The history of the development of a mathematical understanding of electricity and magnetism has been one of the great success stories of science and engineering. With the benefit of this information, a type of phenomena totally unknown up to a few centuries ago has been harnessed in a manner that has revolutionized life in the more advanced human societies. But in a strange contrast, this remarkable record of success in the identification and application of the mathematical relations involved in these phenomena coexists with an almost complete lack of understanding of the basic nature of the quantities with which the mathematical expressions are dealing.

In order to have a reasonably good conceptual understanding of electricity and magnetism, we need to be able to answer questions such as these:

- What is an electric charge?
- What is magnetism?
- What is an electric current?
- What is an electric field?
- What is mass?
- What is the relation between mass and charge?
- How are electric and magnetic forces produced?
- How do they differ from the gravitational force?
- How are these forces transmitted?
- What is the reason for the direction of the electromagnetic force?
- Why do masses interact only with masses, charges with charges?
- How are charges induced in electrically neutral objects?

Conventional science has no answers for most of these questions. To rationalize the failure to discover the explanations, the physicists tell us that we should not ask the questions:

The question “What is electricity?”—so often asked—is… meaningless.

^{36}

(E. N. daC. Andrade)

What is electricity?… Definitions that cannot, in the nature of the case, be given, should not be demanded.^{37}(Rudolf Carnap)

The difficulty in accounting for the origin of the basic forces is likewise evaded. It is observed that matter exerts a gravitational force, an electric charge exerts an electric force, and so on, but the theorists have been unable to identify the origin of these forces. Their reaction has been to evade the issue by characterizing the forces as autonomous, “fundamental conceptions of physics” that have to be taken as given features of the universe. These forces are then assumed to be the original sources of all physical activity.

So far as anyone knows at present, all events that take place in the universe are governed by four fundamental types of forces.

^{38}

As pointed out in Chapter 12, this assumption is obviously invalid, as it is in direct conflict with the accepted * definition *of force. But those who are desperately anxious to have * some *kind of a theory of the phenomena that are involved close their eyes to this conflict.

After having “solved” the problem of the origin of the forces by assuming it out of existence, the theorists have proceeded to solve the problem of the transmission of the basic forces in a similar manner. Since they have no explanation for this phenomenon, they provide a substitute for an explanation by equating this transmission with a different kind of phenomenon for which they believe they have at least a partial explanation. Electromagnetic radiation has both electric and magnetic aspects, and is unquestionably a transmission process. In their critical need for some kind of an explanation of the transmission of electric and magnetic forces, the theory constructors have seized on this tenuous connection, and have assumed that electromagnetic radiation is the carrier of the electrostatic and magnetostatic forces. Then, since the gravitational force is clearly analogous to those two forces, and can be represented by the same kind of mathematical expressions, it has been further assumed that some sort of gravitational radiation must also exist.

But there is ample evidence to show that these forces are *not *transmitted by radiation. As brought out in Volume I, gravitation and radiation are processes of a totally different kind. Radiation is an energy transmission process. A quantity of radiant energy is produced in the form of photons. The movement of these photons then carries the energy from the point of origin to a destination, where it is delivered to the receiving object. No movement of either the originating object or the receiving object is required. At either end of the path the energy is recognizable as such, and is readily interchangeable with other forms of energy.

Gravitation, on the other hand, is *not *an energy transmission process. The (apparent) gravitational action of one mass upon another does not alter the total external energy content (potential plus kinetic) of either mass. Each mass that moves in response to the gravitational force acquires a certain amount of kinetic energy, but its potential energy is decreased by the same amount, leaving the total unchanged. As stated in Volume I, gravitational, or potential, energy is * purely *an energy of position: that is, for any specific masses, the mutual potential energy is determined entirely by their spatial separation.

