PAPERS | JANUARY 01 2024

A “Perpetual Motion Machine” Powered by

Electromagnetism
Hollis Williams

Phys. Teach. 62, 47–49 (2024)

https://doi.org/10.1119/5.0102604

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17 December 2024 15:41:32

A “Perpetual Motion Machine” Powered by
Electromagnetism
Hollis Williams, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

“P
erpetual motion” is a hypothetical type of motion
that continues forever without any external energy
input contributing to the system. Students should
know that this is generally impossible because of energy losses
due to friction or other nonconservative forces, or because
some assumption has been made that violates the first or
second law of thermodynamics (or both). The first law states
that the total energy of an isolated system remains constant
over time, and one of the most common formulations of the
second law states that the entropy of an isolated system over
time cannot decrease. Note that the laws apply to an isolated
system (i.e., one that cannot exchange mass or energy with
its surroundings), whereas a closed system can still exchange
energy even if it cannot exchange mass.1 There have histori-
cally been many purported perpetual motion machines.2,3 A
close analysis of the machine invariably finds either that there
is some assumption that violates the laws of thermodynamics
or that there is some input from an external energy source,
which means that the system is not isolated.4,5 In this article,
Fig. 1. “Perpetual motion machine” using metal balls and
we will consider an amusing example of such a machine, in rails.6
which a ball starts on a platform, falls through a hole, and

17 December 2024 15:41:32

slides down a track formed from two side-by-side stainless Students should think of how they could potentially figure
steel rods.6 I explain how the machine can be used in class out where on the trajectory the ball is being sped up. Probably
to illustrate physical principles, outline the possible mecha- the easiest way to do this is to use video analysis software. A
nisms, and end with an explanation of the correct mechanism. video of a trajectory can be recorded with a mobile phone to
The toy that I have mentioned seems to be a relatively be uploaded to video analysis software and analyzed frame
plausible example of perpetual motion. The end of the rail is by frame. A suitable piece of software that could be used is
fluted so that the ball flies off the end and lands back on the Vernier’s Logger Pro, which is available relatively cheaply for
platform, where the process repeats indefinitely with no ap- science instructors. Alternatively, students could record the
parent input from an external energy source. Figure 1 shows motion of the ball in the slow-motion setting of a smartphone
a view of the device from the side. One can see that the ball and then record the position frame by frame on a desktop
slides down a pair of rods that are placed side by side. I initial- computer. It should be easy to establish that the distance be-
ly suggest that students study the apparatus more closely, ei- tween successive ball positions increases unexpectedly close
ther via a video such as the one at Ref. 6 or ideally with a phys- to the bottom part of the trajectory. This confirms that there
ical version of the toy. Teachers should make sure to purchase is an external energy source, but what is the nature of this
the genuine version of the toy and not cheap alternatives that source?
have a motor in the hole on the upper platform that “fires” the For the purpose of answering this question, I suggest that
sphere down the ramp. This alternative toy looks very similar students should now propose potential mechanisms that
but uses a crude spinning motor to overcome friction in a explain what is seen and then work through the implications
straightforward way. and plausibility of each mechanism. After this, groups of
Students could verbally express or write on a piece of pa- students could argue for or against some of the proposed
per all the things that they notice about the apparatus. They mechanisms, a technique that reinforces concepts learned
should notice quite quickly that the ball describes a parabolic earlier in a physics course, but that also requires a deeper
trajectory when it flies through the air on its way back to the understanding of the concepts as opposed to learning by rote
initial upper platform. The highest point of the trajectory (the or memorization. It would obviously be desirable for students
vertex of the parabola) is higher than this platform, so the ball to have access to the toy shown in Ref. 6. The device can be
must have picked up some extra kinetic energy somewhere bought online for around a hundred dollars, which seems like
during the trip through the hole back to the upper platform. a reasonable price for a toy that will be used many times in
The question is where along the way could this have happened demonstrations to illustrate physical principles.6 The main
and what it is that could have imparted extra speed to the ball. benefit of having a version of the device in class is that stu-

