element. It is written as: where R is the electrical resistance of that material. There is a counterpart to Ohm's law used in magnetic circuits. This law is often called Hopkinson's law, after John Hopkinson, but was actually formulated earlier by Henry Augustus Rowland in 1873. It states that where is the magnetomotive force (MMF) across a magnetic element, is the magnetic flux through the magnetic element, and is the magnetic reluctance of that element. (It will be shown later that this relationship is due to the empirical relationship between the H-field and the magnetic field B, B=μH, where μ is the permeability of the material). Like Ohm's law, Hopkinson's law can be interpreted either as an empirical equation that works for some materials, or it may serve as a definition of reluctance. Hopkinson's law is not a correct analogy with Ohm's law in terms of modelling power and energy flow. In particular, there is no power dissipation associated with a magnetic reluctance in the same way as there is a dissipation in an electrical resistance. 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 electrical current and the Ohm's law analogy becomes, where is the magnetic resistance. This relationship is part of an electrical-magnetic analogy called the gyrator-capacitor model and is intended to overcome the drawbacks of the reluctance model. The gyrator-capacitor model is, in turn, part of a wider group of compatible analogies used to model systems across multiple energy domains. Reluctance Magnetic reluctance, or magnetic resistance, is analogous to resistance in an electrical circuit (although it does not dissipate magnetic energy). In likeness to the way an electric field causes an electric current to follow the path of least resistance, a magnetic field causes magnetic flux to follow the path of least magnetic reluctance. It is a scalar, extensive quantity, akin to electrical resistance. The total reluctance is equal to the ratio of the MMF in a passive magnetic circuit and the magnetic flux in this circuit. In an AC field, the reluctance is the ratio of the amplitude values for a sinusoidal MMF and magnetic flux. (see phasors) The definition can be expressed as: where is the reluctance in ampere-turns per weber (a unit