COMPOSITION
OF FIELDS

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I have to start with clearing up the misconception of magetic attractivity, which we have inherited from the ancestors playing with lodestones. We have been taught through out the millenia that unlike poles attract, while alike poles repulse. Let me set this misconception straight first. When we allow any two permanent magnets to interact freely, without any mechanical limitation or guidance, they will always turn so as to attract. The alike pole orientation repulsive force is conditioned by mechanical limitation of both magnets.

In plain English, when you hold two magnets in alike orientation, and let go of at least one of them, the freed magnet will flip around and attract toward the other magnet. This proves beyond any doubt, that magnetic force is strictly attractive, unless the magnetic field is forced into an alike orientation. The so called repulsive force is caused by distortion of the field in such a manner, that the natural attractivity of the two unlike poles is spatially redirected.

Therefore, we have no real repulsive force when it comes to the underlying principle of magnetic field interaction. We have only an attractive force. This fact changes the odds of 2 attractive and repulsive forces (magnetic and electric) versus single attractive only force of gravitation. After we have realized that magnetic force is strictly attractive, we have one attractive and repulsive electric force against strictly attractive forces of magnetism and gravitation.

DIPOLE MAGNETIC FIELD

The field of a single bar magnet, as described by the lines of force shows somewhat distorted concentric circles. These close upon both poles of a bar magnet, and this is considered to be a single dipole field. When a bar magnet is fractured orthogonal to its polar axis and the fracture is being separated, lines of force parallel to the original magnetic axis crop up within the gap of the fracture. Therefore, it is obvious that the lines of force, or at least that which allows for creation of lines of force, continues through out the body of the magnet closing the external field into real circular paths.

To start with and keeping it simple, I will pretend that this field is without any structuring, that it represents single flow or a static structure, whichever it may be.

QUADRUPOLE MAGNETIC FIELD

When we allow two identical bar magnets to freely attract side on, the resulting field geometry changes rather drastically. The originally visible and detectable outer part of the field of each magnet shrinks from the sides and most of it is redirected so, that the field now shows only between each pair of poles. The two circular paths of the two fields have conglomerated into an almost single circular path. This path proceeds through the two magnets and between each pair of the magnetic poles. (fig. 1)

fig. 1

When we bridge each pole pair by a steel bar the external magnetic field around the magnet pair disappears all together. When the bar magnets are separated by a slight gap, and two pieces of steel are placed in front of each pole of a pair with gaps between the poles and the steel as well as the steel pieces, the lines of force appear within each gap. They are oriented so that the lines of force again describe a closed loop through out the magnets, through out the steel pieces and through out the gaps. (fig. 2)

fig. 2

This experimenting proves again, that the magnetic flux lines of force, and therefore the field itself, close upon itself into a loop, through out the magnet body and through any material.

SIX POLE MAGNETIC FIELD

When we place three identical bar magnets (freely) next to each other into a row, they attract without problem, but the lines of force between the poles indicate two closed loops of magnetic flux. The two loops are individual to the peripheral magnets, but they both share the middle magnet.

When we attempt to place three identical bar magnets next to each other one by one into a bundle, the fist two bars attract, but the third magnet added to the two behaves erratically and tends to find (and finds) some compromise of orientation and position. (This orientation depends on lengths and thickness of the bars and it seems also to depend on the quality of the magnets. The results are inconsistent)

This shows that while magnetic field(s) have no problem to arrange themselves alternately, they have problem to arrange themselves where the alternation is spatially asymmetric.

EIGHT POLE MAGNETIC FIELD

When we place four identical bar magnets (freely) next to each other into a row, they attract without problem. The lines of force among the poles indicate three internal loops of magnetic flux. (fig. 3 top) The two part external loops are individual to the peripheral magnets, but they both share the near middle magnet internal loops. The two middle magnets share their common internal loop and the peripheral magnet’s internal loops.

