19 Magnetostatics

CHAPTER 19

Magnetostatics

As we saw in the preceding pages, one of the principal obstacles to the development of a more complete and consistent theory of electrical phenomena has been the exaggerated significance that has been attached to the points of similarity between static and current electricity, an attitude that has fostered the erroneous belief that only one entity, electric charge, is involved in the two types of phenomena. The same kind of a mistake has been made in a more complete and categorical manner in the current view of magnetism. While insisting that electrostatic and current phenomena are simply two aspects of the same thing, contemporary scientific opinion concedes that there is enough difference between the two to justify a separate category of electrostatics for the theoretical aspects of the static phenomena. But if magnetostatics, the corresponding branch of magnetism, is mentioned at all in modern physics texts, it is usually brushed off as an “older approach” that is now out of date. Strictly static concepts, such as that of magnetic poles, are more often than not introduced somewhat apologetically.

The separation of physical fields of study into more and more subdivisions has been a feature of scientific activity throughout its history. Here in the magnetostatic situation we have an example of the reverse process, a case in which a major subdivision of physics has succumbed to cannibalism. Magnetostatics has been swallowed by a related, but quite different, phenomenon, electromagnetism, which will be considered in Chapter 21. There are many similarities between the two types of magnetic phenomena, just as there are between the two kinds of electricity. In fact, the quantities in terms of which the magnetostatic magnitudes are expressed are defined mainly by electromagnetic relations. But this is not by any means sufficient to justify the current belief that only one entity is involved. The subordinate status that conventional physics gives to purely magnetic phenomena is illustrated by the following comment from K. W. Ford:

As theoretical physicists see it, magnetism in our world is merely an accidental by-product of electricity; it exists only as a result of the motion of electrically charged particles.77

The implication of a confident statement of this kind is that the assertions which it makes are reasonably well established. In fact, however, this assertion that magnetism exists only as a result of the motion of electrically charged particles is based entirely on unsubstantiated assumptions. The true situation is more accurately described by the following quotation from a physics textbook:

It is only within the past thirty years or so that models tying together these two sources of magnetism [magnets and electromagnetism] have been developed. These models are far from perfect, even today, but at least they have convinced most people that there is really only one source of magnetic fields: all magnetic fields come from moving electric charges.78

What this text is, in effect, telling us is that the idea does not work out very well in practice, but that it has been accepted by majority vote anyway. A prominent American astronomer, J. N. Bahcall, has pointed out that “We frequently settle important scientific issues by acclamation rather than observation.”79 The uncritical acceptance of the “far from perfect” models of magnetism is a good example of this unscientific practice.

A strange feature of the existing situation is that after having come to this conclusion that magnetism is merely a by-product of electricity, one of the ongoing activities of the physicists is a search for the magnetic analog of the mobile electric charge, the electron. Again quoting K. W. Ford:

An electric particle gives rise to an electric field, and when it moves it produces a magnetic field as a secondary effect. For symmetry’s sake there should be magnetic particles that give rise to magnetic fields and in motion produce electric fields in the same way that moving electric particles create magnetic fields.

This author admits that “So far the magnetic monopole has frustrated all its investigators. The experimenters have failed to find any sign of the particle.” Yet this will-o’-the-wisp continues to be pursued with an ardor that invites caustic comments such as this:

It is remarkable how the lack of experimental evidence for the existence of magnetic monopoles does not diminish the zeal with which they are sought.80

Ford’s contention is that “the apparent non-existence of monopole particles now presents physicists with a paradox that they cannot drop until they have found an explanation.” But he (unintentionally) supplies the answer to the paradox when he closes his discussion of the monopole situation with this statement:

What concerns the physicist is that, in defiance of symmetry and all the known laws, no magnetic particle so far has been created or found anywhere.

Whenever the observed facts “defy” the “known laws” and the current understanding of the application of symmetry relations to any given situation, it can safely be concluded that the current understanding of symmetry and at least some of the “known laws” are wrong. In the present case, any critical appraisal will quickly show not only that a number of the premises from which the conclusion as to the existence of magnetic monopoles is derived are pure assumptions without factual support, but also that there is a definite contradiction between two of the key assumptions.

