All electrical laws
Hopkinson's law
Also known as the Ohm's law for magnetic circuits.
The magnetomotive force driving flux around a magnetic circuit equals the product of the flux and the circuit's reluctance — the magnetic analogue of Ohm's law.
MMF = Φ × S, S = l / (μ₀μᵣA)
- MMF
- magnetomotive force = N × I (ampere-turns)
- Φ
- magnetic flux (webers)
- S
- reluctance (ampere-turns per weber)
- l, A
- path length (m) and cross-section (m²) of the core
- μᵣ
- relative permeability of the core material
In plain English: Swap volts→ampere-turns, current→flux, resistance→reluctance and every series/parallel trick from circuits works on magnetic cores. Iron has tiny reluctance; even a hairline air gap has huge reluctance and hogs most of the MMF.
Where you'll meet it: Transformer and machine core design, why air gaps dominate an inductor's behaviour, and the standard magnetic-circuit numericals: series cores, parallel limbs, gap plus iron path.
Calculators that use this law
Components this law governs
Transformer (power)MMF = Φ × S sizes the core: enough iron and few enough ampere-turns that the flux path stays low-reluctance and unsaturated.Relay (electromechanical)MMF = Φ × S explains the click: as the gap closes, reluctance drops, flux jumps and the pull-in becomes decisive rather than gradual.Stepper MotorDetent torque with the power off is reluctance: the rotor prefers the lowest-reluctance alignment even without current.Solenoid / ActuatorForce depends on the air gap: reluctance is highest when the plunger is out, which is why solenoids are weak at the start of their stroke and slam at the end.LVDT & Displacement TransducersThe moving core changes the reluctance of each magnetic path, which is what unbalances the two secondary voltages.ContactorAC coils draw a large inrush while the gap is open (high reluctance) and much less once closed — the classic sealed vs inrush VA rating.