MC-A1 · Magnetic circuit

Magnetic Circuits and the Magnetic Ohm’s Law

The flux a coil drives around an iron core behaves just like current looping through a circuit. Pin down what plays the role of current and learn to read a magnetic circuit like an electric one.

What plays the role of current in a magnetic circuit?

The coil pushes flux into the iron, and that loop-spanning stream sits where current sits. Among three candidates, pick the one that fills that slot exactly.

Air gap g0.0 mm

Tap to view H/B/Φ on the core; widen the air gap with the slider and the reluctance rises, so the flux Φ falls.

Flux Φ = F / R (widen the gap)

Φ ≈ 100%  ·  g = 0.0 mm

The flux Φ is the total that crosses the whole section and loops the circuit once. It sits exactly where current sits — Φ = NI / R is the magnetic Ohm’s law.

Electric and magnetic circuits are look-alikes

As voltage drives current, the magnetomotive force F = NI drives flux. As resistance opposes current, reluctance opposes flux. Drop Φ = F/R into the slot of Ohm’s law I = V/R and the magnetic circuit solves itself.

ObserveF = N I

The MMF maps to voltage — the force that drives flux.

What sets the reluctance

In the same shape as electrical resistance R = l/(σA), reluctance is R = l/(μA). It grows with a longer path and shrinks with larger permeability μ or wider area A. Iron has μ thousands of times that of air, so the same MMF pushes far more flux through it.

ChooseR = l / ?

Reluctance scales with length, inverse to permeability and area.

Fill inΦ = F / ?

The magnetic Ohm’s law: flux = MMF / reluctance.

A tiny air gap dominates the reluctance

Cut just a 1 mm air gap into the core and, because air’s μ is so small, the reluctance of that short slit overwhelms the entire long iron path. That is why the air-gap design of motors and generators governs the flux. Reluctances add in series, so the largest term decides the stream.

On your ownΦ = NI / ?

Expand the reluctance and the flux collapses to μANI/l.

Back to the first screen

What filled the current slot exactly was the flux Φ. H is the pressure that drives the stream (the voltage side) and B is how crowded it is (the current-density side), so their slots were off. Only the total that loops the circuit once plays the role of current, and that total is Φ = NI / R, the MMF divided by the reluctance. This is the handle for reading a magnetic circuit like an electric one.

The magnetic Ohm’s law: flux Φ = F / R. The magnetomotive force F = NI drives the flux and the reluctance R = l / (μA) opposes it, so Φ = μANI / l. With voltage→MMF, current→flux, resistance→reluctance, a magnetic circuit solves like an electric one.

Once you hold this handle

The magnetic Ohm’s law is the foundation of this whole subject. In the next unit a coil’s inductance hangs directly on reluctance as L = N²/R (MC-A2), and the flux paths of transformers, motors and generators are all analysed as these series–parallel magnetic circuits. The sense that the air gap dominates reluctance carries straight into the air-gap design of rotating machines.