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Final Answers
© 2000-2016   Gérard P. Michon, Ph.D.

Motors & Generators

  • Homopolar motor:  The first electric motor, by  Michael Faraday  (1831).
  • Faraday's disk  can generate huge currents at a low voltage.
  • Magic wheels:  Two repelling ring magnets mounted on the same axle.
  • Beakman's motor.  Current switches on and off as the coil spins.
  • Tesla turbine.  Stack of spinning disks with outer intake and inner outflow.
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Related articles on this site:

Related Links (Outside this Site)

The Dynamo Process, by  David P. Stern.
Homopolar Generator  by  Gerald Zani  (Brown University).
Ultra-simple Electric Generator  by  William J. Beaty.
The World's Simplest Motor  by  Edmund Scientific.
How  universal motors  &  induction motors  work,   by  Mathias Wendel.
Ampère et l'histoire de l' électricité  (Blondel, Wolff, Wronecki, Pouyllau, Usal).
Arago's Disk  (at Vanderbilt University)  by  Thomas B. Greenslade, Jr.
Manufacturers :   Maxon Motor   |   Aveox   |   Transmagnetics
AXI Model Motors   |   Actro   |   etc.

Videos :

The first plug-in motor:  Curtis & Crocker Electric Motor Co. (1887)
 Robert Van de Graaff 

Motors and Generators

(2008-05-07)   Homopolar Motor   (Faraday, 1831)
The simplest electric motor design.  Low voltage,  high  current.

 Come back later, we're
 still working on this one...

Videos:  3-Part Homopolar Motor  from  DangerouslyFun.com
Homopolar Motor with Brake  by  Rick Crammond  (of Tesla Turbine fame)

(2008-05-08)   Faraday's Disk:  Low Voltage, High Current  (1831)
homopolar  contraption which helps clarify fundamental concepts.

Let's  first  imagine a device with axial symmetry whose characteristics are easy to figure out.  (We'll end up analyzing something even simpler.)

 Homopolar Generator  

Consider a conducting disk  ("copper disk")  spinning rapidly in a small gap between two slightly smaller ring magnets  (axially magnetized).  In the main, the magnetic flux  F  through the copper disk is equal to the surface area  S  of the facing magnets multiplied by an average magnetic induction  B  whose value is roughly the sum of the surface fields of the two magnets.

F   =   B S   =   B  p ( OD 2 - ID 2 ) / 4

Current may travel from the center of the disk  (through a conducting axle)  to the rim, where it's collected either by uniformly distributed brushes or by a circular contact with a pool of mercury.  In a steady regime, each line of current need not be straight but it's rigidly attached to the disk and will thus cut through the above magnetic flux  once per cycle.  If the disk spins at a frequency  n  expressed in hertz  (1 Hz  is  60 rpm)  the voltage  U  between the axle and the rim is thus:

U   =   F n   =   B S n

The internal resistance of this type of generator can be extremely low  (it's basically the resistance of the axle, the disk and the mercury contacts).  Although the voltage is modest, the current produced can be  extremely high.

Here are a few (optimistic) estimates of what would be obtained with readily available neodymium magnets of different sizes  (and prices)  using a thin disk and a small gap between the magnets.  Actual measurements could be  20%  lower, because the values of the induction fields are overestimated.

Voltage at 10,000 rpm, vs. price of a pair of magnets  (color-coded suppliers)
Ref. GradeHeightIDOD FieldmWb10,000 rpmCost
R1401 N450.7"1.75"4.25" 1.0 T7.61267 mV    $250.00
R4000 N450.5"1"4" 0.8 T61000 mV   $220.00
NR012-42NM N420.5"1"3" 0.9 T3.6600 mV   $50.26
RZ0Y0X0 N421"2"3" 1.2 T3500 mV   $190.00
RZ0X84 N420.25"1.5"3" 0.7 T2.4400 mV   $50.30
RY046 N420.375"0.25"2" 1.0 T2333 mV   $33.70
NR0072-40NM N421"0.25"1.5" 1.2 T1.3220 mV   $21.00
RFN40 N0.315"0.216"1.57" 0.9 T1180 mV   $15.00
RX054-N52 N520.25"0.3125"1" 0.9 T0.4169 mV   $10.50
RX032 N420.125"0.1875"1" 0.6 T0.2949 mV   $4.70
RX4C2 N420.125"0.75"1.25" 0.5 T0.2542 mV   $7.50

Polar plates must be used to reduce the magnetic losses from the center holes.  Ring magnets which have very large center holes  (like the huge  NR025 from  Applied Magnets)  are  not  suitable for this application, unless we design for the inside current the same kind of circular contact which is required for the outside current.  To be blunt, we could even rule out entirely the units which have holes larger than  1"  (ID)  in the above table.

