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basic principles

There were many discoveries in electricity and magnetism that ultimately led to the invention of the electric motor, but a fairly clear understanding of motors can be achieved by focusing on only two simple principles:

1. magnets exert forces on each other
2. when an electric current flows through a wire, it produces a magnetic field

A motor makes use of these principles by using the forces between magnets to drive the motion, and by making at least one of those magnets an electromagnet in order to control and direct the forces.

The first principle is the best known. Magnets come with two types of poles, called "north" and "south". In a typical bar magnet, one end is the north pole (often painted red) and the other end is the south pole (often painted silver or white). If we bring two poles of two separate magnets together, they will try to push each other apart if they are the same type of pole (two north poles or two south poles), and they will try to pull each other together if they are different types (one north and one south). These forces between magnets have been recognized since ancient times. Naturally occurring magnets known as lodestones were familiar to ancient philosophers, and were used as compasses for navigation in 12^th century China.1

The second principle was discovered in April 1820 when the Danish scientist Hans Christien Ørsted observed that an electric current in a wire caused a nearby magnetic compass needle to deflect, thereby showing that the current-carrying wire acted like a magnet. This is the principle behind the electromagnet (see the lesson on Basic Electromagnets). In the same year, the French scientist André-Marie Ampère observed and characterized the magnetic forces between two current-carrying wires.

In a general sense, forces between magnets are what drives a motor. An electric motor contains two or more magnets, at least one of which is an electromagnet. In a typical motor, at least one magnet is free to move (often mounted on an axle that can turn, called the "rotor"), while one or more other magnets are fixed nearby. By careful design, the forces between the magnets can be directed to turn the axle.

At least one electromagnet is needed in order to sustain the continuous motion of the motor. If only permanent magnets were used, the motor might initially turn, but it would soon come to rest at a point where the magnetic force can push it no further. By using an electromagnet, the current can be reversed when approaching the resting position (or the path of the current can be changed in some other way), thereby changing the magnetic forces and causing the rotor to continue moving towards a new resting position. (In some designs, the electromagnet is simply turned off when approaching the resting position, so that the rotor coasts around to the other side before the magnet is turned on again -- the Safety Pin Motor is an example of such a design.) Furthermore, an electromagnet can be turned off in order to stop the motor.

magnetic forces on moving charges

One way to understand the forces that drive a motor is to think of them as forces between magnets, in which at least one of the magnets is an electromagnet. Another way to understand the same forces is to think of them as magnetic forces acting directly on electric currents; or, since electric currents are caused by electrons flowing in a conductor, to think of them as magnetic forces acting directly on moving electrons. The force that a magnet exerts on a moving charged particle is called the "Lorentz force", named after the Dutch physicist Hendrick Lorentz. We can describe that force in terms of what scientists refer to as "magnetic field lines".

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Fig. 1:  Field lines around a bar magnet point away from the north pole and towards the south pole. At any point in space, the field line through that point shows the direction the force would be on a north magnetic pole located at that point.

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Fig 2:  Iron filings on a piece of paper above a bar magnet. At each place on the paper, the iron filings pivot to point along the direction of the magnetic force.

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Fig. 3:  Schematic for a "rail gun". In this figure, the magnetic field lines from some external magnetic source (not shown) are pointed downward (blue arrows). An electric current running through the rails and the movable rod generates a Lorentz force on the rod, which pushes it along the rails in the direction of the green arrow. Note that the force is perpendicular to both the current in the rod and the the field lines.

In the early 1800's, the English scientist Michael Faraday introduced the concept of "magnetic lines of force", which led to the modern concept of magnetic field lines. Faraday noticed that if we scatter iron filings around a magnet, the filings line up to form chains along certain directions. Each iron filing is shaped like a miniature needle, long and thin, and all the filings within a small region tend to point in the same direction. Faraday explained this behavior in terms of the forces on the ends of the iron filings. He knew that a piece of iron becomes magnetic when brought near another strong magnet, and so an iron filing in a magnetic field becomes a tiny bar magnet. (An example of magnetizing iron can be found in A Floating Compass, where we use a strong magnet to magnetize a steel needle.) He correctly realized that the reason the iron filings pivot to point in a particular direction must be because there is a magnetic force pulling the north pole of the filing in one direction and the south pole in the opposite direction (see Iron Filings and Magnets for more details). Faraday characterized these forces by "force field lines", which showed the direction of those forces. At any point in space, the field line through that point shows the direction the force would be on a north magnetic pole located at that point (and opposite the direction on a south magnetic pole). By scattering iron filings around a magnet, he could map out the direction of magnetic forces all around the magnet (Fig. 2). Check out Iron and Magnets for our own experiment with some further questions to ponder.

In 1892 the German scientist Hendrik Lorenz published a description of the force on a charged particle moving in a magnetic field.2 He demonstrated that the force at a particular location is perpendicular to the field line at that location, and also perpendicular to the direction of motion of the charged particle. The precise direction of the force is determined by a useful mnemonic called the right hand rule. In the special case where the particle is moving in the same direction as the field line, it feels no magnetic force at all.

Some very simple examples using the Lorentz force to power a motor are shown in Classroom Rail Gun. Figure 3 shows how the Lorentz force can roll a current-carrying rod down a pair of conducting rails. Many more examples of simple motors are listed at the end of this lesson.

motors and generators

Another insight into the behavior of motors involves their similarity to electric generators.

