Magnetomotive force

The magnetomotive force (or mmf for short) $\mathcal{F}$ is the magnetic analog of electromotive force, used in magnetic circuits. It is measured in amperes. It is typically produced by a coil of $N$ turns carrying electric current $I$, which simply gives

It is also connected to Hopkinson's law by

where $\Phi_{B}$ is the magnetic flux and $\mathcal{R}$ is the magnetic reluctance. In the specific case of a solenoid or toroid of mean length or circumference $l$, it can be found from the auxiliary field directly: