic charges), separated by some (usually small) distance. Dipoles can be characterized by their dipole moment, a vector quantity with a magnitude equal to the product of the charge or magnetic strength of one of the poles and the distance separating the two poles. The direction of the dipole moment corresponds to the direction from the negative to the positive charge or from the south to the north pole. (Because of the absence of magnetic monopoles, magnetic dipoles are actually created by current loops or by quantum-mechanical spin.) 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. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... 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. ... Location of the South Pole in the Antarctic continent. ... The North Pole is the northernmost point on any planet. ... In physics, magnetic monopole is a term describing a hypothetical particle that could be quickly clarified to a person familiar with magnets but not electromagnetic theory as a magnet with only one pole. In more accurate terms, it would have net magnetic charge. Interest in the concept stems from particle... In physics, spin is an intrinsic angular momentum associated with microscopic particles. ...


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. Since the direction of a magnetic field is defined as the direction of the force on a north magnetic pole, magnetic field lines point away from a north pole and towards a south pole.


When placed in an electric (E) or magnetic (B) field, equal but opposite forces arise on each side of the dipole creating a torque τ: In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ... Current flowing through a wire produces a magnetic field (M) around the wire. ... In physics, a force is an external cause responsible for any change of a physical system. ... The concept of torque in physics, also called moment or couple, originated with the work of Archimedes on levers. ...

τ = p × E (Electric dipole moment p)
τ = μ × B (Magnetic dipole moment μ)
(note: × corresponds to a vector cross product)

which will tend to align the dipole with the field. In physics and engineering, a vector is a physical entity which has a magnitude which is a scalar (a physical quantity expressed as the product of a numerical value and a physical unit, not just a number). ...

Contents


Physical dipoles, point dipoles, and approximate dipoles

Diagram of a physical dipole, with equipotential surfaces and field lines indicated
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. ... Multipole expansion for electric potentials The (scalar) potential at the point x for an arbitrary charge distribution ρ(x) is given by This can be expanded in (negative) powers of , obtaining (after some work) the multipole expansion where this integral, like the previous one, is over all of space, Pn...


There's no such thing as a magnetic physical dipole, since there are (so far as is known) no magnetic monopoles. A 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, magnetic monopole is a term describing a hypothetical particle that could be quickly clarified to a person familiar with magnets but not electromagnetic theory as a magnet with only one pole. In more accurate terms, it would have net magnetic charge. Interest in the concept stems from particle...


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: it 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. Multipole expansion for electric potentials The (scalar) potential at the point x for an arbitrary charge distribution ρ(x) is given by This can be expanded in (negative) powers of , obtaining (after some work) the multipole expansion where this integral, like the previous one, is over all of space, Pn...


Molecular dipoles

Many molecules have such dipole moments due to non-uniform distributions of positive and negative charges on the various atoms. For example: A molecule is the smallest particle of a pure chemical substance that still retains its chemical composition and properties. ...

 (positive) H-Cl (negative) 

A molecule with a permanent dipole moment is called a polar molecule and is polarized. 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 - November 2, 1966) (born Petrus Josephus Wilhelmus Debije) 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.
  • 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.

Electronegativity is the 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. ... Properties The electron is a fundamental subatomic particle which carries a negative electric charge. ... A molecule is the smallest particle of a pure chemical substance that still retains its chemical composition and properties. ... 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. ...

Field of a point dipole

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

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

That's the magnitude of the field; the field itself is a vector quantity: The tesla (symbol T) is the SI derived unit of magnetic flux density (or magnetic induction). ... The metre, or meter (symbol: m) is the SI base unit of length. ... See Radian (band) for the Austrian trio. ... A degree (in full, a degree of arc), usually symbolized °, is a measurement of plane angle, representing 1/360 of a full rotation. ... The henry (symbol: H) is the SI unit of inductance. ...

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
is the unit vector parallel to r
m is the (vector) dipole moment
μ0 is the permeability of free space

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 vector potential A is In vector calculus, a vector potential is a vector field whose curl is a given vector field. ...

with the same definitions as above.


The electric field of an electric point dipole is

where

E is the field
r, r, are as above
p is the (vector) dipole moment
ε0 is the permittivity of free space.

Notice that this is formally identical to the magnetic field of a point magnetic dipole; only a few names have changed.


The (scalar) potential is

External links

  • USGS Geomagnetism Program

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