Free energy with wires and magnets - can you come out ahead?
The basics of magnets and wires for free energy buffs.
Prepared by Tom Napier. Copyright © 1998, All rights reserved.
Over-unity motors and generators -- the bottom line
Prepared by Tom Napier. Copyright © 1999, All rights reserved.
Some months ago I posted a detailed analysis of the forces between magnets and
current carrying wires. (See "The basics of magnets and wires for free energy
buffs.") For the benefit of those who found its 3400 words a bit much to wade
through here is the "executive summary." See my earlier article if you want more
Point 1. Under ideal conditions the electrical power output generated when you
move a conductor through a magnetic field is exactly equal to the mechanical power
input needed to move the conductor.
Point 2. This applies to every microscopic piece of conductor, no matter in which
direction it moves, at what speed it moves or how strong the field is.
Point 3. The sum of the output electrical power round any closed loop is equal to
the sum of the input mechanical power, less any resistive losses in the conductor and
frictional losses in the moving parts.
Point 4. Thus the output power from a electrical generator of any type is always
less than the input power. No external devices such as commutators, tuned circuits
or diodes can change this.
Point 5. Under ideal conditions the mechanical power output generated when you
pass a current through a conductor in a magnetic field is exactly equal to the
electrical power input applied.
Point 6. This applies to every microscopic piece of conductor, no matter in which
direction it moves, at what speed it moves or how strong the field is.
Point 7. The sum of the output mechanical power round any closed loop is equal to
the sum of the input electrical power, less any resistive losses in the conductor and
frictional losses in the moving parts.
Point 8. Thus the output power from a electric motor of any type is always less
than the input power. No external devices such as commutators, tuned circuits or
diodes can change this.
Point 9. When you test a motor or a generator it can be very difficult to measure
both the mechanical and the electrical powers with sufficient accuracy to compute the
real efficiency. The calculated efficiency may be either higher or lower than the
The bottom line: You don't have an over-unity system until you can demonstrate a
stand-alone device which drives itself and simultaneously generates a non-zero output
Machines which use magnets
Magnets are fascinating things, the way they push and pull and twist each other with no apparent connection between them. It's tempting to suppose that there must be some way of arranging them to extract energy from them. For example, one of the earliest perpetual motion machines proposed to use a lodestone, (a lump of naturally magnetic iron ore) to pull a ball up a slope towards a hole through which it would drop to cycle back to the start. This didn't work.
Neither do its modern derivatives, and for the same reason. Any work which a magnet does on an object has to be undone to get back to the starting position. (This is also why an unbalanced wheel won't work.) Moving something in a closed loop in either a magnetic or a gravitational field causes it neither to gain or lose net energy. Since this applies to all objects, it applies to every part of a machine, no matter how complicated it is. There's no way of combining many zeros to get a positive result.
This doesn't stop people proposing motors which are driven only by magnetic fields. These motors have rotors which are pushed or pulled most of the way around a circle by some arrangement of magnets. There's nothing impossible about this, but the designers then expect the rotor to suddenly ignore the magnetic field and to complete the cycle. This gets the rotor back to its starting point after delivering a net output of energy. This is impossible.
Machines which use magnets and wires
So forget magnets acting alone. Let's mix in some wires and electric currents. Our whole civilization depends on devices which move wires in magnetic fields to generate electrical power and other devices which pass an electric current through a wire to generate motion; that is, on electrical generators and electric motors.
People are always asking me whether their odd configuration of wires and magnets will generate a power output from lesser input power. The answer is no, but it is not always clear from elementary physics textbooks why this is so. Textbooks are inclined to describe the forces involved without explaining what the implications are.
Generating voltages in wires
Let's start with generators. If you have a uniform magnetic field, say between the poles of a horse-shoe magnet, and you move a straight wire through the field so that the field, the length of the wire and the direction of motion are all at right angles to each other then a voltage will appear between the ends of the wire. In this simple case it is easy to calculate the voltage, it is equal to BvL volts. L is the length of the wire in meters, B is the strength of the field in webers/square-meter and v is the velocity of motion in meters/second. To put this effect in perspective, 1 weber/square meter (10,000 Gauss) is a much stronger field than you can get from a small permanent magnet. To generate a field this strong and a meter across would require an electromagnet weighing several tons. Wiggling a few inches of wire in the field of a small magnet will produce a few millivolts. It makes no difference whether it is the conductor or the field which is moving, only the relative motion counts.
