Magnetic flux

The magnetic flux (symbol: Φ ) is a physical quantity to describe the magnetic field. It is - similar to the electric current - the result of a magnetic power, and flows through a magnetic resistance. Since the vacuum is itself such a magnetic resistance, the magnetic flux is not tied to a specific, " medium " and is described on field sizes.

General

For example, considering a small cylinder made ​​of a material with a given magnetic conductivity, to the magnetic power (as determined by its length, and the magnetic field strength H) To present such a current is proportional to a cross-sectional area. Analogous to the electrical resistance is defined as the magnetic resistance Rm and comes to the relation:

There is, for example, in the simplest linear, homogeneous case between existing with the distance d to each other pole pieces of a magnet, the magnetic field strength H, prevails along the distance d, the magnetic potential:

By this magnetic tension forms between the pole pieces of the magnetic flux from. According to the magnetic resistance of the material located between the pole pieces (or empty space ) to provide a certain amount of magnetic flux. The magnetic resistance is bonded to the magnetic permeability as a substance or a natural constant as an ohmic resistance to the material constant of the electric conductivity of the resistance material bound.

As a rule, you do not work directly with the magnetic flux, but with the associated magnetic flux density in the field theory. The reason for this is that only one flow to a particular area can be assigned in the room, but not discrete field points: There is no function Φ (x, y, z), wherein x, y, z denote position coordinates. Draw Risch therefore the magnetic flux is represented as a kind of "tube" ( flux tube ). To avoid these difficulties, it is therefore worked best with the vector magnitude of the magnetic flux density. Conversely, thus the magnetic flux through an area A of the magnetic flux density B be derived. In general, the magnetic flux is therefore defined by a surface oriented as:

Special cases

• If the magnetic field is homogeneous and the surface is not curved, the magnetic flux is equal to the scalar product of the magnetic flux density B and the area A vector ( normal vector of the surface ):

• Since the magnetic field is source free ( magnetic monopoles are hypothetical particles ) are the magnetic flux density lines are always self-contained. This is in the Maxwell's equations expressed as:

Therefore, the magnetic flux through a closed surface is a space segment is always zero, as is true for the integral theorem of Gauss:

Linked flux, flux linkage, induced magnetic flux

As concatenated flux ( flux linkage, magnetic flux or bobbin flux) of the magnetic flux of an inductor or coil is referred to, which results in the integration of the magnetic flux density B across the area Av, which is formed by the coil, together with their supply lines:

As integration area Av any oriented area can be used, which is bounded by the short-circuited coil. Because there is no magnetic monopole charges, occurs during the calculation of the flow exclusively in the edge line but not on the exact shape of the surface. The adjacent diagram shows a coil surface the example of a coil with three windings. In a conventional coil arrangement, the surface of the magnetic field lines in the coil core N is pierced times when the field is approximately homogeneous in the core. The result then is: wherein the magnetic flux is of a thread or the cross-sectional area of the magnetic core.

Clearly, the flux linkage are described in the following form: The induced voltage in a coil results from the change of the area enclosed by a single turn magnetic flux. If, connected as in a coil by a further turn in series with the first results in this turn an equally large induced voltage, insofar as both windings comprise the same river. Both induced voltages add up, due to the series connection of the turns. In turns for the entire coil is thus an induced voltage is proportional to the change of. This total voltage present at the terminals of the coil and thus of the linked magnetic flux and not the simple magnetic flux of the current-voltage relationship, and the inductance of the coil is taken into account.

In the electrical engineering literature, it has been widely adopted to describe the magnetic flux in the magnetic core and the magnetic flux through the plane spanned by the coil surface. The choice of different character should not lead to the obvious fallacy here is that it is an ordinary magnetic flux from the various new physical size on the flux linkage. Because the flux linkage of a coil is physically considered nothing more than the ordinary magnetic flux, which is obtained for the special case of a coil surface. The election of a new character, however it useful to distinguish the coil flux of the magnetic flux which penetrates the cross-section of the coil core.

Unit of measurement

The unit of magnetic flux in the SI unit system is Weber, the unit symbol Wb:

Illustration of the magnetic force flow

While it is relatively easy to fall for the electrical flow and the underlying electric charge Q in C (or As) to develop a clear idea of ​​it, namely that of a correspondingly large number of electrons capable of such one second to maintain a current of 1 A, which falls in the magnetic flux measured in Wb (or Vs), far more severe.

One of the ways is to the in some (older) textbooks of physics to be found concept of time sum of the voltage or voltage sum time, also called on the basis of the concept of force impulse surge to access:

If you draw namely the induction voltage in a conductor loop as a function of time, shows that the area under the voltage curve at constant intensity of the excitation field always remains the same, no matter how fast or slow vonstattengeht the flux change. Accordingly, is one of the foot attributable to the concept of voltage-time sum definitions of magnetic force flow as follows:

Formulated Slang: A magnetic power flow of 1 Weber (or 1 Vs ) is the " amount of magnetism ", in which they can for one second to maintain a voltage of 1 V surrounding circuit when they disappear. ( See also voltage-time area )

Quantum theory

When considering quantum phenomena (eg Aharonov - Bohm effect, the quantum Hall effect) is the magnetic flux quantum

So the ratio of the Planck's quantum of action and the elementary charge, a convenient size. In superconductors the flux quantum has an amount of

On. The experimental finding that, in various attempts to superconductors (as in the magnetic flux through a superconducting ring ) gave the indication that the carriers here have the charge may be implied point to the existence of Cooper pairs.