# The mystery of the magnetic train

This past week, thanks to Laughing Squid and other sources, a lot of people watched and were amazed by this simple demonstration of electromagnetism in action.

It is billed as the “world’s simplest electric train,” and it is almost certainly the case.  Using only a battery, some strong magnets and some (bare) coiled copper wire, one can make the “train” travel numerous circuits through the copper “track,” until the battery is completely drained.

This caught my attention because it is a very clever twist on one of Michael Faraday’s original discoveries!  Not electromagnetic induction, as I reflexively thought, but a homopolar motor.  Below is an animation of such a motor that I whipped up in my office.

A simple homopolar motor.  Just in case you don’t believe it actually works, a longer video is here.

This particular homopolar motor design is ridiculously simple: a pair of neodymium magnets are stuck (by magnetic force only) to the bottom of an AA battery. A wire loop is balanced on the top of the battery, bent so that it touches the magnets on the bottom.  When the connection is made, the wire will start to spin immediately, and will in general start spinning so fast that it will flip itself off of its perch.  More sophisticated and stable designs exist, but this one is quick and showy.

So how does the homopolar motor work, and the “magneto-electric” train shown in the video?  Both of them depend on the relationship between moving electric charges and magnetism, albeit in somewhat different ways.

Our story begins at the birth of what we now call “electromagnetism,” the beginning of a theory of nature that considers electricity and magnetism to be inextricably linked.  It began in 1820, when the Danish physicist Hans Christian Oersted demonstrated that a magnetic compass needle can be deflected by an electric current, proving that moving electrical charges produce a magnetic field.  Before this stunning experiment, it was generally assumed that electricity and magnetism were two completely separate physical phenomena.

What Oersted discovered, in essence, is that electricity flowing through a long straight wire creates a circulating magnetic field around it, as illustrated below.

A few of the magnetic field lines around an electrical current, I, in a really long wire.

For those unfamiliar with this graphical depiction of “fields,” I have written a “basics” post on the subject. One should picture these fields circulating around the wire at all heights and distances, being denser closer to the wire. Without going into too much detail how we know this, we note that the B-field represents a field of force that interacts with any permanent magnet brought nearby.  Such a permanent magnet will tend to do two things in a magnetic field: it will rotate to line up its North Pole with the field lines, and it will be drawn into a region with a stronger field, i.e. denser collection of field lines.

The field lines circulate around an electrical current in a sense that can be determined by the “right-hand rule”: pointing the thumb of your right hand in the direction of the current, the field lines will circulate in a sense determined by your fingers.

We can use this right-hand rule to also describe the fields around a loop of circulating current; in such a case, the field lines appear roughly as shown below.

The field of a magnetic dipole.

Once we’ve made a closed loop, the field lines are fundamentally different from the straight wire.  The field lines of the long wire have a handedness — that is, they circulate around in a right-handed sense — but they do not have a “side” to them.  The loop, however, has what we might call a “top” and a “bottom” or, more appropriately, a “North” and “South” pole.  The North side of the loop is the side from which the field lines emanate, while the South side is the side into which the field lines pass.  This loop has two poles, and is therefore referred to as a dipole.

This language of poles is suggestive of a regular bar magnet and the magnetic Earth, and that is of course the point — to a good approximation, a loop of current, the Earth, and a simple bar magnet all have a similar dipole field structure.  For instance, here’s a sketch of the magnetic field of the Earth, with corresponding bar magnet superimposed.

The Earth as a gigantic bar magnet. Note that magnetic North (the magnet’s South pole) is angled from the true North pole. (source)

The takeaway lesson here is that a loop of current will behave pretty much the same as an ordinary permanent magnet; that is, North and South poles will attract, while North-North and South-South combinations will repel.

This immediately gives us a simple explanation of how the “magneto-electric train” works!  When we place our battery, capped with magnets, inside the coil, we complete a circuit and a current flows through the coil.  The coil is, in essence, multiple loops of current stacked on top of one another, and the result is that the region of coil between the permanent magnets is a magnet itself!

We illustrate the situation below.  What happens: the “virtual bar magnet” created by the current flowing through the coil pushes the magnet in front and pulls the magnet behind. Of course the battery between them gets taken along for the ride!

