Flux Cutting

Part of Generators and Motors

The physical mechanism by which a moving conductor in a magnetic field generates an electromotive force.

Why This Matters

“Flux cutting” is the intuitive model for understanding how generators produce electricity. When a wire moves through a magnetic field — or equivalently, when a magnetic field moves past a wire — the wire “cuts” through the field lines and an EMF is induced. This model makes generator behavior concrete and predictable in a way that pure equations do not.

For anyone building a generator from scratch, flux cutting is the mental tool that answers practical questions: Why does output drop when the coil face is aligned with the field? Why do more conductors under the pole face produce more voltage? Why does a longer conductor in the field produce more EMF than a short one? All these answers follow directly from the flux cutting picture.

This concept also bridges the gap between the laboratory demonstration — a wire moved by hand near a magnet — and the engineering reality of a spinning rotor with hundreds of conductors. The transition from simple to complex is just a matter of scale and geometry, not a change in the underlying physics.

The Basic Mechanism

When a straight conductor of length L moves with velocity v perpendicular to a magnetic field of strength B, the free electrons in the conductor experience a force. This force, given by F = qv × B, pushes electrons along the conductor, creating a separation of charge — positive at one end, negative at the other. This charge separation is the EMF.

The magnitude is EMF = B × L × v, where B is in Tesla, L in meters, and v in meters per second. This formula is the flux cutting rule in its simplest form. A 0.1-meter conductor moving at 5 m/s through a 0.5 T field produces 0.25 V. Doubling any of the three factors doubles the EMF.

The direction of the induced EMF follows Fleming’s right-hand rule (for generators): point the thumb in the direction of motion, the index finger in the direction of the magnetic field, and the middle finger points in the direction of conventional current flow in the conductor. This rule is worth memorizing and practicing until it becomes automatic.

Conductor Velocity and the Sine Factor

In a rotating generator, the conductor velocity is not always perpendicular to the field. A conductor at the top or bottom of a circular path (where it moves parallel to the field) cuts no flux at all and contributes zero EMF. A conductor at the sides of the path moves perpendicular to the field and contributes maximum EMF.

At an intermediate angle θ from the perpendicular, the effective velocity perpendicular to the field is v × sin(θ). Thus the instantaneous EMF from a single conductor is: e = B × L × v × sin(θ). As the rotor turns, θ changes continuously, and the output is sinusoidal.

This sine variation is not a defect — it is the natural result of circular motion in a uniform field. Understanding it tells you why generators produce AC naturally, and why producing DC requires rectification or a commutator. It also tells you that the peak EMF occurs when the conductor is moving fastest perpendicular to the field, which happens when the conductor is at the midpoint between the poles.

Maximizing Flux Cutting in Rotor Design

The flux cutting formula has three terms: B, L, and v. Good rotor design maximizes all three within physical constraints.

Maximizing B: The field strength in the air gap between rotor and stator depends on the magnet or field coil strength and the length of the air gap. Every millimeter of air gap reduces field strength significantly because air has much lower magnetic permeability than iron. Keep the mechanical clearance between rotor and stator as small as possible — 0.5 to 1.5 mm for well-made machines, 2–3 mm for rougher construction. Use the best available magnet material and concentrate the flux into the gap with properly shaped pole pieces.

Maximizing L: The active conductor length is limited by the physical size of the machine. For a given rotor diameter and core length, maximizing L means filling the rotor slots with as many conductors as possible and making the core as long as practical. Longer cores produce more voltage but also more weight and more bearing load.

Maximizing v: Conductor velocity equals ω × r, where ω is angular velocity in radians per second and r is the radius of the conductor’s path. Larger diameter rotors and higher RPM both increase v. There are limits: at very high surface speeds, centrifugal force stresses the windings, and at very high RPM, bearing wear and vibration become problems. For hand-built generators, surface speeds of 5–15 m/s are manageable.

Multiple Conductors and Series Connection

A single conductor in a magnetic field produces a tiny EMF — fractions of a volt. Practical generators use many conductors connected in series so their EMFs add. With N conductors in series, each contributing the same EMF, the total output is N times the per-conductor EMF.

The conductors are arranged in slots around the rotor circumference. Not all of them are under the poles at any given moment, so only the conductors actively cutting flux contribute to the instantaneous EMF. The others are passing through the interpolar spaces where the field is weak.

To get the maximum number of conductors cutting flux simultaneously, you want the pole arc (the circumferential extent of the magnet face) to cover as large a fraction of the rotor surface as possible. A pole arc spanning about 70% of the pole pitch is a common practical optimum — enough coverage to keep many conductors active, but not so wide that adjacent poles interfere.

Winding Pitch and How It Affects Output

Winding pitch refers to how far apart the two sides of a coil are placed around the rotor. A full-pitch winding places the two sides one pole pitch apart, so when one side is under a north pole, the other is under a south pole — their EMFs add perfectly.

A short-pitch (chorded) winding places the sides closer together, less than one pole pitch apart. The two sides are not simultaneously under opposite poles, so their EMFs do not add perfectly. This reduces total output slightly but significantly reduces the harmonic distortion in the waveform. For power applications where a clean sine wave matters, a short pitch of about 80–85% is standard.

For a rebuilt civilization where winding precision is limited, full-pitch winding is simpler to execute and wastes no output. The resulting harmonics in the waveform are acceptable for resistive loads like lighting and heating. Only when powering motors or electronic equipment sensitive to waveform quality does short-pitch winding become important.

Diagnosing Flux Cutting Problems

If a generator produces less output than expected, the flux cutting formula tells you where to look. Check each term systematically.

Low field (B): Measure the air gap field with a compass or gauss meter. A weak field indicates demagnetized permanent magnets, excessive air gap, or a poor magnetic circuit return path. Check that the stator yoke (the iron path that completes the magnetic circuit) is intact and properly dimensioned.

Short active length (L): If the rotor is not properly positioned axially inside the stator, some conductors are outside the magnetic field region and do not contribute. Check that the rotor is centered within the stator core length. Also check for broken conductors — an open circuit in one slot means all conductors in series with it contribute nothing.

Low velocity (v): Measure actual RPM and compare to design. Low RPM from a prime mover (waterwheel, engine) will proportionally reduce output. Check that the drive coupling is not slipping and that the prime mover is running at design speed.

If all three terms check out and output is still low, suspect a wiring error that is causing some conductors to be connected with reversed polarity, so their EMFs subtract rather than add.