Definitions

# Magnetomotive force

[mag-nee-tuh-moh-tiv, -nee-]

Magnetomotive force is any physical cause that produces magnetic flux, i.e. any charge or electron in motion. In other words, it is a field of magnetism (measured in tesla) that has area (measured in square meters), so that (Tesla)(Area)= Flux. It is analogous to electromotive force or voltage in electricity. MMF usually describes electric wire coils in a way so scientists can measure or predict the actual force a wire coil can generate.

In this context, the word "force" is used in a general sense of "work potential", and is analogous to, but distinct from mechanical force measured in newtons.

The standard definition of magnetomotive force involves current passing through an electrical conductor, which accounts for the magnetic fields of electromagnets as well as planets and stars. Permanent magnets also exhibit magnetomotive force, but for different reasons.

## Units

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

$begin\left\{matrix\right\}1,operatorname\left\{Gi\right\} & = & \left\{frac \left\{10\right\} \left\{4pi\right\}\right\} mbox\left\{AT\right\} & approx & 0.795773 mbox\left\{AT\right\}end\left\{matrix\right\}$

## Equations

The magnetomotive force $mathfrak F$ in an inductor is given by:

$mathfrak F = N I$
and
$mathfrak F = Phi mathfrak R$

where N is the number of turns of the coil, I is the current in the coil, Φ is the magnetic flux and $mathfrak R$ is the reluctance of the magnetic circuit. The latter equation is sometimes known as Hopkinson's law.

## Magnetomotive force in a generator

A spinning magnet produces a magnetic flux. In the presence of a generator coil, the rotational energy of a spinning magnet is converted into electricity inside the coil. The voltage induced in the coil is proportional to the coil's number of turns while the current induced in the coil is inversely proportional to its resistance (or more generally, its impedance or OHM's). Therefore the power induced inside a coil with respect to a changing external magnetic field increases in proportion to the number of turns and the amperage induced in the coil. This can also be thought in terms of the ratio of power generated divided by the rate of cycling, or rotational speed, the quotient of which is torque.

## References

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