DOI: 10.1119/5.0102604 THE PHYSICS TEACHER t Vol. 62, January 2024 47

dents can study its motion up close and obtain video images. This explanation does not work for reasons explained in the
An exercise that I would suggest is to create a montage of the previous paragraph. Studying videos of the motion confirms
toy by superimposing between 10 and 20 balls at their loca- that the ball does not accelerate any more than it would under
tions over the course of one cycle. For example, if T is the time free fall in the initial half of the cycle. This can also be con-
needed for one cycle (around 1 s), then images of the ball firmed by dropping several balls through the hole in quick
could be superimposed at times from T/20 up to T in steps of succession such that it would seem to be difficult to correctly
T/20. This would then allow students to calculate the speed time the electronics such that all the balls return to the start-
of the ball at different locations along its trajectory and quan- ing platform.
titatively confirm the statement above that the ball obtains a The correct explanation involves electromagnetic induc-
burst of speed close to the bottom part of its trajectory. tion. The electromagnet is always switched off and is then
Students will quickly notice that both the balls and rails switched on momentarily by a sensor when the ball is at the
are made of metal, which offers an immediate clue that mag- lowest point of the rail. In that case, how is the ball “boosted”
nets might be involved. The device does not look to have an by the magnet, since we normally think of magnets as at-
on/off switch, so the magnet is not switched on continuously. tracting objects toward them, rather than pushing them? The
At any rate, a constant or slowly varying magnetic field would answer to this is Lenz’s law and the presence of eddy currents.
not be able to produce the phenomenon that is observed, When a magnetic field is switched on in the presence of a
since energy will be lost during each cycle due to friction. An- conductive object, an eddy current (or Foucault current) is
other possibility is that the device simply runs for an extreme- induced in the object. An eddy current is a loop of electrical
ly long time, but does not run indefinitely. Obviously, we current induced in a conductor by a time-varying magnetic
cannot watch the machine for an indefinite amount of time, field in the conductor. This process is governed by Faraday’s
but the machine does not seem to be “grinding to a halt” after law of induction, also known as the Maxwell–Faraday equa-
watching a dozen consecutive cycles. As expected, inspection tion or Maxwell’s third equation.7
shows that there is an electromagnet in the base of the device, Electromagnetic induction is the effect whereby a chang-
although instructors may wish not to reveal this to students. ing magnetic field induces a current. A well-known example
Video analysis can confirm that the ball accelerates at the is a bar magnet moved through a stationary wire loop to
lowest point of the rail, where it is in contact with the top of induce a current around it. The “change” can be relative, so
the base. This lowest point looks to be around two-thirds it could be the magnet moving through the loop or the loop

17 December 2024 15:41:32

along the bottom, which matches the location of the magnet moving back and forth along a magnet that is at rest. More
in the base of the machine. specifically, time-dependent magnetic fields are coupled with
The first possibility that will likely occur in discussion is nonconservative electric fields. The electric field produced by
quite simple. Before seeing the electromagnet in the base of a stationary set of charges is conservative, but in this case, the
the device, students might guess that the magnet is always effect of the electric field is equivalent to that of a (noncon-
switched on once the device is started and is not controlled. servative) magnetic field (i.e., the line integral between two
This possibility can be removed immediately because if it points depends on the path taken, and the circulation around
were always switched on continuously, the magnet would take a closed loop is not zero). In the case of the magnet passing
at least as much kinetic energy from the ball as it imparted through the wire loop, we know that the wire loop is station-
to the ball. The second possibility is that the electromagnet ary while the magnet moves through and provides a changing
is switched on when the ball passes through the hole in the magnetic field. A current is produced, so an EMF (electromo-
platform: this electromagnet accelerates the ball toward the tive force) must be driving it. The magnetic field cannot itself
bottom of the ramp faster than it would accelerate by freely be the source of the EMF because magnetic fields only act on
falling under gravity. By timed electronics, the electromag- moving charges. Logically, the changing magnetic field must
net is switched off before the ball reaches the lowest point in have an associated nonconservative electric field (nonconser-
the ramp, which allows it to continue around the rest of the vative because conservative fields are electrostatic, and elec-
ramp, where it is launched back to the starting platform with trostatic fields cannot contribute to net EMFs). The induced
the extra speed that it obtained when the electromagnet was EMF around a closed curve is the same as the voltage drop
switched on. The process is then repeated indefinitely. This (i.e., the same as the line integral of the electric field around
explanation is incorrect, however, as the extra kinetic energy that curve). Mathematically, this is encoded by Maxwell’s
imparted in this way would be insufficient to allow the ball to third equation in integral form:
travel all the way back to the starting platform. The presence
E
of a CPU in the base of the device confirms that the actual
mechanism is slightly subtler than this and involves sensors.
A related possibility is that the electromagnet is always where E and B denote the electric and magnetic fields, re-
switched on and pulls the ball down as it is traveling down- spectively. In other words, the induced EMF around a closed
ward, but now the moving ball in the magnetic field creates curve is equal to the rate of decrease of magnetic flux over an
a change in the current flow that is sensed by a controller in open surface that has that same curve as its boundary. If one
the CPU, which switches the magnet off at the right moment. uses the curl theorem, the same equation can be written in