As explained by Ford, the magnetic monopole for which the physicists are searching so assiduously is a particle which “gives rise to magnetic fields; that is, a magnetic charge. If such a particle existed, it would, of course, exhibit magnetic effects due to the charge. But this is a direct contradiction of the prevailing assumption that magnetism is a “by-product of electricity.” The physicists cannot have it both ways. If magnetism is a by-product of electricity (that is, electric charges, in current thought), then there cannot be a magnetic charge, a source of magnetic effects, analogous to the electric charge, a source of electric effects. On the other hand, if a particle with a magnetic charge (a magnetic monopole) does exist, then the physicists’ basic theory of magnetism, which attributes all magnetic effects to electric currents, is wrong.

It is obvious from the points brought out in the theoretical development in the preceding pages that the item of information which has been missing is an understanding of the physical nature of magnetism. As long as magnetism is assumed to be a by-product of electricity, and electricity is regarded as a given feature of nature, incapable of explanation, there is nothing to guide theory into the proper channels. But once it is recognized that magnetostatic phenomena are due to magnetic charges, and that such a charge is a type of motion—a rotational vibration—the situation is clarified almost automatically. Magnetic charges do, indeed, exist. Just as there are electric charges, which are one-dimensional rotational vibrations acting in opposition to one-dimensional rotations, there are magnetic charges, which are two-dimensional rotational vibrations acting in opposition to two-dimensional rotations. The phenomena due to charges of this nature are the subject matter of magnetostatics. Electromagnetism is a different phenomenon that is also two-dimensional, but involves motion of a continuous, rather than vibratory, nature.

The two-dimensionality is the key to understanding the magnetic relations, and the failure to recognize this basic feature of magnetism is one of the primary causes of the confusion that currently exists in many areas of magnetic theory. The two dimensions of the magnetic charge and electromagnetism are, of course, scalar dimensions. The motion components in the second dimension are not capable of direct representation in the conventional spatial reference system, but they have indirect effects that are observable, particularly on the effective magnitudes. Lack of recognition of the vibrational nature of electrostatic and magnetostatic motions, which distinguishes them sharply from the continuous motions involved in current electricity and electromagnetism, also contributes significantly to the confusion. Magnetostatics resembles electromagnetism in those respects in which the number of effective dimensions is the determining factor, whereas it resembles electrostatics in those respects in which the determining factor is the vibrational character of the motion.

Our findings show that the absence of magnetic monopoles is not a “defiance of symmetry.” The symmetry exists, but a better understanding of the nature of electricity and magnetism is required before it can be recognized. There is symmetry in the electric and magnetic relations, and in some respects it is the kind of symmetry envisioned by Ford and his colleagues. One type of magnetic field is produced in the same manner as an electric field, just as Ford suggests in his explanation of the reasoning underlying the magnetic monopole hypothesis. But it is not an “electric particle” that produces an electric field; it is a certain kind of motion—a rotational vibration—and a magnetic field is produced by a similar rotational vibration. The electric current, a translational motion of a particle (the uncharged electron) in a conductor, produces a magnetic field. As we will see in Chapter 21, a translational motion of a magnetic field likewise produces an electric current in a conductor. Here, too, symmetry exists, but not the kind of symmetry that would call for a magnetic monopole.

The magnetic force equation, the expression for the force between two magnetic charges, is identical with the Coulomb equation, except for the factor t/s introduced by the second scalar dimension of motion in the magnetic charge. The conventional form of the equation is F = MM’/d2. As in the other primary force equations, the terms M’ and d2 are dimensionless. From the general principles applying to these force equations, as defined in Chapter 14, the missing term in the magnetic equation, analogous to 1/s in the Coulomb equation, is 1/t. The space-time dimensions of the magnetic equation are then F = t2/s2 × 1/t = t/s2.

Like the motion that constitutes the electric charge, and for the same reasons, the motion that constitutes the magnetic charge has the outward scalar direction. But since magnetic rotation is necessarily positive (time displacement) in the material sector, all stable magnetic charges in that sector have displacement in space (negative), and there is no independent magnetic phenomenon corresponding to the negative* electric charge. In this case there is no established usage that prevents applying the designations that are consistent with the rotational terminology, and we will therefore refer to the magnetic charge as negative, rather than using the positive* designation, as in application to the electric charge.