Looking at this effect in isolation, we have a length of wire moving continuously in a uniform field. No work is needed to keep the wire moving since, once we have started it off, it is generating no electrical power output. It took some energy to overcome the wire's inertia when we started it moving and some more energy to establish the initial field between the ends of the wire but we will overlook them. (When the wire stops moving we can, in principle, recover that energy.)
Completing the loop
Suppose we want either to measure the voltage generated or to do something useful with it. To attach a voltmeter or a load resistance we must complete a loop which contains the bit of wire we are looking at. Suppose we truly have a uniform field and that it is very large, at least in the direction we are moving. Imagine, for example, that we are traveling north on rails between the poles of a magnet which is several miles wide. Our test wire extends from east to west and the field goes from down to up. We are traveling fast enough to generate one volt between the ends of the wire.
To make it easy, we are sitting at the east end of the wire so we can hook up our voltmeter up to the east end without any trouble. How do we connect the voltmeter to the west end of the wire? With another wire, of course. But that wire is also going from east to west and is traveling at the same velocity as the first one. It also has a voltage of one volt induced in it. The west end of both wires have the same voltage on them; when we connect them together the net voltage around the circuit is zero and that is what our voltmeter will show. No matter what route the second wire takes from east to west it will have exactly the same voltage across it as the test wire. If we connect a load resistor to the loop of wire no current will flow and no output power will be generated.
What this shows is that in order to generate a voltage in a loop of wire one of two conditions must hold. 1) the field in one part of the loop must be different from the field in another part or, 2) the velocity of one part of the loop must be different from the velocity of another part of the loop.
Types of loops
The first condition can be met, for example, by using a small magnet and a large loop so that only a part of the loop is in the strong field.
Obviously this limits the length of time we can generate a voltage at any given velocity.
One way to meet the second condition would be to slide the wire through the field on rails. Since the rails would not be moving they would not contribute to the voltage.
These illustrate a general principle which says that so long as the product of a magnetic field and the area of a loop remains constant no
voltage is generated round the loop. Either the area of the loop or the strength of the field must change to generate a voltage. You can vary the strength of the field within the loop by moving the loop from a weak field to a strong field, that was Case 1 above, or by changing the effective area of the loop, as in Case 2 above.
Another way to vary the effective area of a loop is to rotate it in the field. This makes its effective area go from +A to -A and back to +A every complete turn. Or look at it this way, twice per turn one side of the loop will, briefly, be moving in the opposite direction to the other. It will generate a voltage which adds to the first side's voltage rather than subtracting. Half a turn later the loop will be generating a voltage in the opposite sense. Thus, if we hook up the two ends of the loop to slip rings we will see an output voltage which alternates as the loop turns. Not only can we measure the voltage but we can get a useful output. We have just invented the alternator.
If the two ends of the loop are connected to a split ring around the shaft then a brush on each side of the ring will pick up pulses of voltage which all have the same polarity. By adding loops, each at a slightly different angle, and connecting each to a pair of segments on a commutator, at any moment the brushes will connect only to the loop which is moving fastest in the field. This gives an almost steady output voltage, resulting in a DC generator.
What happens elsewhere in the loop?
Let's go back to that original piece of wire. If it is not at right angles to the field or if it is not moving at right angles to its length the voltage generated will be less than in the right angle case. It will be proportional to the sines of the angle between the motion and the field and the sine of the angle between the wire and its direction of motion. If the motion is along the field or the wire is moving lengthwise no voltage will be generated.
By using this relationship we can, at least in theory, calculate the voltage round any loop of wire moving at any velocity in any magnetic field by adding up the contributions from each little piece of wire. Some quite ingenious ideas fall flat when this is done. The inventors have looked only at the interesting part of their machine and have ignored the fact
that all magnetic fields loop back on themselves somewhere. The voltage generated in that part of the loop also has to be taken into account. It often cancels out the voltage in the rest of the system.
Where does energy come in?
As I mentioned, moving a wire through a field requires no energy. That rotor I mentioned will spin until friction stops it. (I know, I'm ignoring eddy current losses here.) You can hang a voltmeter on the output and measure the voltage without any significant effect. By giving the loop of wire many turns you can generate as big an output voltage as you please. Using a stronger field, a faster rotor speed or a longer rotor also increases the output voltage. Unless some current flows no energy is needed to keep things moving.