48 THE PHYSICS TEACHER t Vol. 62, J anuary 2024

differential form as
ator, the ring flies upward off the top of the coil in dramatic
fashion.8,9 Explaining why an AC current has this effect is not
an easy exercise.9 In this study, we have not settled the issue of
In the scenario that we are studying, the time-dependent whether the voltage source of this device is AC and whether
magnetic field induces an eddy current in the ball, which pro- this plays a role in the ability of the ball to dramatically “fly”
duces its own magnetic field. Lenz’s law states that the current from the rails to the platform, similar to the jumping ring. If
induced in a circuit due to a changing magnetic field takes a instructors are able to purchase the device, it would be an in-
direction that opposes the change in magnetic flux and exerts teresting student project to use an oscilloscope to determine
a force that opposes the motion. This law is somewhat quali- if the current in the electromagnet is AC and explain exactly
tative, but it successfully predicts the direction of an induced why and how this works in the toy.
current, which is sufficient for our purposes. Another, more
concrete way of stating it is that the polarity of the field pro- References
duced by the eddy current opposes the polarity of the mag- 1. A. Carter, Classical and Statistical Thermodynamics (Pren-
netic field that is doing the inducing. This causes the ball to tice-Hall, New Jersey, 2001).
be repelled away from the electromagnet by a magnetic force 2. J. H. Stamper, “Another perpetual motion machine,” Phys.
that accelerates it. The end of the rail is then cleverly designed Teach. 14, 507–508 (1976).
so that the ball flies off the end and lands back on the starting 3. R. A. Morse, “A perpetual motion demonstration??” Phys.
platform, where the process can repeat itself again indefi- Teach. 25, 354 (1987).
nitely. The description that I have proposed is confirmed by 4. D. A. Berry, “A perpetual motion toy?” Phys. Teach. 20, 319
(1982).
online descriptions of the product, which describe the toy as
5. J. Kore, “Using Phun to study ‘perpetual motion’ machines,”
being a “magnetic induction” perpetual motion simulator.6
Phys. Teach. 50, 278–279 (2012).
A subtler objection to this proposed solution is that the mag-
6. Amazon.com, “Perpetual Machine Simulator – Perpetual
nitude of the eddy currents depends on the concentration of Motion Device, Marble Machine Kinetic Art Desk Decor
free electrons in a metal, so that meaningful eddy currents Desk Top Decoration Gift for Children and Adults,”
are in reality expected in balls made of copper or aluminum, https://www.amazon.com/Perpetual-Machine-Simulator-
for example, but not balls made of steel. However, the mate- Decoration-Children/dp/B0B73X41TS.

17 December 2024 15:41:32

rial used for the balls is described in the online product de- 7. J. Bolton, An Introduction to Maxwell’s Equations (The Open
scription only as “metal” rather than stainless steel, whereas University, Milton Keynes, UK, 2006).
the rails are explicitly described as being made of “stainless 8. R. N. Jeffery and F. Amiri, “Thomson’s jumping ring over a
steel.”6 long coil,” Phys. Teach. 56, 176–180 (2018).
Finally, I observe that this investigation has been mainly 9. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman
theoretical and that there are a few remaining questions that Lectures on Physics (Addison-Wesley, Reading, MA, 1964),
could be resolved empirically by students with access to the II:16-5, http://feynmanlectures.caltech.edu/II_16.
device. The motion of the ball and the way it “jumps” due to html#Ch16-S3.
Lenz’s law is quite similar to a classic demonstration known
Hollis Williams is a postdoctoral researcher at King Abdullah University
as Thomson’s jumping ring, where an aluminum or copper
of Science and Technology. He is interested in various aspects of physics
ring is placed on the end of an electromagnet. When the coil education and theoretical physics and has published articles on fluid
is connected to a direct current generator, the ring briefly dynamics, quantum mechanics, and particle physics.
jumps upward because of induced currents in the ring. How- Division of Physical Sciences and Engineering, King Abdullah
ever, if the coil is connected to an alternative current gener- University of Science and Technology, Thuwal 23955-6900, Thuwal,
Saudi Arabia; hollis.williams@kaust.edu.sa

THE PHYSICS TEACHER t Vol. 62, January 2024 49