Magnetic circuit

The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials like iron, although there may be air gaps or other materials in the path.

The relation between magnetic flux, magnetomotive force, and magnetic reluctance in an unsaturated magnetic circuit can be described by Hopkinson's law, which bears a superficial resemblance to Ohm's law in electrical circuits, resulting in a one-to-one correspondence between properties of a magnetic circuit and an analogous electric circuit.

Using this concept the magnetic fields of complex devices such as transformers can be quickly solved using the methods and techniques developed for electrical circuits.

Some examples of magnetic circuits are: Similar to the way that electromotive force (EMF) drives a current of electrical charge in electrical circuits, magnetomotive force (MMF) 'drives' magnetic flux through magnetic circuits.

The unit of magnetomotive force is the ampere-turn (At), represented by a steady, direct electric current of one ampere flowing in a single-turn loop of electrically conducting material in a vacuum.

The unit is named after William Gilbert (1544–1603) English physician and natural philosopher.

The magnetomotive force can often be quickly calculated using Ampère's law.

In practice this equation is used for the MMF of real inductors with N being the winding number of the inducting coil.

The flux through an element of area perpendicular to the direction of magnetic field is given by the product of the magnetic field and the area element.

It does not properly model power and energy flow between the electrical and magnetic domains.

This is because electrical resistance will dissipate energy whereas magnetic reluctance stores it and returns it later.

In electrical circuits, Ohm's law is an empirical relation between the EMF

The magnetic resistance that is a true analogy of electrical resistance in this respect is defined as the ratio of magnetomotive force and the rate of change of magnetic flux.

Here rate of change of magnetic flux is standing in for electric current and the Ohm's law analogy becomes,

It is a scalar, extensive quantity, akin to electrical resistance.

In an AC field, the reluctance is the ratio of the amplitude values for a sinusoidal MMF and magnetic flux.

is the reluctance in ampere-turns per weber (a unit that is equivalent to turns per henry).

Magnetic flux always forms a closed loop, as described by Maxwell's equations, but the path of the loop depends on the reluctance of the surrounding materials.

The concentration of flux in low-reluctance materials forms strong temporary poles and causes mechanical forces that tend to move the materials towards regions of higher flux so it is always an attractive force(pull).

where This is similar to the equation for electrical resistance in materials, with permeability being analogous to conductivity; the reciprocal of the permeability is known as magnetic reluctivity and is analogous to resistivity.

Longer, thinner geometries with low permeabilities lead to higher reluctance.

[citation needed] The following table summarizes the mathematical analogy between electrical circuit theory and magnetic circuit theory.

Objects in the same row have the same mathematical role; the physics of the two theories are very different.

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 Ampère's law, the excitation is the product of the current and the number of complete loops made and is measured in ampere-turns.

By Stokes's theorem, the closed line integral of H·dl around a contour is equal to the open surface integral of curl H·dA across the surface bounded by the closed contour.

Since, from Maxwell's equations, curl H = J, the closed line integral of H·dl 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.

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.