What happens when current flows?
Let's just stop there and look at another phenomenon which occurs when you play with wires and magnets. This time let's hold that wire in the uniform field in a fixed position and pass a current through it. What happens is that the wire tries to move in a direction at right angles to both the field and the current. The force needed to keep the wire still is given by ilB where i is the current in amps, l is the length of the wire in meters and B is the field strength in webers per square meter. The force is measured in Newtons.
If we let the wire go it will start moving across the field. Its acceleration will be proportional to the current times the field strength. In Newtonian physics there is no limit to how fast it will go. (This principle has been proposed for firing payloads into space.) However, when the wire moves a voltage is generated across its ends. This is where we came in. The faster the wire moves the higher the voltage generated. This voltage acts in the opposite direction to the current we are feeding in, making it harder and harder to force that current through the wire. For a given current, low speed equals low back voltage and hence low electrical power input. A high speed generates a high back voltage and thus requires a high electrical input power. Now the mechanical energy out is simply equal to the force exerted times the speed. Low speed equals low output power and high speed equals high output power. Are you beginning to see a pattern? Low mechanical power out equals low electrical power in; high mechanical power out equals high electrical power in.
Computing the input and output powers
The power in watts which we are feeding into the wire is the product of the current and the voltage. If the wire is moving at a constant velocity and is lifting a weight at so many meters per second. Then the mechanical power being generated is just the product of the velocity times the force on the wire. The force is proportional to the current and the back voltage is proportional to the velocity so the input power is proportional to the output power. When you trouble to multiply out all the units it turns out that the mechanical power out is exactly equal to the electrical power in. (With the usual provisos about friction and resistive losses being negligible.)
Turn things around
Exactly the same thing applies the other way round when you apply mechanical power to a wire. As the wire moves it generates a voltage proportional to its velocity. If a current flows the electrical output power is proportional to the product of the voltage and the current, that is, it is proportional to the product of the current and the velocity. Now when a current flows in the wire it generates a force on the wire. Surprise, surprise, this force acts to oppose the motion of the wire. To keep it moving you have to push it harder. The mechanical energy you must apply is proportional to the velocity and the reverse force caused by the output current. In this case the output electrical power is equal to the
input mechanical power.
In a way this is rather wonderful. It means that we can convert mechanical power into electrical power or electrical power into mechanical power with practically no losses. This is impractical with thermal power.
Unfortunately, since the equality of power in and power out applies to each little piece of wire, no matter how it is moving and in whatever magnetic field, you can never come out ahead. Any device, no matter how ingenious, which generates an output current also generates a force opposing its motion. Any device which generates motion from a current also
generates a back voltage which opposes the input current.
A practical case
The alternator I described will spin happily with almost no input power until you connect something to its output terminals. Then a current will flow which is given by the output voltage divided by the total resistance of the wire loop plus the resistance the load you apply. If the loop resistance is not zero the output voltage will drop. The useful output power is this lower voltage times the current so it pays to use low resistance wire.
By allowing a current to pass you are applying a mechanical load to the alternator. It thus requires more input power to keep it turning. The more output power you take the more difficult it becomes to turn the rotor. I have a DC motor with a built-in reduction gearbox. It is easy to turn its output shaft by hand when its leads are open circuit but almost impossible to turn it if they are shorted together. Power out, at best, equals power in.
What about the homopolar generator?
Sometimes it can be quite hard to see just where the current loop is. Faraday discovered that if you turn a conducting disk in a magnetic field you can measure a voltage between the shaft of the disk and its rim. This device, the homopolar generator and its equivalent, the homopolar motorhave been baffling people ever since.
Consider a disk which is rotating in a uniform magnetic field. The field passes through the disk at right angles to its surface. Any radius of that disk is moving through the field. The parts of the radius near the shaft are moving slowly and the parts near the rim are moving quickly but they are all moving in the same direction so the voltages generates by each little bit of the radius all add up. The result is a voltage all round the rim of the disk which is higher than the voltage at the center.