Although positive magnetic charges do not exist in the material environment, except under the influence of external forces in a situation that will be discussed later, the two-dimensional character of the magnetic charge introduces an orientation effect not present in the electric phenomena. All one-dimensional (electric) charges are alike; they have no distinguishing characteristic whereby they can be subdivided into different types or classes. But a two-dimensional (magnetic) charge consists of a rotational vibration in the dimension of the reference system and another in a second scalar dimension independent of the first, and therefore perpendicular to it in a geometrical representation. The rotation with which this second rotational vibration is associated divides the atom into two halves that can be separately identified. On one side of this dividing line the rotation appears clockwise to observation. The scalar direction of the magnetic charge on this side is therefore outward from a clockwise rotation. A similar charge on the opposite side is a motion outward from a counterclockwise rotation.

The unit of magnetic charge applies to only one of the two rotating systems of the atom. Each atom therefore acquires two charges, which occupy the positions described in the preceding paragraph, and are oppositely directed. Each atom of a magnetic, or magnetized, substance thus has two poles, or centers of magnetic effect. These are analogous to the magnetic poles of the earth, and are named accordingly, as a north pole, or north-seeking pole, and a south pole.

These poles constitute scalar reference points, as defined in Chapter 12. The effective direction of the rotational vibration that constitutes the charge located at the north pole is outward from the north reference point, while the effective direction of the charge centered at the south pole is outward from the south reference point. The interaction of two magnetically charged atoms therefore follows the same pattern as the interaction of electric charges. As illustrated in Figure 22, which is identical with Figure 20, Chapter 13, except that it substitutes poles for charges, two north poles (line a) move outward from north reference points, and therefore outward from each other. Two south poles (line c) similarly move outward from each other. But, as shown in line b, a north pole moving outward from a north reference point is moving toward a south pole that is moving outward from a south reference point. Thus like poles repel and unlike poles attract.

Figure 22

  S N S N
(a) | ◄── | ──►   |    
(b)     | ──► ◄── |    
(c)     |   ◄── | ──► |

On this basis, when two magnetically charged atoms are brought into proximity, the north pole of one atom is drawn to the south pole of the other. The resulting structure is a linear combination of a north pole, a neutral combination of two poles, and a south pole. Addition of a third magnetically charged atom converts this south pole to a neutral combination, but leaves a new south pole at the new end of the structure. Further additions of the same kind can then be made, limited only by thermal and other disruptive forces. A similar linear array of atoms with north and south poles at opposite ends can be produced by introducing atoms of magnetizable matter between the magnetically charged atoms of a two-atom combination. Separation of this structure at any point breaks a neutral combination, and leaves north and south poles at the ends of each segment. Thus no matter how finely magnetic material is divided, there are always north and south poles in every piece of the material.

Because of the directional character of the magnetic forces they are subject to shielding in the same manner as electric forces. The gravitational force, on the other hand, cannot be screened off or modified in any way. Many observers have regarded this as an indication that the gravitational force must be something of a fundamentally different nature. This impression has been reinforced by the difficulty that has been experienced in finding an appropriate place for gravitation in basic physical theory. The principal objective of the theorists currently working on the problem of constructing a “unified theory,” or a “grand unified theory,” of physics is to find a place for gravitation in their theoretical structure.

Development of the theory of the universe of motion now shows that gravitation, static electricity, and magnetostatics are phenomena of the same kind, differing only in the number of effective scalar dimensions. Because of the symmetry of space and time in this universe, every kind of force (motion) has an oppositely directed counterpart. Gravitation is no exception. it takes place in time as well as in space, and is therefore subject to the same differentiation between positive and negative as that which we find in electric forces. But in the material sector of the universe the net gravitational effect is always in space—that is, there is no effective negative gravitation—whereas in the cosmic sector it is always in time. And since gravitation is three-dimensional, there cannot be any directional differentiation of the kind that we find in magnetism.

Because of the lack of understanding of the true relation between electromagnetic and gravitational phenomena, conventional physical science has been unable to formulate a theory that would apply to both. The approach that has been taken to the problem is to assume that electricity is fundamental, and to erect the structure of physical theory on this foundation, further assumptions being made along the way as required in order to bring the observations and measurements into line with the electrically based theory. Gravitation has thus been left with the status of an unexplained anomaly. This is wholly due to the manner in which the theories have been constructed, not to any peculiarity of gravitation. If the approach had been reversed, and physical theory had been constructed on the basis of the assumption that gravitation is fundamental, electricity and magnetism would have been the “undigestable” items. The kind of a unified theory that the investigators have been trying to construct can only be attained by a development, such as the one reported in this work, that rests on a solid foundation of understanding in which each of these three basic phenomena has its proper place.

