A magnetic circuit is a closed path containing a magnetic flux. It generally contains magnetic elements such as permanent magnets, ferromagnetic materials and electromagnets, but may also contain air gaps and other materials. Magnetic flux, is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field. ... In physics, magnetism is a phenomenon by which materials exert an attractive or repulsive force on other materials. ... Magnetic lines of force of a bar magnet shown by iron filings on paper A magnet is an object that has a magnetic field. ... Ferromagnetism is a phenomenon by which a material can exhibit a spontaneous magnetization, and is one of the strongest forms of magnetism. ... An electromagnet is a type of magnet in which the magnetic field is produced by a flow of electric current. ...

Some examples of magnetic circuits are:

• horseshoe magnet with iron keeper (low-reluctance circuit)
• horseshoe magnet with no keeper (high-reluctance circuit)
• electric motor (variable-reluctance circuit)

Electric motors of various sizes. ...

Magnetic circuit laws

If Φ is the magnetic flux in the circuit, in webers; F is the magnetomotive force applied to the circuit, in ampere-turns; and R is the reluctance of the circuit, in ampere-turns per weber, then it follows from Ampere's law that: Weber is a surname of German origin, derived from the noun meaning weaver. The German pronunciation is ˈveËŒbeʁ, while in English it is more likely to be pronounced ˈwɛˌbÉš or ˈweËŒbÉš. In some cases, following migration to English-speaking countries, it has been anglicised to the English... In physics, the magnetomotive force produces magnetic flux. ... The ampere (symbol: A) is the SI base unit of electric current equal to one coulomb per second. ... Magnetic reluctance is the resistance of a material to a magnetic field. ... In physics, Ampères law is the magnetic equivalent of Gausss law, discovered by André-Marie Ampère. ...

This is analogous to Ohm's law in electrical circuits, where the current is equal to the voltage (sometimes called electromotive force) divided by the resistance of the circuit. Here, magnetic flux, magnetomotive force and reluctance are analogous to current, voltage and resistance respectively. A voltage source, V, drives an electric current, I , through resistor, R, the three quantities obeying Ohms law: V = IR Ohms law, named after its discoverer Georg Ohm [1], states that the potential difference between two points along a connected path and the current flowing through it are... In electricity, current refers to electric current, which is the flow of electric charge. ... International danger high voltage symbol. ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ...

If A is the area, μ is the permeability of the material, and l is the length Permeability has several meanings: In electromagnetism, permeability is the degree of magnetisation of a material in response to a magnetic field. ...

This is similar to the equation for electrical resistance in materials. Longer, thinner geometries with low permeabilities lead to higher reluctance. Low reluctance, like low resistance in electric circuits, is generally preferred.

Magnetic circuits obey other laws that are similar to electrical circuit laws. For example, the total reluctance R_T of reluctances R₁,R₂... in series is:

(this also follows from Ampere's law and is analogous to Kirchhoff's voltage law for adding resistances in series). Also, the sum of magnetic fluxes Φ₁,Φ₂... into any node is always zero: In physics, Ampères law is the magnetic equivalent of Gausss law, discovered by André-Marie Ampère. ... Kirchhoffs circuit laws are a pair of laws that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff. ...

.

This follows from Gauss's law and is analogous to Kirchhoff's current law for analysing electrical circuits. In physics and mathematical analysis, Gausss law gives the relation between the electric flux flowing out a closed surface and the electric charge enclosed in the surface. ... Kirchhoffs circuit laws are a pair of laws that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff. ...

Together, the three laws above form a complete system for analysing magnetic circuits, in a manner similar to electric circuits. Comparing the two types of circuits shows that:

• The equivalent to resistance is reluctance, R, in "ampere-turns per tesla" or in "rels".
• The equivalent to current is flux, F, in "webers" or in "lines per square inch".
• The equivalent to voltage is mmf, M, in "ampere-turns".

Magnetic circuits can be solved for the flux in each branch by application of the magnetic equivalent of Kirchhoff's Voltage Law (KVL) for pure source/resistance circuits. Specifically, whereas KVL states that the voltage excitation applied to a loop is equal to the sum of the voltage drops (resistance times current) around the loop, the magnetic analogue states that the magnetomotive force (achieved from ampere-turn excitation) is equal to the sum of MMF drops (product of flux and reluctance) across the rest of the loop. (If there are multiple loops, the current in each branch can be solved through a matrix equation--much as a matrix solution for mesh circuit branch currents is obtained in loop analysis--after which the individual branch currents are obtained by adding and/or subtracting the constituent loop currents as indicated by the adopted sign convention and loop orientations.) Per Ampere's law, the excitation is the product of the current and the number of complete loops made and is measured in ampere-turns. Stated more generally: Kirchhoffs circuit laws are a pair of laws that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff. ... In physics, Ampères law is the magnetic equivalent of Gausss law, discovered by André-Marie Ampère. ...

MMF = NI = closed line integral of H dot dl

(Note that, per Stokes's theorem, the closed line integral of H dot dl around a contour is equal to the open surface integral of curl H dot dA across the surface bounded by the closed countour. Since, from Maxwell's equations, curl H = J, the closed line integral of H dot dA evaluates to the total current passing through the surface. This is equal to the excitation, NI, which also measures current passing through the surface, thereby verifying that the net current flow through a surface is zero ampere-turns in a closed system that conserves energy.) This article is about path integrals in the general mathematical sense, and not the path integral formulation of physics which was studied by Richard Feynman. ... In mathematics, a surface integral is a definite integral taken over some surface that may be a curved set in space; it can be thought of as the double integral analog of the path integral. ... Maxwells equations (sometimes called the Maxwell equations) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... This article is about the cURL command line tool. ...

More complex magnetic systems, where the flux is not confined to a simple loop, must be analysed from first principles by using Maxwell's equations. Maxwells equations (sometimes called the Maxwell equations) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ...

References

• Magnetic Circuit Analysis from Electrical Energy Technology course notes by Joe G. Zhu, University of Technology, Sydney (PDF)
• Magnetic-Electric Analogs by Dennis L. Feucht, Innovatia Laboratories (PDF)