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The "Law of Relative Motion" that will pertain to all types of particles no matter what they are composed of is basically Ampere's 1825 Law:
Two bodies on orbits will have an attraction that will vary proportionally with the cosine of the angle of the planes of their orbits, and they will have a torque that will tend to make the orbits parallel and become oriented in such a way that both objects in both orbits are traveling in the same direction. . The attraction and torque thus produced will be proportional to the relative mass and velocity of the bodies.
Perhaps this can be stated in a simpler fashion:Objects traveling on parallel paths in the same direction tend to attract.
Objects traveling on parallel paths but moving in opposite directions tend to repel.
If the paths of these objects are not parallel then a torque will exist which will tend to make these paths parallel in a direction in which both objects are traveling the same way
We shall consider magnetism and find out if our Law of Relative Motion gives us in reality, the same answers as our observations of magnetism. . We know that electrons will repel each other, but by examining Figure 1. we arrive at a situation when they will attract each other. . In this figure we see wire A B and wire A' B' parallel to it. . The arrows indicate the direction that the electrons are flowing through the wires. . Actually these electrons will be going in various ziz-zag paths but experimentation has shown us that the net effect is the same as if they are traveling straight along the wire. . So we will consider that they do just that.
In reality when we have two wires such as these and the wires are carrying currents in the same direction, the wires will attract. . So this seems to agree with our Law of Relative Motion that says objects traveling on parallel paths in the same direction will attract. . Now consider wires C D and C' D'; the arrows again indicate the direction the electrons are flowing. . In these wires the electrons are traveling in opposite directions. . The "Law of Relative Motion" says that when things move on parallel paths in opposite directions they will repel. . Such is the case here which means that this law still holds true.
The way in which we obtained our "Law of Relative Motion" is found by observing these same wires. . If the wire A B was not parallel to wire A' B' but was inclined at an angle to it, we would not have as strong an attraction. . Ampere's 1825 law and our "Law of Relative Motion" tell us that this attraction varies with the cosine of the angle of the two wires. . As the angle becomes 90 degrees the cosine is zero and no attraction takes place. . As the angle is increased beyond 90 degrees the cosine is negative and the wires will repel. . We also have a torque which will tend to make the wires parallel and become oriented in such a way that the electrons in both of the wires are going in the same direction. . The reason for this attraction and repulsion is that the speed of light, or rather the speed of action at a distance, is trying to remain a constant regardless of the speed of the electrons. . We will investigate this constancy of the speed of light in future pages; at this point we shall proceed to see if our "Law of Relative Motion" continues to predict the behavior of other wires with electrons flowing through them.
A look at figure 2. shows a current flowing through coil A B which will be a fixed coil. . The electrons are traveling in the direction of the arrows. . We are going to pass a current through a much smaller coil A' B', the arrows showing us that the electrons are traveling in the same direction as coil A B. . We shall make this small coil parallel to the big one, but we will place this little coil on gimbals so that it may tilt in any direction. . We now find that coil A' B' will not stay parallel to the large coil but it tilts in the direction shown. . We are told that this tilt is because of collection of magnetic lines of force at the poles, but since we are trying to do away with the lines of force, as a tool, let us see if our Law of Relative Motion will retain its usefulness in this situation. . As we look at both A and A' the electrons in both orbital type paths are traveling on parallel paths in the same direction. . At B and B' the electrons are also moving in the same direction and on parallel paths. .
These points will also tend to attract but points B B' are closer together than points A A'. . Therefore since this attraction varies in intensity inversely proportional to the square of the distance, we can expect the pull at B B' to be greater than the pull at A A', and the little coil at A'B' should tilt. . If we were to move coil A' B' at different positions around the large coil, the small coil would tilt in respect to the varying distances of A A' to B B'. . We now can see the reason iron filings sprinkled around such a coil as A B, will give an illusion of magnetic lines of force. . We must consider each speck of iron as coil A' B' and being acted upon by both points A and B of the large coil. . In actual practice we will get this tilting in any size magnet because magnets are composed of small spinning electrons that when locked on certain orbitals in iron are in effect extremely tiny magnets. .
If we were to place the large coil A B on gimbals also, it would swing along with the small coil, A' B' to such a position that both of the coils would now be parallel. . What we have accomplished here now is that we have successfully used our "Law of Relative Motion" to eliminate magnetic lines of force when wires are wound on coils. . In the following section we shall test our new law using two more electrical devices: the electric motor and the generator.
We want to keep firmly in mind during the remainder of these proceedings that the electron has no such thing as a negative charge. . Remember, we're going to try and eliminate that from our mind. . We want to view the electron as nothing more than a high speed object that will obey the rules of our Law of Relative Motion.