Aside from the effects of the difference in the number of scalar dimensions, the properties of the rotational vibration that constitutes a magnetic charge are the same as those of the rotational vibration that constitutes an electric charge. Magnetic charges can therefore be induced in appropriate materials. These materials in which magnetic charges are induced behave in the same manner as permanent magnets. In fact, some of them become permanent magnets when charges are induced in them. However, only a relatively small number of elements are capable of being magnetized to a significant degree; that is, have the property known as ferromagnetism.

The conventional theories of magnetism have no explanation of the restriction of magnetization (in this sense) to these elements. Indeed, these theories would seem to imply that it should be a general property of matter. On the basis of the assumptions previously mentioned, the electrons which conventional theory regards as constituents of atoms are miniature electromagnets, and produce magnetic fields. In most cases, it is asserted, the magnetic fields of these atoms are randomly oriented, and there is no net magnetic resultant. “However, there are a few elements in whose atoms the fields from the different electrons don’t exactly cancel, and these atoms have a net magnetic field… in a few materials… the magnetic fields of the atoms line up with each other.”81 Such materials, it is asserted. have magnetic properties. Just why these few elements should possess a property that most elements do not have is not specified.

For an explanation in terms of the theory of the universe of motion we need to consider the nature of the atomic motion. If a two-dimensional positive rotational vibration is added to the three-dimensional combination of motions that constitutes the atom it modifies the magnitudes of those motions, and the product is not the same atom with a magnetic charge; it is an atom of a different kind. The results of such additions will be examined in Chapter 24. A magnetic charge, as a distinct entity, can exist only where an atom is so constituted that there is a portion of the atomic structure that can vibrate two-dimensionally independently of the main body of the atom. The requirements are met, so far as the magnetic rotation is concerned, where this rotation is asymmetric; that is, there are n displacement units in one of the two magnetic dimensions and n+1 in the other.

On this basis, the symmetrical B groups of elements, which have magnetic rotations 1-1, 2-2, 3-3, and 4-4, are excluded. While the magnetic charge has no third dimension, the electric rotation with which it is associated in the three-dimensional motion of the atom must be independent of that associated with the remainder of the atom. The electric rotational displacement must therefore exceed 7, so that one complete unit (7 displacement units plus an initial unit level) can stay with the main body of the magnetic rotation, while the excess applies to the magnetic charge. Furthermore, the electric displacement must be positive, as the reference system cannot accommodate two different negative displacements (motion in time) in the same atomic structure. The electronegative divisions (III and IV) are thus totally excluded. The effect of all of these exclusions is to confine the magnetic charges to Division II elements of Groups 3A and 4A.

In Group 3A the first element capable of taking a magnetic charge in its normal state is iron. This number one position is apparently favorable for magnetization, as iron is by far the most magnetic of the elements, but a theoretical explanation of this positional advantage is not yet available. The next two elements, cobalt and nickel, are also magnetic, as their electric displacement is normally positive. Under some special conditions, the displacements of chromium (6) and manganese (7) are increased to 8 and 9 respectively by reorientation relative to a new zero point, as explained in Chapter 18 of Volume I. These elements are then also able to accept magnetic charges.

According to the foregoing explanation of the atomic characteristics that are required in order to permit acquisition of a magnetic charge, the only other magnetic (in this sense) elements are the members of Division II of Group 4A (magnetic displacements 4-3). This theoretical expectation is consistent with observation, but there are some, as yet unexplained, differences between the magnetic behavior of these elements and that of the Group 3A elements. The magnetic strength is lower in the 4A group. Only one of the elements of this group, gadolinium, is magnetic at room temperature, and this element does not occupy the same position in the group as iron, the most magnetic element of Group 3A. However, samarium, which is in the iron position, does play an important part in many magnetic alloys. Gadolinium is two positions higher in the atomic series, which may indicate that it is subject to a modification similar to that applying to the lower 3A elements, but oppositely directed.