All that has been said about gravitation is equally applicable to electrostatics and magnetostatics. Each member of any system of two or more objects (apparently) interacting electrically or magnetically has a potential energy determined by the magnitudes of the charges and the intervening distance. As in the gravitational situation, if the separation between the objects is altered by reason of the static forces, an increment of kinetic energy is imparted to one or more of the objects. But its, or their, potential energy is decreased by the same amount, leaving the total unchanged. This is altogether different from a process such as electromagnetic radiation which carries energy *from * one location *to *another. Energy of position in space cannot be propagated in space. The concept of transmitting this kind of energy from one spatial position to another is totally incompatible with the fact that the magnitude of the energy is *determined by *the spatial separation.

As stated earlier, the coexistence of an almost total lack of conceptual understanding of electric and magnetic fundamentals with a fully developed system of mathematical relations and representations seems incongruous. In fact, however, this is the normal initial result of the manner in which scientific investigation is usually handled. A complete theory of any physical phenomenon consists of two distinct components, a mathematical formulation and a conceptual structure, which are largely independent. In order to constitute a complete and accurate definition of the phenomenon, the theory must be both conceptually and mathematically correct. This is a result that is difficult to accomplish. In most cases it is practically mandatory to approach the conceptual and mathematical issues separately, so that this very complex problem is reduced to more manageable dimensions. We either develop a mathematically correct theory that is conceptually imperfect (a “model”), and then attack the problem of reconciling this theory with the conceptual aspects of the phenomena in question, or alternatively, develop a theory that is conceptually correct, as far as it goes, but mathematically imperfect. and then attack the problem of accounting for the mathematical forms and magnitudes of the physical relations.

As matters now stand in conventional science, the requirement of conceptual validity is by far the most difficult to meet. With the benefit of the mathematical techniques now available it is almost always possible to devise an accurate, or nearly accurate, mathematical representation of a physical relation on the basis of those physical factors that are *known *to enter into the particular situation, and the * currently accepted concepts* of the nature of these factors. The prevailing policy, therefore, is to give priority to the mathematical aspects of the phenomena under consideration. Vigorous mathematical analysis is applied to models which admittedly represent only certain portions of the phenomena to which they apply, and which, as a consequence, are conceptually incorrect, or at least incomplete. Attempts are then made to modify the models in such a way that they move closer to conceptual validity while maintaining their mathematical validity.

There is a sound reason for following this “mathematics first” policy in the normal course of physical investigation. The initial objective is usually to arrive at a result that is useful in practical application; that is, something that will produce the correct mathematical answers to practical problems. From this standpoint, the issue of conceptual validity is essentially irrelevant. However, scientific investigation does not end at this point. Our inquiry into the subject matter is not complete until we (1) arrive at a conceptual understanding of the physical phenomena under consideration, and (2) establish the nature of the relations between these and other physical phenomena.

A mathematical relation that is unexplained conceptually is of little or no value toward accomplishing these objectives. It cannot be extrapolated beyond the range for which its validity has been experimentally or observationally verified without running the risk of exceeding the limits of its applicability (as will be demonstrated in Volume III). Nor can it be extended to any area other than the one in which it originated. As it happens, however, many physical problems have resisted all attempts to discover the conceptually correct explanations. Many of the frustrated theorists have reacted by abandoning the effort to achieve conceptual validity, and are now contending that mathematical agreement between theory and observation constitutes “experimental verification.” Obviously this is not true. Such a “verification,” or any number of similar mathematical correlations, tell us only that the theory is *mathematically * correct. As has been emphasized at several points in the preceding discussion, mathematical validity does not, in any way, assure conceptual validity. It gives no indication whether the interpretation that is being given to the mathematical relations is right or wrong. The inevitable result of the currently prevailing policy is to overload physical science with theories that are mathematically correct but conceptually wrong.

Solutions for the many long-standing problems of physical science clearly cannot be obtained as long as the attacks on the problems are terminated when mathematical agreement is achieved. But even if this defect in present practice is corrected, it is doubtful whether the answers to most of these difficult problems can be obtained by the prevailing method of devising a mathematical solution first, and then looking for a conceptual explanation. The reason is that a valid mathematical expression can be constructed to fit almost any model. As Einstein states the case:

It is often, perhaps even always, possible to adhere to a general theoretical foundation by securing the adaptation of the theory to the facts by means of artificial additional assumptions.

