Magnetomotive force

Magnetic Circuits
Conventional Magnetic Circuits Magnetomotive force $\mathcal F$ Magnetic flux Φ Magnetic reluctance $\mathcal R$
Phasor Magnetic Circuits Complex reluctance Zμ
Related Concepts Magnetic permeability μ
Gyrator-capacitor model variables Magnetic impedance zM Effective resistance rM Magnetic inductivity LM Magnetic capacitivity CM

Magnetomotive force (MMF) (SI Unit: Ampere) is any physical driving (motive) force that produces magnetic flux. In this context, the expression "driving force" is used in a general sense of "work potential", and is analogous, but distinct from force measured in newtons. Magnetomotive force is so named because it plays a role in magnetic circuits analogous to that of electromotive force (voltage) in electric circuits.

SI versus CGS units

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

The CGS unit of magnetomotive force is the gilbert (Gi), established by the IEC in 1930 [1]. The gilbert is defined differently, and is a slightly smaller unit than the ampere. The unit is named after William Gilbert (1544–1603) English physician, astronomer and natural philosopher.

The conversion factor between the SI and CGS units is $\frac {10}{4\pi}$ (≈ 0.795774715) ampere for every gilbert.

Between the CGS unit and SI unit, the MKS unit magnetomotive force was the ampere-turn At.

Equations

The magnetomotive force $\mathcal{F}$ in an inductor or electromagnet consisting of a coil of wire is given by:

$\mathcal{F} = N I$

where N is the number of turns of wire in the coil and I is the current in the wire.

The equation for the magnetic flux in a magnetic circuit, sometimes known as Hopkinson's law, is:

$\mathcal{F} = \Phi \mathcal{R}$

where Φ is the magnetic flux and $\mathcal{R}$ is the reluctance of the magnetic circuit. It can be seen that the magnetomotive force plays a role in this equation analogous to the voltage V in Ohm's law: V = IR.

References

• The Penguin Dictionary of Physics, 1977, ISBN 0-14-051071-0