The highlighted  RY046  (from  K&J Magnetics )  is nice enough.  Two  stacked pairs of these, would yield  70%  more voltage  (up to  570 mV  at  10,000 rpm).  With 3 pairs, we would obtain  700 mV  (at a cost of  $96.00).

If made out of pure copper, a  quarter-inch rod will have a resistance of about  0.5 mW  per meter of length.  For a half-axle of length  L=1.5", that's  0.02 mW  (That would be 0.01 mW  if both sides of the axle are used to carry current,  but substtuting brass for copper increases the resistance by a factor of 4.)  It would be an  overkill  to have a copper disk with an axle-to-rim resistance  much  below that.  Let's estimate what this entails for the thickness  (e)  of the disk:

Consider the disk at rest.  Let  s  be the resistivity of copper.  The electric field  E  inside the disk is radial and the current density  j  is proportional to it  (that's Ohm's law:  j = sE).  At a distance  r  from the axis, the current density is equal to the total current  I  divided by the lateral area of the relevant cylinder.  Thus:

j   =   I / (2pr e)   =   s E

(Incidentally, by Gauss's law, there's a static charge  eI/s  on the axle.)  The voltage  U  is the integral of  E dr  from axle  (r)  to rim  (r) :

U   =   ò  E dr   =   [ I / (2p s e) ] Log ( r1 / r0 )

This gives the resistance of the disk as  R   =   U/I.  On the other hand, the resistance of the half-axle of length  L  is:

R   =   L / (p s r02 )

Using  2r0 = 0.25",  2r1 = 2"  and  L = 1.5",  those two are equal when:

e   =   ( r02 / L )  Log ( r1 / r0 )   =   0.026 "   =   0.66 mm

Such a thickness should provides good enough structural integrity and doesn't force too large a gap between the magnets, (which would reduce the field, the flux and the voltage).  This corresponds to  22-gauge copper sheet  (thickness 0.025" = 0.635 mm).  Also usable are 24-gauge  (0.508 mm)  or  20-gauge  (0.8128 mm).  18-gauge copper is just about 1 mm  (0.04") which is probably too thick.

Making it Simpler :

As mentioned above, the lines of current are rigidly attached to the copper disk  (as they are related to the trajectories of charged particles which interact with the copper lattice).  However, the magnetic field lines are not similarly bound to the magnet.  If a magnet rotates around its axis of symmetry, the magnetic field stays the same.  Thus,  nothing  is induced on the copper disk if the magnets spins...

So, if we let the magnets spin at the same rate as the copper disk, we obtain exactly the same effect as if the magnets were stationary!  If we do that, we can bypass all of the precision machining and the risky business of maintaining a small gap between two powerful magnets:  Just sandwich the copper disk between the two magnets and spin the whole thing as a massive flywheel!

 Spinning Magnet  

Actually, we don't even  really  need the copper disk to produce the effect.  If you're in a hurry  (or can only afford one magnet)  just attach the magnet(s) to a quarter-inch screw with washers and spin that with a drill...  Use brushes (bare wire) and a voltmeter to observe the potential difference between the axis and the rim.  (A capacitor between the leads stabilizes the voltage.)

WARNING :   Spinning large neodymium magnets can be hazardous !

Neodymium magnets are brittle and their density is  7.5 g/cc.  This gives an RY046 magnet a mass of  143 g,  a moment of inertia of  0.000187  and a rotational energy of about  102.4 J  at  10,000 rpm.  A flywheel of 3 pairs would be 6 times that.

For an actual high-current generator  (with mercury contacts, casing, etc.)  a copper disk squeezed between two magnets has several advantages:  Voltage is highest on the equator of the rotor  (slightly above the surface of the magnets)  and a solid disk has lower resistance than mere magnet plating.

 Direction of Magnetic Field (B) Incidentally, the above voltage measurement tells you about the polarity of your magnet.  If the mechanical and magnetic north-south orientations are identical  (see sign conventions)  then the rotation tends to make the rim electrically more  positive  than the axis.

In the case of the Earth, the  North Magnetic Pole  is (currently) a  south  pole  (the north poles of small magnets point to it).  Thus, the rotation of the Earth creates an electromotive force  (emf)  which makes the equatorial regions more  negative  than the polar ones  (by about  100 kV).

Calculation Tools, courtesy of  K&J Magnetics  and  Magnetic Component Engineering
Copper supplies   |   Wikipedia :   Faraday Disk

 Two opposing ring magnets on an axle 
 will roll when a rim-to-rim current flows.
(2008-05-13)   Magic Wheels
Two  repelling  RY046  on one axle.

