A coil carrying current produces magnetic field around its turns. In a magnetic-circuit model, the driving quantity is the magnetomotive force (MMF):

$$\mathcal F=NI,$$

where $N$ is the number of turns and $I$ the current.

Reluctance

A magnetic path resists the establishment of flux through its reluctance:

$$\mathcal R=\frac{\ell}{\mu A},$$

for a uniform section of length $\ell$, permeability $\mu$ and cross-sectional area $A$.

Longer paths and smaller areas have greater reluctance, while larger permeability reduces it.

Hopkinson's law

For a simple linear magnetic circuit,

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

This resembles Ohm's law, with MMF analogous to voltage, flux analogous to current and reluctance analogous to resistance.

Air gaps

Air has much lower permeability than a ferromagnetic core, so even a short air gap can contribute a large fraction of the total reluctance.

Series paths

Reluctances along a common flux path add approximately:

$$\mathcal R_{\mathrm{tot}}=\sum_i\mathcal R_i.$$

The analogy is useful only while the material is approximately linear and leakage and fringing remain controlled.