In 1820, Ørsted and Ampere described how an electric current can produce a magnetic field: a key principle in the operation of motors known as Ampere's law.3 In 1831, Michael Faraday discovered a closely related principle. He discovered that a changing magnetic field can induce an electric current. This principle is the fundamental principle behind the electric generator, and is known as Faraday's law.4 By spinning a coil of wire inside a magnetic field, or by spinning a magnet inside a coil of wire, a generator can produce a current in the wire, thereby providing electric power.

In a very real sense, Faraday's law and Ampere's law are converses of each other. A current produces a magnetic field (Ampere), while a [changing] magnetic field produces a current (Faraday). This relation also reflects the connection between a motor and a generator. By sending an electric current through a motor, electrical energy is transformed into the energy of movement. By turning a crank on a generator, the energy of motion of the crank is transformed into the electrical energy of the current in the wire. In fact, an electric motor and an electric generator are the same device. A generator is just a motor used in reverse. As the marvelous video below shows, a motor can be turned by hand to generate electric power, which can then be used to turn another motor.

examples of simple motors

Sciphile.org hosts a number of lessons on electric motors. Check out the curriculum about Magnets and Motors for suggestions about how to put some of them together into a coherent presentation.

Here are a few favorite examples, in order of increasing complexity.

Although not often identified as an electric motor, the rail gun (Classroom Rail Gun) is in some sense the simplest possible electric motor. It moves in a straight line rather than a circle, and it is a direct demonstration of the Lorentz force on a current-carrying wire.

Many other simple motors can be found in the class of "homopolar" motors. A homopolar motor is one that does not contain a commutator. In most commercial motors, the commutator is the rotary switch that periodically reverses the current in the rotor, thereby keeping a steady rotating force. In contrast, homopolar motors achieve a steady force by rotating on an axle that is parallel to the magnetic field. Two examples in Minimalist Motors show the general idea. Two other favorites in this category are the Faraday Motor and An Electric Screw Motor.

A few other devices convert electrical energy into motion, and perhaps ought to be classified with electric motors. Loudspeakers are a good example where electrical energy is converted into the motion of the speaker diaphragm. Generally however, a loudspeaker is usually classified as a nuisance rather than a motor. See the lesson on Homemade Headphones from Picnic Supplies  for more annoying ideas.

Safety Pin Motor demonstrates a motor design that contains a rotary switch. Strictly, the commutator in this motor does not reverse the current. It merely turns the power off for half a rotation and allow the rotor to coast around to the other side before turning the power back on. However, this lesson is very good for showing the basic idea behind the rotary switch.

question to ponder

• Why can't we make a motor just out of permanent magnets?

It's a little hard to understand this issue just by looking at the forces on magnets. Experience with a single pair of magnets shows us that two magnets will not be able to keep each other moving indefinitely. In particular, if they are completely free to move, two magnets will just rotate until they are attracting each other and then come together and stick with north and south poles touching. However, one might still wonder if some more complicated arrangement of magnets could continue the motion.

An easier way to look at this issue is to think in terms of energy. The law of conservation of energy states that energy can neither be created nor destroyed, it can only change from one form of energy to another. This is a fundamental law of physics that has its roots deep in the mathematical structure of physical law.5 As an example, chemical energy in a battery might be converted into  electrical energy of a current flowing through a wire, which in turn might be converted into kinetic energy of motion by turning a wheel, and also into heat energy through resistive heating of the wire, and friction between the wheel and the road. In no case, however, is energy lost. As long as we account for all the types of energy that can be converted, we will see that the total amount of energy is always the same as what we started with.

In order for a motor to lift an object against the force of gravity, or in order for it to accelerate a car down the road, or even keep it moving at a steady pace against the force of friction, the motor must supply energy, and that energy has to come from somewhere. For a motor constructed solely of permanent magnets, there is no way to get energy from the magnets indefinitely. Initially, energy in the magnetic field can be converted into kinetic energy to move the magnets, but if that energy is transferred somewhere else (to lift an object or drive a car for instance) the magnets will slow down and we cannot get that energy back. In the case of an electromagnet, electrical energy supplied to the motor can continually be converted into kinetic energy to keep the magnets moving, and drive the motor against a load.

further reading:

John Jenkins has compiled a beautiful visual summary of early motors at: http://www.sparkmuseum.com/MOTORS.HTM.

Frederick Gregory at the University of Florida has written a nice description of some of the history surrounding Ørsted's discovery.

Dr. David Stern at NASA has written a concise summary that puts the work of Faraday and Ørsted in a larger context.

• 1. http://en.wikipedia.org/wiki/Lodestone
• 2. Lorentz, Hendrik Antoon (1892), "La Théorie electromagnétique de Maxwell et son application aux corps mouvants at the Internet Archive", Archives néerlandaises des sciences exactes et naturelles 25: 363–552.
• 3. More precisely, Ampere's law relates the strength of the magnetic field as measured around a closed loop, to the electric currect that passes through the loop. See e.g. http://en.wikipedia.org/wiki/Amp%C3%A8re%27s_circuital_law
• 4. More precisely, Faraday's law of induction relates the flux of the magnetic field through a closed circuit to the voltage in the circuit, which can be used to drive a current. See e.g. http://en.wikipedia.org/wiki/Electromagnetic_induction
• 5. In 1915, a German mathematician named Emma Noether established a correspondence between invariances in the laws of physics and conservation principles. In particular, her work indicated that there was a connection between the conservation of energy and the invariance of the laws of physics over time. In other words, assuming the laws of physics to be the same today as they were yesterday, and the same again tomorrow, Noether was able to prove the conservation of energy. The proof is a bit technical, and is recommended only for geeks with a background in Lagrangian mechanics.