^{39}

Consequently, the mathematical expressions cannot be relied upon to furnish the necessary clues to a conceptual understanding.

The important contribution of the Reciprocal System of theory to the solution of these problems is that it enables attacking them from the opposite direction; that is, first arriving at a conceptual understanding by deduction from very general basic relations, and then developing the mathematical aspects of the established conceptual relationships. In other words, instead of getting a mathematical answer and then looking for a conceptual explanation to fit it, we start by getting a conceptual answer and then look for a mathematical way of expressing it. In general, this is a much simpler procedure, but it could not be utilized on any extensive scale until a unified general theory was available, so that conceptual answers could be obtained by deductive processes. The Reciprocal System of theory satisfies this requirement.

The clarification of the basic aspects of electricity and magnetism provides a dramatic example of the power of this new method of approach to physical problems. It is no longer necessary to deny the existence of answers to the questions listed at the beginning of this chapter, or to content ourselves with pseudo-answers such as the “curved space” explanation of gravitation. Two of these questions, “What is mass?” and “What is an electric current?” have already been answered in the previous pages of this and the preceding volume. Those involving magnetism will be answered in the general discussion of that subject which begins with Chapter 19, and the process of induction of charges will be explained in Chapter 18. The answers to all of the other questions in the list will be developed in this present chapter. When these presentations are complete, we will have provided simple and logical explanations for every one of these items with which present-day science is having so much difficulty.

In the universe of motion all physical entities and phenomena are motions, combinations of motions, or relations between motions. It follows that the development of the structure of the theory that describes this universe is primarily a matter of determining just what motions and combinations of motions can exist under the conditions specified in the postulates. Thus far in our discussion of electrical phenomena we have been dealing only with *translational *motion, the movement of electrons through matter, and the various effects of that motion, the mechanical aspects of electricity, so to speak. We will now turn our attention to the electrical phenomena that involve * rotational *motion.

As we saw in Volume I, gravitation is a three-dimensional rotationally distributed scalar motion. Objects having only one or two *effective *dimensions of scalar rotation were found to exist, but these objects, sub-atomic particles, have only a limited role in physical phenomena. In view of the general pattern of generating motions of greater complexity by combining motions of different kinds, the possibility of superimposing one-dimensional or two-dimensional scalar rotation on gravitating objects to produce phenomena of a more complex nature naturally suggests itself. On analyzing the situation, however, we find that the addition of ordinary rotationally distributed motion in less than three dimensions to the gravitational motion would merely modify the magnitude of that motion, and would not result in any new kinds of phenomena.

There is, however, a modification of the rotational distribution pattern that we have not yet explored. Three general types of simple motion (scalar motion of physical locations) have thus far been considered: (1) translation, (2) linear vibration, and (3) rotation. We now need to recognize that there is a fourth type: * rotational vibration, *a motion that is related to rotation in the same way that linear vibration is related to translational motion. Vectorial motion of this type is uncommon—the motion of the hairspring of a watch is an example—and it is largely ignored in conventional physical thought, but it plays an important part in the basic motion of the universe.

At the atomic level, rotational vibration is a rotationally distributed scalar motion that is undergoing a continuous change from outward to inward and vice versa. As in linear vibration, the change of scalar direction must be continuous and uniform in order to be permanent. Like the motion of the photon of radiation, it is therefore a simple harmonic motion. As noted in the discussion of thermal motion in Chapter 5, when such a simple harmonic motion is added to an existing motion it is coincident with that motion (and therefore ineffective) in one of the scalar directions, and has an effective magnitude in the other scalar direction. Every added motion must conform to the rules for the combination of scalar motions that were set forth in Volume I. On this basis, the effective scalar direction of a self-sustaining rotational vibration must be outward, in opposition to the inward rotational motion with which it is associated. A similar addition with an inward scalar direction is not stable, but can be maintained by an external influence, as we will see later.