In pure roll, a current of  1 A  between the two rims imparts the axle a speed of 8.6 cm/s in one second. (One "D" battery can provide more than that.)

(2008-05-07)   Beakman's Motor: A simple educational demonstration.
A DC motor where the rotor is just a coil powered 50% of the time.

This simple design didn't have an established name when it appeared on the science-oriented TV show Beakman's World which aired  among the CBS Saturday-morning shows,  on December 3, 1994.  It was first described online as  Beakman's Electric Motor  by  Christopher M. Palmer,  in 1997. 

There were 91 episodes of "Beakman's World" made between 1992 and 1998.  Reruns have been airing again regularly since since 2006.  Electric motors are discussed in episode 42  (the 16th in season 2).
  Episode 42:   Electric Motors, Beakmania & Time :   Video in Portuguese

The rotor of Beakman's motor is entirely made from one piece of varnished wire  (even its mechanical axis just consists of the two ends of the wire, sticking out from the coil).  The "brushes" that feed the coil for only 50% (or so) of each cycle are merely obtained by scraping the insulating varnish off the upper part of the wire which will touch the conducting craddle  (it's only necessary to do this on one side, the wire on the other side can have its insulation removed completely).

Many articles and videos about this motor are now available on the Internet by several authors, including  Stan Pozmantir and Simon Quellen Field.  Chris Palmer's original  (at fly.hiwaay.net/~palmer/motor.html)  apparently vanished before  June 2011  (thanks to  Tim Winters  for pointing that out, on 2013-06-09)  but  excerpts  and  complete copies  can still be found.

To his original article, Palmer had added the following personal comment, which he had received from the late Mark Ritts (1946-2009):

I play  "Lester,"  the guy in the rat suit on  "Beakman's World,"
and I'm delighted to see my personal favorite Beakman experiment
so faithfully rendered and explained on the Web.  Thanks!

Mark "Lester" Ritts,   Los Angeles, California

The price to pay for the great simplicity of the Beakman motor is a total lack of usefulness.  As nothing can be attached to the axis of the motor, the success of a completed device can only be measured by how fast it runs  without load.

This was precisely the goal for the  motor contest  which Walter Lewin ran as part of his freshman class at MIT on electricity and magnetism  (8.02)  in 1984, 1988 and 2002.  The 2002 award ceremony honored JungEun Lee (4700 rpm) as well as a contestant not enrolled in the class  (Daniel Wendel, 4900 rpm).  Tim Lo (1250 rpm)  received a special prize for  most artistic design.  The runners-up were Adam Kumpf (4100 rpm)  and  Ryan Damico (2500 rpm).  Only 6 of the 225 motors entered by students for extra credit ran at or above  2000 rpm.

Building this motor is a great classroom activity which can be completed in a single class period.  Like Walter Lewin at MIT, high-school teachers are making it more fun by letting the students compete for the fastest motor.

To measure motor speed, the traditional way with strobe lights (as used by Pr. Lewin) is best replaced by some form of electric frequency measurement.  An adequate signal can be obtained directly from the supply voltage, because of the battery's internal resistance  (Brian Lamore).

Alternately, you can built a general-purpose probe to measure the occultations of the light from a laser beam received by a photoelectric cell  (this is another fun project by itself).  Such a probe allows measurements without touching the running motor of a student  (and the rotor need not be marked with white paint either).  Make the device portable and simple to use by attaching the laser pointer and the photocell to the ends of a rigid bow  (like a hacksaw frame).

In a Beakman motor, the spinning coil produces  two  occulations per revolution if the laser is pointed at the fringe, but there are twice as many if the laser is allowed to go through the coil  (the occulattion pattern is asymmetrical unless the beam goes through the center of the rotor).  Using the "fringe" methods (the only one available if the coil is not hollow) the motor's rpm is actually 30 times the observed frequency of occultation measured in Hz.  The conversion factor to use is only 15 with the "center" method.

Videos:  Trivial Electric Motor   |   Final assembly of a Beakman motor
Mark Ritts (1946-2009)   American actor and puppeteer  ("Lester the Rat" on  Beakman's World, CBS)

(2008-05-08)   Tesla Turbine   (Nikola Tesla, 1913)
Spinning stack of disks set in motion by a centripetal flow of fluid.

 Come back later, we're
 still working on this one...

15,000 rpm Tesla turbine, using hard-drive platters  by  "Luke Luck"

visits since May 8, 2008
 (c) Copyright 2000-2016, Gerard P. Michon, Ph.D.