Hopkinson’s Law (Magnetic Ohm’s Law)

Φ = F / S

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Result
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Formula

Φ = F / S (flux = MMF / reluctance)

Description

Hopkinson’s law is the magnetic equivalent of Ohm’s law: magnetic flux equals magnetomotive force divided by reluctance, exactly as current equals voltage divided by resistance. It lets a magnetic circuit be analysed with the same techniques as an electric one—series and parallel reluctances, source MMFs, and flux division.

Variables

  • Φ — Magnetic flux (weber)
  • F — Magnetomotive force (ampere-turns)
  • S — Reluctance (ampere-turns/weber)

Practical Notes

Unlike electric current, magnetic flux dissipates no power flowing through reluctance—reluctance stores rather than dissipates energy. The analogy breaks down at saturation, where µr and hence reluctance become flux-dependent.

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