A scalar motion in the form of a rotational vibration will now be identified as a *charge. *A one-dimensional motion of this type is an *electric charge. *In the universe of motion, any basic physical phenomenon such as a charge is necessarily a motion, and the only question to be answered by an examination of its place in the physical picture is what kind of a motion it is. We find that the observed electric charge has the properties that the theoretical development identifies as those of a one-dimensional rotational vibration, and we can therefore equate the two.

It is interesting to note that conventional science, which has been at so much of a loss to explain the origin and nature of the charge, does recognize that it is scalar. For instance, W. J. Duffin reports that experiments which he describes show that “charge can be specified by a single number,” thus justifying the conclusion that “charge is a *scalar *quantity.”^{40}

However, in current physical thinking this electric charge is regarded as one of the fundamental physical entities, and its identification as a motion will no doubt be a surprise to many persons. It should therefore be emphasized that this is not a peculiarity of the theory of the universe of motion. Irrespective of our findings, based on that theory, a charge is necessarily a motion on the basis of the * definitions* that are employed in conventional physics, a fact that is disregarded because it is inconsistent with present-day theory. The key factor in this situation is the definition of *force. *It was brought out in Chapter 12 that force is a property of motion, not something of a fundamental nature that exists in its own right. An understanding of this point is essential to the development of the theory of charges, and some further consideration of the relevant facts is therefore appropriate in the present connection.

For application in physics, force is defined by Newton’s second law of motion. It is the product of mass and acceleration, F = *ma*. Motion, the relation of space to time, is measured on an individual mass unit basis as speed, or velocity, v, (that is, *each* unit moves at this rate), or on a collective basis as momentum, the product of mass and velocity, mv, formerly called by the more descriptive name “quantity of motion.” The time rate of change of the magnitude of the motion is dv/dt (acceleration, a) in the case of the individual unit, and m dv/dt (force, ma) when measured collectively. Thus force is, in effect, defined as the time rate of change of the magnitude of the total quantity of motion, the “quantity of acceleration” we might call it. From this definition it follows that a force is *a property of a motion.* It has the same standing as any other property, and is not something that can exist as an autonomous entity.

The so-called “fundamental forces of nature,” the presumably autonomous forces that are currently being called upon to explain the origin of the basic physical phenomena, are necessarily properties of underlying motions; they *cannot *exist as independent entities. Every “fundamental force” must originate from a fundamental motion. This is a logical requirement of the definition of force, and it is true regardless of the physical theory in whose context the situation is viewed.

Present-day physical science is unable to identify the motions that the definition of force requires. An electric charge, for instance, produces an electric force, but so far as can be determined from observation, it does this on its own initiative. There is no indication of any antecedent motion. This apparent contradiction of the definition of force is currently being handled by ignoring the requirements of the definition, and treating the electric force as an entity generated in some unspecified way by the charge. The need for an evasion of this kind is now eliminated by the identification of the charge as a rotational vibration. It is now clear that the reason for the lack of any evidence of a motion being involved in the origin of the electric force is that *the charge itself is the motion.*

An electric charge is thus a one-dimensional analog of the three-dimensional motion of an atom or particle that we identified as mass. The space-time dimensions of mass are t^{3}/s^{3}. In one dimension this is t/s. Rotational vibration is a motion similar to the rotation that constitutes mass, differing only in the periodic reversal of scalar direction. It follows that the electric charge, a one-dimensional rotational vibration, also has the dimensions t/s. The dimensions of the other electrostatic quantities can be derived from those of charge. The *electric field intensity, *a quantity that plays an important part in many of the relations involving electric charges, is the charge per unit area, t/s × 1/s^{2} = t/s^{3}. The product of field intensity and distance, t/s^{3} × s = t/s^{2}, is a force, the * electric potential*.

For the same reasons that apply to the production of a gravitational field by a mass, the electric charge is surrounded by a force field. However, there is no interaction between mass and charge. As brought out in Chapter 12, a scalar motion that alters the separation between A and B can be represented in the reference system either as a motion AB (a motion of A toward B) or a motion BA (a motion of B toward A). Thus the motions AB and BA are not two separate motions; they are merely two different ways of representing the *same *motion in the reference system. This means that scalar motion is a mutual process, and cannot take place unless the objects A and B are capable of the *same kind *of motion. Consequently, charges (one-dimensional motions) interact only with charges, masses (three-dimensional motions) only with masses.