Now we shall take a look at a generator and a motor, or at least a simple circuit of the same. . Here is where we utilize the fact that the object's mass is going to be determined by the speed through its relative surroundings. . In general relativity we found that relative mass is increased as an object's speed is increased, but what is its speed increased in relation to? . Einstein has also told us that no point in the universe can be said to be standing still. . So we can only assume that if an object goes faster in regard to us, then it might not be going faster in regard to another person, who let us say, might be going on a similar path as the object and close to the same speed as the object. . It is necessary to realize at this point that mass is going to be determined by the relative speed of an object through its surroundings.
In Figure 3. (below) we have a basic motor circuit. . We have a conductor in which electrons are flowing in the direction indicated by the arrow. . Do not confuse the electron flow with the current flow that some of the texts use that is opposite to electron flow. . We see two magnets on either side of this conductor, the arrows going around them indicating the direction electrons woud have to go if they were electromagnets. . An electron is moving in its orbit from A' to X'. . This is the part of its orbit that is parallel to the direction of electron flow through the conductor.
An electron in the conductor (above figure 3.) will have a parallel path to the orbit of the electron in the magnet because these orbits will tend to make themselves parallel. . Now as the electron in the conductor moves along path A X it will be going faster along path A X than a similar electron travels from A' to X' because of the added speed of the electron itself (electron flow) going through the conductor. . Now all of the electrons in the large magnets are lined up in the same planes and are, in fact, the cause of the magnet. . These electrons are, in a sense, saying to the electrons that are inside the conductor: "This is your orbit. You are at rest in this orbit along with the rest of us and from our point of view we are all stationary and it is the rest of the universe that is moving." . Since Galileo and Einstein both said that all motion is relative and that there is no fixed point in the universe that is standing still, then we must admit that if the electron in the conductor sees his neighbors on both sides of him, revolving at the same speed on parallel orbits then he might obtain this point of view, which we as outside observers would consider faulty. . Anyway this electron is not going to listen to our point of view and it is going to follow a geodesic. . A geodesic is the path of least resistance, and in this particular case, the geodesic will result from our point of view, as to what standing still means, against what standing still means to the electron. . Let us return to consider the electron in the conductor. . It is now being moved along path A X faster than it would have traveled if it had not been pushed through the conductor as well. . The neighboring electrons in the magnets are going to exert a drag on the electron in the conductor at this point and the result will be the same as if the orbiting electron was a rapidly spinning wheel and we had grabbed it all at once at point X. . What would we expect to happen if someone gave us a spinning wheel and we grabbed it by the rim? . It would pivot around the spot where we had grabbed it. . The same thing happens here and our conductor is forced downward. . We could use other points on the orbit, for instance, a point directly opposite from A X and say that in order for the electron to stay with his neighbors it would have to be accelerated instead of held back. . The result in either case, however, would be the same.
The physicist would say at this point why doesn't the author simply explain that since the electron is in the same plane as shown because of magnetic influence then it will only be necessary to give the relativity formula showing the relative mass of the electron, m, with the rest mass of the electron mo. . The formula is: m = mo /(1 - V2/C2)1/2 . This would show that a much greater force will be needed to move the electron through path A X because we are trying to move it at a higher speed now that is approaching the speed of light, and this means that considerably more force is needed to do this. . The electron in the conductor will be trying to spin and also orbit around a nucleus that is in the conductor, but yet stay at rest compared to the electrons in the magnets. . With either view the conductor still moves down, and we have explained why it moves down without using any magnetic lines of force, which incidentally everyone always agreed never existed in the first place. . I think that even Michael faraday who gave us these lines of force over a hundred years ago would have been one of the first to eliminate them if he could have found a better method of explaining magnetic phenomena.
It is hoped that even the physicist has gained something from the way we associated the relativity formula and the way in which different points of view of whatever is at rest will give us our geodesic, or path of least resistance, in which an object moves.
In Figure 4. (below) we are going to move the conductor physically downward this time.
The above figure 4. will be in effect a small electric generator. . As we move the conductor downward, the electron in its orbit is covering the A X section of its orbit but it has its own orbital speed plus the speed that we are moving the entire conductor. . Here we have a similar situation as existed in figure 3. . It would be as if the magnets alongside the conductor would apply the brakes to the electron every time it came to this section of its orbit. . Since we are physically holding the conductor and forcing it downward then the conductor cannot move in any direction except this. . Something has to give, however, and we force the electron to move through the conductor this time. . As the brakes are being applied to this electron, that is spinning and revolving at a speed already close to that of the speed of light, then the orbit will tend to pivot at point X and the whole orbit will be displaced in the direction shown. . Experimentation again shows us that this is the direction electrons will flow in a wire when a wire is pushed between magnets in this manner.
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