Magnetomotive force

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In physics, the magnetomotive force (abbreviated mmf or MMF, symbol ${\displaystyle {\mathcal {F}}}$) 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: $${\displaystyle {\mathcal {F}}=\Phi {\mathcal {R}},}$$ where Φ is the magnetic flux and ${\displaystyle {\mathcal {R}}}$ 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]

1. ${\displaystyle {\mathcal {F}}=NI}$
   where N is the number of turns in a coil and I is the electric current through the coil.
2. ${\displaystyle {\mathcal {F}}=\Phi {\mathcal {R}}}$
   where Φ is the magnetic flux and ${\displaystyle {\mathcal {R}}}$ is the magnetic reluctance
3. ${\displaystyle {\mathcal {F}}=HL}$
   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.