The linear motion of the electric charge analogous to gravitation is subject to the same considerations as the gravitational motion. As noted earlier, however, it is directed outward rather than inward, and therefore cannot be added directly to the basic vibrational motion in the manner of the rotational motion combinations. This restriction on outward motion is due to the fact that the outward progression of the natural reference system, which is always present, extends to the full unit of outward speed, the limiting value. Further outward motion can be added only after an inward component has been introduced into the motion combination. A charge can therefore exist only as an addition to an atom or sub-atomic particle.

Although the scalar direction of the rotational vibration that constitutes the charge is always outward, both positive (time) displacement and negative (space) displacement are possible, as the rotational speed may be either above or below unity, and the rotational vibration must oppose the rotation. This introduces a rather awkward question of terminology. From a logical standpoint, a rotational vibration with a space displacement should be called a negative charge, since it opposes a positive rotation, while a rotational vibration with a time displacement should be called a positive charge. On this basis, the term “positive” would always refer to a time displacement (low speed), and the term “negative” would always refer to space displacement (high speed). Use of the terms in this manner would have some advantages, but so far as the present work is concerned, it does not seem advisable to run the risk of adding further confusion to explanations that are already somewhat handicapped by the unavoidable use of unfamiliar terminology to express relationships not previously recognized. For present purposes, therefore, current usage will be followed, and the charges on positive elements will be designated as positive. This means that the significance of the terms “positive” and “negative” with respect to rotation in reversed in application to charge.

In ordinary practice this should not introduce any major difficulties. In this present discussion, however, a definite identification of the properties of the different motions entering into the combinations that are being examined is essential for clarity. To avoid the possibility of confusion, the terms “positive” and “negative” will be accompanied by asterisks when used in the reverse manner. On this basis, an electropositive element, which has low speed rotation in all scalar dimensions, takes a positive* charge, a high speed rotational vibration. An electronegative element, which has both high speed and low speed rotational components, can take either type of charge. Normally, however, the negative* charge is restricted to the most negative elements of this class, those of Division IV.

Many of the problems that arise when scalar motion is viewed in the context of a fixed spatial reference system result from the fact that the reference system has a property, *location,* that the scalar motion does not have. Other problems originate for the inverse reason: scalar motion has a property that the reference system does not have. This is the property that we have called *scalar direction, *inward or outward.

We can resolve this latter problem by introducing the concept of positive and negative reference points. As we saw earlier, assignment of a reference point is essential for the representation of a scalar motion in the reference system. This reference point then constitutes the zero point for measurement of the motion. It will be either a positive or a negative reference point, depending on the nature of the motion. The photon originates at a negative reference point and moves outward toward more positive values. The gravitational motion originates at a positive reference point and proceeds inward toward more negative values. If both of these motions originate at the same location * in the reference system, *the representation of both motions takes the same form in that system. For example, if an object is falling toward the earth, the initial location of that object is a positive reference point for purposes of the gravitational motion, and the scalar direction of the movement of the object is inward. On the other hand, the reference point for the motion of a photon that is emitted from that object and moves along exactly the same path in the reference system is negative, and the scalar direction of the movement is outward.

One of the deficiencies of the reference system is that it is unable to distinguish between these two situations. What we are doing in using positive and negative reference points is compensating for this deficiency by the use of an auxiliary device. This is not a novel expedient; it is common practice. Rotational motion, for instance, is represented in the spatial reference system with the aid of an auxiliary quantity, the number of revolutions. Ordinary vibrational motion can be accurately defined only by a similar expedient. Scalar motion is not unique in its need for such auxiliary quantities or directions; in this respect it differs from vectorial motion only in that it has a broader scope, and therefore transcends the limits of the reference system in more ways.

