# Magnetic tension

Physical size
Surname Magnetic (source) voltage
Magnetic penetration
Formula symbol ${\ displaystyle V _ {\ mathrm {m}}, U _ {\ mathrm {m}}, \ Theta}$ Size and
unit system
unit dimension
SI A. I.
Gauss ( cgs ) Gb = Bi / (4π) L 01/02 · M 02/01 · T -1
esE ( cgs ) statA L 02/03 · M 01/02 · T -2
emE ( cgs ) Gb = Bi / (4π) L 01/02 · M 02/01 · T -1

The magnetic voltage or magnetic source voltage (symbol: or ) is the path integral over the magnetic field strength in electrodynamics . In the case of a closed path, also known as circulation, one speaks of magnetic flow , or flow through for short. The flow is equal to the total electric current enclosed by this circulation, which is composed of the conduction current plus the displacement current . ${\ displaystyle V _ {\ mathrm {m}}}$ ${\ displaystyle U _ {\ mathrm {m}}}$ ${\ displaystyle H}$ ${\ displaystyle \ Theta}$ Magnetic tension is formally similar to electrical tension . It matters in the magnetic circuit . ${\ displaystyle U}$ ## units

The unit of magnetic tension in the SI is the ampere . In the past, the ampere as the unit of the flow was called an ampere turn (unit symbol: Aw, AW), since the same current can "wind through" the circuit several times; at a cylindrical coil , the magnetic voltage (to a good approximation) the current intensity in the coil multiplied by the number of turns.

In the Gaussian system of units and electromagnetic system of units (EMU), the unit Gilbert (symbol: Gb) is used for the flow .

## Flooding Act

The law of flux describes the relationship between the magnetic flux and the enclosed current.

${\ displaystyle \ Theta = \ oint _ {\! \! \! {\ mathcal {S}}} {\ vec {H}} \ cdot \ mathrm {d} {\ vec {s}} = I}$ ## Hopkinson's law

With the magnetic flux and the magnetic resistance , the magnetic voltage depends on Hopkinson's law${\ displaystyle \ Phi}$ ${\ displaystyle R _ {\ mathrm {m}}}$ ${\ displaystyle V _ {\ mathrm {m}}}$ ${\ displaystyle V _ {\ mathrm {m}} = R _ {\ mathrm {m}} \ cdot \ Phi}$ together. This law is the magnetic equivalent of Ohm's law for electrical circuits. In contrast to the electrical circuit (in the absence of variable magnetic fields) the sum of all voltages in a mesh circuit is not zero, but the magnetic flow.

## Magnetic tension around a line cable Division of the magnetic flow into several equal partial voltages around a conductor.${\ displaystyle \ Theta}$ ${\ displaystyle V _ {\ mathrm {m}} (\ alpha)}$ Imagine level fans around a straight electrical line conductor. In this case, the magnetic tension can be given as a function of the angle between two surfaces: ${\ displaystyle \ alpha}$ ${\ displaystyle V _ {\ mathrm {m}} (\ alpha) = {\ frac {\ alpha} {2 \, \ pi}} \, \ Theta = {\ frac {\ alpha} {2 \, \ pi} } \, I}$ If one were to look at a bundle of ladders, each of which is traversed by the current , would be . ${\ displaystyle n}$ ${\ displaystyle I}$ ${\ displaystyle \ Theta = n \ cdot I}$ The relationship applies to the magnetic field strength${\ displaystyle H}$ ${\ displaystyle H = {\ frac {\ mathrm {d} V _ {\ mathrm {m}} (\ alpha)} {\ mathrm {d} s}} = {\ frac {\ mathrm {d} V _ {\ mathrm {m}} (\ alpha)} {r \, \ mathrm {d} \ alpha}}}$ ,

where a segment of the field length is the magnetic field strength with and the radius of the circle around the current on which the field is measured. In this formula is synonymous with . ${\ displaystyle \ mathrm {d} s}$ ${\ displaystyle l}$ ${\ displaystyle l = \ alpha \ cdot r}$ ${\ displaystyle r}$ ${\ displaystyle I}$ ${\ displaystyle V _ {\ mathrm {m}}}$ ${\ displaystyle \ Theta}$ ## Magnetic flow of a coil

In the case of a solenoid with the number of turns through which a current flows, the following applies as a good approximation: ${\ displaystyle N}$ ${\ displaystyle I}$ ${\ displaystyle \ Theta = \ sum _ {n} R _ {\ mathrm {m}, n} \, \ Phi _ {n} = \ sum _ {n} \ Theta _ {n} = N \ cdot I}$ .

This also applies to other coil shapes in which there are hardly any magnetic field lines between the windings or if a magnetic circuit ( iron core or ferrite core ) consists of a material with high relative permeability . In the latter case, conclusions can be drawn about the magnetic field strength from its iron path length and the backward flow and - if the permeability number is known - the magnetic flux density.

## literature

• Günter Springer: Expertise in electrical engineering. 18th edition, Verlag Europa-Lehrmittel, Wuppertal, 1989, ISBN 3-8085-3018-9 .
• Horst Stöcker: Pocket book of physics. 4th edition, Verlag Harry Deutsch, Frankfurt am Main 2000, ISBN 3-8171-1628-4 .