This highlights an important point that wasn’t covered in the original video above — at least according to my experiments, it is necessary to make sure that the two magnets on either end of the battery have their North poles pointing in opposite directions!  Otherwise, they are either both pushing or both pulling, and the “train” doesn’t move.

Here’s my own short demonstration of the “magneto-electric train.”  It is surprisingly easy and cheap to put together.  I used a AAA battery as the power source, and a pair of strong neodymium magnets I had on hand; to give the train more “oomph,” additional magnets could be used on either side of the battery. I used 18 gauge copper wire for the coil, and wrapped it around a 1/2” ring stand to coil it.  It is important that the wire be uncoated — otherwise current will not flow and nothing will happen!  The 18 gauge wire seemed like the right balance of being easy to bend but rigid enough to hold a shape.  Also, it was all I could find at short notice.

With this explained, we can now turn back to the homopolar motor, which uses similar physics to make it spin.  Again, we have an electric current producing a magnetic field that interacts with a permanent magnet, but the interaction is a little more complicated.

A little extra history is worth sharing here.  We have already noted that the first link between electricity and magnetism was discovered by Oersted in 1820.  A number of scientists immediately saw the possibility of building an electric motor, including Michael Faraday‘s supervisor Humphry Davy, but their attempts to make one failed.  In 1821, however, Michael Faraday began his first real scientific job as Assistant Superintendent of the House of the Royal Institution.  Inspired by Davy’s work, he began his own investigations and quickly invented the homopolar motor; the illustration of his original device is shown below.*

Illustration of Faraday’s magnetic rotation device, via Wikipedia.

There are two devices pictured here.  The one on the right is closest to mine: a hanging wire dips into a container of electrically-conducting mercury, with an electrical ground coming through the bottom and a permanent magnet in the center of the container.  When a current is run through the wire and the mercury, the wire circles around the magnet.  In the system on the left, the wire is fixed in the center of the container, and the magnet ends up circling around the wire when the current is applied.

There is one significant difference between the magneto-electric train and the homopolar motor.  Where the train uses the magnetic field of a current to push magnets, the motor uses the field of a magnet to push the electrical current.

To explain the the motor, we therefore need one more piece of information: how a magnetic field effects moving charges.  An electric current produces a magnetic field, but the moving charges of an electric current also experience a force due to a magnetic field.  If we look at a single charge, we know from experiment that the force on it due to magnetism satisfies a different sort of “right-hand rule,” as shown below.

For this right-hand rule, we point our index finger in the direction the charge is moving, our middle finger in the direction that the magnetic field is pointing, and our thumb points in the direction of the force the charge experiences.  Therefore, an upward-moving positively-charged particle moving in a magnetic field pointing West will experience a force to the South.  One consequence of this is that a charge particle moving parallel to a magnetic field will experience no magnetic force at all.

I was asked an interesting question about this recently: why does a charged particle experience a “right-hand rule” force?  Why not a left-hand rule?  The answer is that a negatively-charged particle does move in the opposite direction, following the left-hand rule!  Since the definition of what we call a positive charge and what we call a negative charge was somewhat arbitrarily chosen by Benjamin Franklin in the mid-1700s, we might very well have spoken of a left-hand rule if he had chosen differently!

Now let’s see how this applies to the homopolar motor, as illustrated below.  The current (and therefore the electric charge) flows from the top of the battery through both arms of the wire loop and down through the magnet at the bottom.  Using our new right-hand rule on the right side of the wire, we see that the force on the moving charges, and therefore the wire, points out of the screen; we mark several of these points with red dots.  Using the right-hand rule on the left side of the wire, we see that the force on the moving charges, and therefore the wire, points into the screen; we mark these points with blue dots.   (Don’t be afraid to actually hold your hand up to visualize things — this is exactly what physicists-in-training, and physicists like me, do.)

The net result: the right side of the loop gets pulled, the left side gets pushed.  The wire loop spins around its balance point on the battery, and we have a motor!

Both the homopolar motor and the magneto-electric train are really eye-catching demonstrations.  They use same physics that makes all electric generators and electric motors work, but somehow their simplicity really drives home the fact that this is fundamental physics at play, and not some clever engineering trick.  I encourage everyone to give them a try — it is remarkably inexpensive to play with some of the greatest scientific discoveries in history!

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* Michael Faraday, “Description of an electro-magnetical apparatus for the exhibition of rotary motion,” Quarterly Journal of Science 12 (1821), 283.