Although the scalar direction of the rotational vibration that constitutes the electric charge is always outward, positive* and negative* charges have different reference points. The motion of a positive* charge is outward from a positive reference point toward more negative values, while that of a negative* charge is outward from a negative reference point toward more positive values. Thus, as indicated in the accompanying diagram, Figure 20, while two positive* charges (line a) move outward from the same reference point, and therefore away from each other, and two negative* charges (line c) do likewise, a positive* charge moving outward from a positive reference point, as in line b, is moving *toward *a negative* charge that is moving outward from a negative reference point. It follows that like charges repel each other, while unlike charges attract.

As the diagram indicates, the extent of the inward motion of unlike charges is limited by the fact that it eventually leads to contact. The outward movement of like charges can continue indefinitely, but it is subject to the inverse square law, and is therefore reduced to negligible levels within a relatively short distance.

- | + | - | + | |

(a) | | | <=|=> | | | |
---|---|---|---|---|

(b) | |=> | <=| | ||

(c) | | | <=|=> | | |

Electric charges do not participate in the basic motions of atoms or particles, but they are easily produced in almost any kind of matter, and can be detached from that matter with equal ease. In a low temperature environment, such as that on the surface of the earth, the electric charge plays the part of a temporary appendage to the relatively permanent rotating systems of motions. This does not mean that the role of the charges is unimportant. Actually, the charges often have a greater influence on the outcome of physical events than the basic motions of the atoms of matter that are involved in the action, but from a structural standpoint it should be recognized that the charges come and go in much the same manner as the translational (kinetic or thermal) motions of the atom. Indeed, as we will see shortly, charges and thermal motion are, to a considerable degree, interconvertible.

The simplest type of charged particle is produced by imparting one unit of one-dimensional rotational vibration to the electron or positron, which have only one unbalanced unit of one-dimensional rotational displacement. Since the effective rotation of the electron is negative, it takes a negative* charge. As indicated in the description of the sub-atomic particles in Volume I. each uncharged electron has two vacant dimensions; that is, scalar dimensions in which there is no effective rotation. We also saw earlier that the basic units of matter, atoms and particles, are able to orient themselves in accordance with their environments; that is, they assume the orientations that are compatible with the effective forces in those environments. When produced in free space—as, for instance, from the cosmic rays—the electron avoids the restrictions imposed by its spatial displacement (such as the inability to move through space) by orienting in such a way that one of its vacant dimensions coincides with the dimension of the reference system. It can then occupy a fixed position in the natural system of reference indefinitely. In the context of a stationary spatial reference system, this uncharged electron, like the photon, is carried outward at the speed of light by the progression of the natural reference system.

If this electron enters a new environment, and becomes subject to a new set of forces, it can reorient itself to conform to the new situation. On entry into a conducting material, for instance, it encounters an environment in which it is able to move freely, inasmuch as the speed displacement in the motion combinations that constitute matter is predominantly in time, and the relation of the space displacement of the electron to the atomic time displacement is motion. Furthermore, the environmental factors favor such a reorientation; that is, they favor an increase in speed above the previous unit level in a high speed environment, and a decrease in a low speed environment. The electron therefore reorients with its active displacement in the dimension of the reference system. This is either a spatial or a temporal reference system, depending on whether the speed is below or above unity, but the two systems are effectively parallel. They are actually two sections of a single system, as they represent the same one-dimensional motion in two different speed ranges.

Where the speed is above unity, the representation of the variable magnitude is in the temporal coordinate system, and the fixed position in the natural reference system appears in the spatial coordinate system as a movement of the electrons (the electric current) at the speed of light. Where the speed is below unity, these representations are reversed. It does not follow that the progression of the electrons along the conductor takes place at these speeds. In this respect, the electron aggregate is similar to a gas. The individual electrons are moving at high speeds, but in random directions. Only the net excess of the motion in the direction of the current flow—the electron drift, as it is usually called—is effective as a unidirectional movement.

