A battery, a magnet and a bent wire — the simplest electric motor there is.
This is a simulation bench, not a build guide.
About this bench
What it is. An independent, from-scratch simulation of the homopolar motor,
written for this page. The magnet is modelled as its equivalent surface current and the field is
integrated numerically; the torque is obtained by walking the wire and summing
I dl × B. The closed-form answer is used only as an
oracle to check the integral against, never as the thing computed.
The original. The device is Michael Faraday’s, first reported in 1821
(“On some new electro-magnetical motions, and on the theory of magnetism”,
Quarterly Journal of Science 12, 74–96), where he immersed a permanent magnet in
mercury and connected a battery to the assembly. André-Marie Ampère spun a
cylindrical magnet about its axis with a steady current in 1822. The battery-magnet-wire form is
a twentieth-century classroom descendant of both. Everything here is public domain physics; no
code, art or text from any other implementation is used.
What differs from the real thing. This bench simulates a rigid ideal: a
uniformly magnetised cylinder, contacts that are points rather than sliding areas, a wire of zero
thickness, and drag lumped into a single coefficient. It has no thermal model, no contact bounce,
no magnet conductivity, and no eddy currents. The drag coefficient is calibrated to put
the classic geometry near 1900 rpm and is labelled as such everywhere it is used, because no
source read for this page gives one.
Safety, stated as a result rather than a warning
In an ordinary motor the back-EMF rises with speed and chokes the current off. That is what
keeps a running motor from drawing its stall current. In this machine the motor constant is so
small that the back-EMF never becomes a factor: the numbers on this page show the current
drooping by well under one per cent between stall and running speed, so a cell connected this way
sits at essentially its short-circuit current for as long as the contact holds, and nearly all of
the energy goes into heat. A shorted cell gets hot. This page is a simulation.
It deliberately does not describe how to assemble one.
Neodymium magnets snap together hard enough to pinch skin or chip, and two or
more swallowed magnets can pinch through the gut — a medical emergency. Keep them away from
small children.
Trademark search
A TMview search was run for this page on 2026-09-21 and is reproduced verbatim in
CREDITS.txt and, on its own, in tmview-findings.txt. The exact string homopolar motor returned zero
records worldwide, in any class, in any office, at any status; the only record
containing the word “homopolar” at all is COMPACT PULSED HOMOPOLAR GENERATOR, US
73451783, OIME, Inc., Nice class 7, Ended, filed 1983.
No clearance is claimed. A database search is not a legal opinion, TMview covers
participating offices only, and it does not cover unregistered or common-law rights.
Sources
Read in full means the full text was retrieved as born-digital text. Nothing on
this page is cited from a scanned page image.
Provenance of the findings
Runs entirely in your browser. No account, no network calls, no analytics.
The claim this bench was built to test
“The magnet’s field spins with the magnet and drags the current around.”
Every noun in that sentence is wrong in a different way. The bench below computes the torque
without ever being told how fast the magnet turns — because that quantity is not in the
force law — and the motor turns perfectly well with the magnet clamped. Whether the field
“rotates” is a real and still-live argument in the teaching literature, and it is
reproduced further down with both sides’ own measurements. It has nothing to do with the
torque.
Cross-section through the spin axis. Grey lines are the field; the gold line is the
current path; the green dots are the sliding contacts and the dotted chords are the circles
they trace.The rotor, seen obliquely, turning at the simulated speed slowed 50×.
Only the radial geometry has a movable inner contact. On the axis, the
flux threaded is exactly zero and the motor can never reverse.
This control is here to change nothing. Watch the torque while you move
it: the magnet’s rotation rate is not an argument of the force law.
Calibrated, not documented. No source read for this page gives the
friction of a real build, so the whole range is offered instead of one number.
What this geometry does:
Flux threaded by a circle of this radius, at the contact plane. The torque is
proportional to the difference between the two contacts’ values, so the shaded
band is the whole of it. The curve is not monotone: past the marked radius, reaching further
out costs torque, because the return flux outside the rim has the opposite sign.
Six candidate laws, priced on this geometry
One of these is the Lorentz force integrated along the path. The others are
things people say. Each row is evaluated on the geometry you have set above, so the rows that
agree and the rows that fail change as you move the controls — which is the point: a wrong
law is not wrong everywhere, and knowing where it survives is how it stays believed.
Does the field rotate with the magnet?
Faraday asked it, changed his mind about it, and it is still argued. The 2022 experiment below
rotated the disc, the closing wire and the magnet in all eight combinations and read the answer
off an indicator LED; its authors concluded that “it remains impossible to tell if the
field co-rotates with the magnet or if it remains stationary”. This bench does not
adjudicate either. It computes both hypotheses — the same line integral with the
conductor’s velocity shifted by the magnet’s — and reports where they differ.
And the test that can fail
Eight cases in which two hypotheses agree is worth nothing unless the comparison is capable of
disagreeing. Break the axial symmetry and it does. This is the same restriction the 2022 paper
states in words — an apparent paradox only arises when a magnet spins about its own
symmetry axis — here as a number.