Dipole

A dipole is the physical arrangement of two poles (Greek prefix di -, two ), so a Zweifachpol, which typically results from thresholding of two adjacent and oppositely charged vectors (eg electric charge with directed distance ), which is a so-called dipole field produce; The thresholding is performed such that the distance vector of charges converges to zero at the same time the charge strength inversely proportional to the distance to diverge ( the so-called " dipole limit ").

A dipole is completely characterized by the direction and magnitude of its dipole moment vector

Wherein the constant is a positive number, and the dipole moment is hereinafter referred to simply as ( dipole vector ).

A dipole may be created, for example, electric charges, but can also be separated without spatial charges as in the existing magnetic dipole (there are only notional, no real magnetic charges ).

Except in electromagnetism dipoles occur even in various other fields such as acoustics or on fluid dynamics. Characteristic is always the directional dependence and the decrease of the generated field with at large distances r.

The term of the dipole is not identical with that of the dipole, which describes a specific group of electric circuits in its meaning.

• 2.1 Physical dipole
• 2.2 point dipole
• 2.3 dipole in the multipole expansion
• 2.4 dipole in an external field

Occurrence

Electric dipoles

Electric dipoles require the separation of charges and occur rarely at the macroscopic scale on. At the microscopic scale, however, electric dipoles are very common. For example, they are generated by asymmetric molecules such as the water molecule.

Also in biological muscle and nerve fibers emerge through electric dipole moments constructed voltages that can be measured, for example in the electrocardiogram.

Magnetic dipoles

Because of the lack of real magnetic monopoles magnetic fields always go out of magnetic dipoles and their overlays. Therefore, macroscopically obvious dipole fields are very common in magnetism. A long bar magnet can be described to a good approximation as a magnetic dipole. Also, the Earth's magnetic field is similar to outdoor a dipole field with dipole axis from north to south.

A magnetic dipole is formed in general from an stromumflossenen surface or is connected with the spinning of particles.

As well as larger dipole configurations are referred to, the field is not a pure dipole field, but this is similar, in contrast to quadrupole and more higher orders of the multipole.

Temporally variable dipoles

A dipole field decreases ~ 1 / r ³ (r: distance ). For large distances, the enclosed surface area increases with ~ r ², the product goes but with ~ 1 / r approaches zero. In large distance a static dipole field vanishes. This also follows directly from the intuition: from a distance, the poles are physically indistinguishable, their field contributions cancel.

Time-varying dipoles are quite different. First they allow distant stars are in the sky and the sun supplies the earth with radiant energy. A mathematical model of a simple variable dipole is the Hertzian dipole. Systems with dimensions on the order of the wavelength dipole antennas hot.

Physical Description

Each dipole is characterized by its dipole moment, a vector quantity, which includes direction and amount. Stands for an electrical and hereinafter for any dipole moment, whereas, a magnetic dipole moment in a rule is referred to.

Physical dipole

A physical dipole consists of two opposite charges in a sufficiently short distance d The dipole moment is defined as

The field at a great distance, that is, for then only depends on and is no longer of q and d individually. The greater the distance, the more the field approaching the one Punktdipols. At small distances the field which is different from what is reflected by non-vanishing higher multipole moments.

Point dipole

The point dipole is created when an extended dipole is reduced to a point of no monopole moment, without changing the dipole moment. This corresponds to the limiting case at large distances and leads to the charge distribution

Using

• The nabla operator
• The delta function

The point dipole generates the field potential

Using

• Of the polar angle (measured from the dipole axis )
• The electric field constants

And the vector field

Using

• Of the unit vectors

Dipole in the multipole expansion

Fields that arise from a spatially limited charge distribution, can be split by the multipole expansion by various proportions that fall at different speeds at large distances. At large distances then always dominated the first non-vanishing Term The dipole term as the second term in the expansion therefore is manifested particularly when the monopoly term ( total charge ) disappears. An arbitrary charge distribution then has the dipole moment

If the monopole term, however, does not disappear, so can the value of the dipole moment change by shifting the coordinate origin and thus is not clearly defined.

The next higher term is the quadrupole moment, the field decreases.

Dipole in an external field

A dipole in an external field, which is not produced by himself, - (electric field or magnetic field ) - has the potential energy:

In an inhomogeneous external field acting on a dipole force:

These two expressions are mathematically identical over the Grassmann identity when the magnetic field is irrotational.

Sometimes, therefore, to use a slightly different, equivalent convention for the definition of the magnetic moment, namely

With the magnetic field constant

Then you write of vornhererin also in the magnetic case

With the magnetic field strength

Displays a dipole is not in the direction of an external field, a torque acts on him:

There are two dipoles in the field of the other, as result of dipole-dipole forces, which decrease according to the field gradient with.

References and footnotes

• Magnetism
• Electrostatics