If you mount a sliding contact at any point on the rim you can measure this voltage. It won't be a large voltage since only a single conductor is moving through the field and parts of it are not moving at the full speed. Suppose you had a copper disk 20 cm (8") in diameter, turning at 10,000 revolutions per minute, and that you could put it in a uniform 0.1 weber field. (This would be a very dangerous thing to try!) The rim will be moving at 105 m/s so the mean velocity of a radius is half that. The length of the radius is 0.1 meters and the field is 0.1 webers so the voltage will be 0.52 Volts, about a third of what you'd get from an alkaline cell!
If your disk had a low resistance, and if the brush contact and the external circuit also had a low resistance, then quite a substantial current would flow from the shaft to the rim. Because the voltage is generated on all radii of the disk you could put brushes all round the rim and reduce the effective generator resistance. Unfortunately the frictional forces on the edge of the rim chew up a lot of input power. As in any other generator, the motion of the disk is resisted by the force which the magnetic field exerts on the output current. Thus homopolar generators are only useful if you need a high current at a low voltage and don't care how much energy it takes to turn the disk.
As a footnote, I mentioned using a uniform magnetic field. You might think that having a field just between the shaft and the point on the rim where the brush is placed would be more efficient. Unfortunately, when the field is not uniform over the whole disk local currents are generated in the disk, heating it up and wasting input power. This "eddy-current" effect is the basis of the magnetic brake. Electricity meters are one common application and some car speedometers also depend on this effect.
The homopolar motor
If you pump a huge current into the disk the magnetic field will generate enough force on it to make it rotate despite the brush friction. (Early experimenters made contact to the rim of the disk by making it pass through pools of mercury. Since mercury vapor is rather poisonous this is not done any more.) Unfortunately, generating large direct currents at low voltages is a notoriously inefficient process. AC can be transformed down to get a low voltage but the rectifying device needed to convert the output to DC tends to drop about half a volt, making the efficiency less than 50% before you start moving anything. About the only device which can generate large currents at low voltages at all efficiently is, you guessed it, a homopolar generator.
Defeating your own object
One hopeful inventor thought that you could generate an output voltage without generating a reverse force by attaching the magnets generating the field to the rotating disk. Unfortunately, this doesn't work. Only relative motion of the field and the current carrying disk generates a voltage. What misled this inventor was that he did measure a voltage when he connected a meter between the shaft and the rim of the disk. He hadn't realized that the ring magnets were generating two fields, one in the disk between the magnets and another toroidal field in the space around the disk. The disk wasn't generating a voltage but the wire leading to the meter was being cut by this rotating field and was generating a small voltage. Connecting a current meter would have shown an output current. However, this current would have reacted on the rotating field to slow the disk down. As I said before, you have to consider what is happening
everywhere in the system, not just focus on one part of it and ignore the rest.
The effect was the same as if the disk and magnets were stationary and a contact had been spun round the edge of the disk. The wire going to the contact would have been moving in a magnetic field and all the usual rules would apply.
No arrangement of wires and magnetic fields and moving parts is going to generate more electrical power than the input mechanical power or generate more mechanical power than the input electrical power. If you want to experiment, by all means have fun, but please don't think you are going to bring about an energy revolution. Above all, spend only your own money, not other people's unless you want to spend the rest of your life dodging irate investors.
Additional notes by Eric:
A perpetual motion of new "inventors" thinks they are making fresh attempts at this "engineering holy grail". I've had scores of people tell me that they are hoping to fine tune some collection of wires and magnets that can finally come out ahead. Justifications are given along the lines, "if I try hard enough" "it must be possible because it is needed", "xyz book reports someone did it and then forgot how", or "my new theory of physics explains why it can work". My prize money for proof of free energy will be awarded if anyone can show me the real thing working - and I have no interest in someone's new theory until they win the prize. I feel the existing formulas comprising relationships between energy, motion, current, magnet flux lines, fields, etc. do a fine job of explaining evidence.
What about systems involving batteries?
Putting an occasional back surge of voltage in a battery can help get a temporary increase of performance. Also, most batteries after being discharged and disconnected can revive a little on their own. FE claims involving batteries never are operated indefinitely which would show if they are just running down the batteries. Most demonstrations I know of (like the farces Joe Newman puts on) involve pathetic means of comparing input and output energy levels. Motors/generators with big sparks are only wasting excess energy and likely creating illegal noise on radio frequency bands.