If we give vanadium credit for some magnetic properties on the strength of its behavior in some alloys, all of the Division II elements of both the 3A and 4A groups have a degree of magnetism under appropriate conditions. The larger number of magnetic elements in Group 4A is a reflection of the larger size of this 32 element group, which puts 12 elements into Division II. There are a number of peculiarities in the relation of the magnetic properties of these 4A elements, the rare earths, to the positions of the elements in the atomic series that are, as yet, unexplained. They are probably related to the other still unexplained irregularities in the behavior of these elements that were noted in the discussions of other physical properties. The magnetic capabilities of the Division II elements and alloys carry over into some compounds, but the simple compounds such as the binary chlorides, oxides, etc. tend to be non-magnetic; that is, incapable of accepting magnetic charges of the ferromagnetic type.

In undertaking an examination of individual magnetic phenomena, our first concern will be to establish the correct dimensions of the quantities with which we will be working. This is an operation that we have had to carry out in every field that we have investigated, but it is doubly important in the case of magnetism because of the dimensional confusion that admittedly exists in this area. The principal reason for this confusion is the lack in conventional physical theory of any valid general framework to which the dimensional assignments of electric and magnetic quantities can be referred. The customary assignment of dimensions on the basis of an analysis into mass, length, and time components produces satisfactory results in the mechanical system of quantities. Indeed, all that is necessary to convert these mechanical MLT assignments to the correct space-time dimensions is to recognize the t3/s3 dimensions of mass. But extending this MLT system to electric and magnetic quantities meets with serious difficulties. Malcolm McCaig makes the following comment:

Very contradictory statements have been made about the dimensions of electrical quantities. While some writers state that it is impossible to express the dimensions of all electrical and magnetic quantities in terms of mass, length, and time, others such as Jeans and Nicolson do precisely that.82

The nature of the problem that the theorists face in attempting to arrive at an accurate and consistent set of MLT dimensions can be seen by comparing the dimensions that have been assigned to one of the basic electric quantities, electric current, with the correct space-time dimensions that we have identified in the preceding pages. Current, in MLT terms, is asserted to have the dimensions M1/2L1/2T-1. When converted to space-time dimensions, this expression becomes (t3/s3)½ × s½ × t-1 = t½/s. The correct dimensions are s/t. The reason for the discrepancy is that the MLT dimensions are taken from the force equations, and therefore reflect the errors in the conventional interpretation of those equations. The further error due to the lack of distinction between electric charge and electric quantity is added when dimensions are assigned to the electric current, and the final result has no resemblance to the correct dimensions.

The SI system and its immediate predecessors avoid a part of the problem by abandoning the effort to assign MLT dimensions to electric charge, and taking charge as an additional basic quantity. But here, again, the distinction between charge and quantity is not recognized, leading to incorrect dimensions for electric current. These dimensions are stated as Q/T, the space-time equivalent of which is 1/s, instead of the correct s/t. Both the MLT and the MLTQ systems of dimensional assignment are thus wrong in almost every electric and magnetic application, and they serve no useful purpose.

In our study of electrical fundamentals we were able to establish the correct dimensions of the electric quantities by using the mechanical dimensions as a base and taking advantage of the equivalence of mechanical and current phenomena. This approach is not feasible in application to magnetism, but we have a good alternative, as our theory indicates that there is a specific dimensional relation between the magnetic quantities and the corresponding electric quantities, the dimensions of which we have already established.

The basic difference between electricity and magnetism is that electricity is one-dimensional whereas magnetism is two-dimensional. However, the various permutations and combinations of units of motion that account for the differences between one physical quantity and another are phenomena of only one scalar dimension, the dimension that is represented in the reference system. No more than this one dimension can be resolved into components by introduction of dimensions of space (or time). It follows that addition of a second dimension of motion to an electrical quantity takes the form of a simple unit of inverse speed, t/s. The dimensions of the magnetic quantity corresponding to any given electric quantity are therefore t/s times the dimensions of the electric quantity. The dimensions thus derived for the principal magnetic quantities are shown in Table 30.

Table 30: Electrical Analogs of Principal Magnetic Quantities

Electric Magnetic

t

dipole moment t2/s dipole moment
t/s charge t2/s2 flux
t/s2 potential t2/s3 vector potential
t/s3 flux density t2/s4 flux density
t/s3 field intensity t2/s4 field intensity
t2/s2 resistivity t3/s3 inductance
t2/s3 resistance t3/s4 permeability

Here, then, we have a solid foundation for a critical analysis of magnetic relations, one that is free from the dimensional inconsistencies that have plagued magnetism ever since systematic investigation of magnetic phenomena was begun. In the next chapter we will apply the new understanding of magnetic fundamentals to an examination of magnetic quantities and units.