Magnetic reluctance

Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is defined as the ratio of magnetomotive force (mmf) to magnetic flux. It represents the opposition to magnetic flux, and depends on the geometry and composition of an object.

Magnetic reluctance in a magnetic circuit is analogous to electrical resistance in an electrical circuit in that resistance is a measure of the opposition to the electric current. The definition of magnetic reluctance is analogous to Ohm's law in this respect. However, magnetic flux passing through a reluctance does not give rise to dissipation of heat as it does for current through a resistance. Thus, the analogy cannot be used for modelling energy flow in systems where energy crosses between the magnetic and electrical domains. An alternative analogy to the reluctance model which does correctly represent energy flows is the gyrator–capacitor model.

Magnetic reluctance is a scalar extensive quantity. The unit for magnetic reluctance is inverse henry, H⁻¹.

The term reluctance was coined in May 1888 by Oliver Heaviside. The notion of "magnetic resistance" was first mentioned by James Joule in 1840. The idea for a magnetic flux law, similar to Ohm's law for closed electric circuits, is attributed to Henry Augustus Rowland in an 1873 paper. Rowland is also responsible for coining the term magnetomotive force in 1880, also coined, apparently independently, a bit later in 1883 by Bosanquet.

Reluctance is usually represented by a cursive capital ${\displaystyle {\mathcal {R}}}$.

In both AC and DC fields, the reluctance is the ratio of the magnetomotive force (MMF) in a magnetic circuit to the magnetic flux in this circuit. In a pulsating DC or AC field, the reluctance also pulsates (see phasors).

The definition can be expressed as follows: $${\displaystyle {\mathcal {R}}={\frac {\mathcal {F}}{\Phi }}}$$ where

It is sometimes known as Hopkinson's law and is analogous to Ohm's law with resistance replaced by reluctance, voltage by MMF and current by magnetic flux.