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In physics, the magnetomotive force (abbreviated mmf or MMF, symbol ${\mathcal {F}}$ ) is a quantity appearing in the equation for the magnetic flux in a magnetic circuit, Hopkinson's law.^[1] It is the property of certain substances or phenomena that give rise to magnetic fields:

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

where

Φ

is the magnetic flux and

{\mathcal {R}}

is the reluctance of the 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

, since it is the cause of magnetic flux in a magnetic circuit:^[2]

${\mathcal {F}}=NI$
where $N$ is the number of turns in a coil and $I$ is the electric current through the coil.
${\mathcal {F}}=\Phi {\mathcal {R}}$
where $Φ$ is the magnetic flux and ${\mathcal {R}}$ is the magnetic reluctance
${\mathcal {F}}=HL$
where $H$ is the magnetizing force (the strength of the magnetizing field) and $L$ is the mean length of a solenoid or the circumference of a toroid.

^ Waygood, p. 137
^ Smith, pp. 495–506