This idea of an “electron gas” is generally accepted in present-day physics, but it is conceded that “The simple theory runs into greater difficulties when examined in more detail.”^{41} As noted previously, the prevailing assumption that the electrons of this electron gas are derived from the structures of the atoms encounters many problems. There is also a direct contradiction in the specific heat values. “The electron gas would be expected to contribute an extra 3/2 R to the specific heat of metals,”^{41} but no such specific heat increment is found experimentally.

The theory of the universe of motion supplies the answers to both of these problems. The electrons whose movement constitutes the electric current are not derived from the atoms, and are not subject to the restrictions that apply to this origin. The answer to the specific heat problem is provided by the nature of the electron motion. The motion of these uncharged electrons (units of space) through the matter of the conductor is equivalent to motion of the matter through extension space. At a given temperature, the atoms of matter have a certain speed relative to space. It is immaterial whether this is extension space or electron space. The motion through electron space (movement of the electrons) is part of the thermal motion, and the specific heat due to this motion is part of the specific heat of the atom, not something separate.

Once the reorientation of the electrons takes place in response to the environmental factors, it cannot be reversed against the forces associated with those factors. The electrons therefore cannot leave the conductor in the uncharged state. The only active property of an uncharged electron is a space displacement, and the relation of this space to extension space is not motion. However, an electron can escape from the conductor by acquiring a charge. A combination of rotational motions (an atom or particle) with a net displacement in space (a speed greater than unity) can move only in time, as indicated earlier, and one with a net displacement in time (a speed less than unity) can move only in space, as motion is a relation *between *space and time. But unit speed (the natural zero or datum level) is unity in *both * time and space. It follows that a motion combination with a net speed displacement of zero can move in *either *time or space. Acquisition of a unit negative* charge (actually positive in character) by the electron, which, in its uncharged state has a unit negative displacement, reduces the net speed displacement to zero. and allows the electron to move freely in either space or time.

The production of a charged electron in a conductor requires only the transfer of sufficient energy to an uncharged electron to bring the existing kinetic energy of that particle up to the equivalent of a unit charge. If the electron is to be projected into space, an additional amount of energy is required to break away from the solid or liquid surface and to overcome the pressure exerted by the surrounding gas. At energies below this level, the charged electrons are confined to the conductor in the same manner as when they are uncharged.

The necessary energy for the production of the charge and the escape from the conductor can be supplied in a number of ways, each of which therefore constitutes a method of producing freely moving charged electrons. A convenient and widely used method furnishes the required energy by means of a voltage differential. This increases the translational energy of the electrons until they meet the requirements. In many applications the necessary increment of energy is minimized by projecting the newly charged electrons into a vacuum rather than requiring them to overcome a gas pressure. The cathode rays used in x-ray production are streams of charged electrons projected into a vacuum. The use of a vacuum is also a feature of the thermionic production of charged electrons, in which the necessary energy is imparted to the uncharged electrons by means of heat. In photoelectric production, the energy is absorbed from radiation.

Existence of the electron as a free charged unit is usually of brief duration. Within a short time after it has been produced by one transfer of energy and ejected into space, it again encounters matter and enters into another energy transfer by means of which the charge is converted back into thermal energy or radiation, and the electron reverts to the uncharged condition. In the immediate neighborhood of an agency that is producing charged electrons both the creation of charges and the reverse process that transforms them back into other types of energy are going on simultaneously. One of the principal reasons for the use of a vacuum in electron production is to minimize the loss of charges by way of this reverse process.

Charged electrons in space can be observed—that is, detected by various means—and because of the presence of the charges they are subject to electric forces. This enables control of their motions, and unlike its elusive uncharged counterpart, the charged electron is an observable entity that can be manipulated to produce physical effects of various kinds.

It is not feasible to isolate and examine individual charged electrons in matter as we do in space, but we can recognize the presence of such particles by evidence of freely moving charges within the material aggregates. Aside from the special characteristics of charges, these charged electrons in matter have the same properties as the uncharged electrons. They travel readily through good conductors, less readily through poor conductors, they move in response to voltage differences, they are restrained by insulators, which are substances that do not have the necessary open dimensions to allow free electron motion, and so on. In their activities in and around aggregates of matter, these charged electrons are known as *static electricity.*

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