When we place four identical bar magnets (freely) into a bundle, they attract without problem. The lines of force between the poles indicate four internal loops of magnetic flux. Each magnet shares magnetic flux loops with its peripheral neighbor, but not with the magnet diagonally across the four pole face. (fig. 3, bottom right)

When we force four bar magnets into two adjoining rows, each row consisting of the same polarity but the rows being of opposite polarity, the symmetry of magnetic flux loops becomes single-dimensional, as the two loops of magnetic flux are parallel. (fig.3, bottom left)

fig. 3

COHERENT MULTIPOLE MAGNETIC FIELD

When we place (freely) any larger quantity of identical bar magnets next to each other into a bundle, they attract without problem and the loops of magnetic flux are shared. When we compare the attractive force values between a row and a bundle, we find out that the bundle, or in this case a checkerboard of polar faces, is the preferred and strongest conglomeration. (fig. 4)

fig. 4

When we check the lines of force above such checkerboard of polar faces, we can realize that the field protrudes above the faces creating somewhat fuzzy surface of two dimensionally alternating magnetic fields. The portions of individual flux paths protruding outside the material of the bars describe geometrical semicircles. The semicircles do not extend above the checkerboard array face farther than the distance between centers of the individual poles. This means that the extent of the field above the checker board array, detectable by a piece of steel, will be different when a non magnetized steel piece approaches the face, as it has to pick up the field at its natural distance. But once the field of the checkerboard tied into the piece of steel, it will extend while the steel is being retracted and the steel will detect the field at a greater distance.

I have to note here that this is also the case with Van der Walls force. When you approach very slowly water surface with your finger, the water surface will “jump” at your finger (any “wetting” material will do) at a certain distance. When you retract your finger, the water will stick to it for a greater distance before it tears apart. In all fairness, it has to be pointed out that the cohesive forces in water come into the picture once the finger got wetted. But it also has to be pointed out that the “jumping” of water can have only one reason, that reason being a surface field somewhat similar to the surface of magnetic flux above a checker board of magnetic pole array face.

INCOHERENT MULTIPOLE MAGNETIC FIELD

SPATIALLY INCOHERENT FIELD

When we force identical bar magnets into a bundle so, that some bars are oriented with alike poles next to each other while others are not, it is equivalent to bundling of non identical bar magnets. The individual flux loops are shared unequally among the bars. This results in some of the loops curving closer to the surface and some extending farther from the surface. (fig. 5) The two dimensional alternate symmetry of the loop organization of a checkerboard array is broken and the lines of force may begin to describe winding paths. Now I said the symmetry is broken, but that is so from our human point of view. When a large quantity of disparate magnets is arrayed, the arrangement does not gain an appreciable external field on the sides of the bars of the conglomerate. That means the array is still energetically symmetrical, only that this symmetry becomes as spatially complex as the symmetry of the array itself, and this symmetry is not what we consider symmetrical from aesthetic considerations.

fig. 5

QUANTITATIVELY INCOHERENT FIELD

When we bundle (freely) any even quantity of spatially identical bar magnets of different strength, the face of the array shows again distortions in the protruding surface magnetic field. This situation is equivalent in its result to the spatially incoherent array.

COMPLETELY INCOHERENT FIELD

When we place (freely) any quantity of spatially different bar magnets with different strengths, we get a really “messy” surface magnetic field, where some lines of force are shared across other lines of force. The two dimensional organization of lines of force above such face becomes a real jumble, but this jumble is not scalable. What I mean is, when you make a cross section at different distances along the plane of such a multi-polar face, the pattern of polarities changes at each cross section.

FIELD WITH UNDETERMINABLE POLARITY

The more diverse are the components (bar magnets) within an array and the larger is the array, the more diverse and farther reaching is its surface magnetic field.

When we approach a magnetic array with a sheet of steel, the steel gets attracted to it at any mutual orientation, but has preferred orientation(s). When the steel is allowed to come into contact with the array and is thick enough not to achieve magnetic saturation, its free side is free of magnetic flux. This proves that steel can tie multitude of flux path orientations within itself and does not really become quite an equivalent of a temporary magnet.

When an array is approached by a single and relatively large permanent magnet, the resulting force is attractive and it does not matter what is the mutual orientation of the permanent magnet and the array. The quantitative force at particular orientations differs, but the two objects are always attractive.

When an array is approached by a single and relatively small permanent magnet, lets say the size of one pole in the array the resulting force is attractive but directed toward the nearest and/or largest opposite pole in the array.

When an array is approached by another array, they are again only attractive disregards their mutual orientation. There are again preferred orientations, that is face to face, and the orientations have different quantitative values of attraction, but the force between them is strictly attractive no matter what. (fig. 6) Figure six also shows, why the flat face attracts along inverse square cube, rather than along inverse square. The difference is in the proximity of the area of the whole field. Figure 6, top shows how the flux begins to interact at greater distance. Figure 6, bottom shows the increase in interaction at a smaller distance.

fig. 6

SPHERICAL ARRAY

When we figure that a spherical magnetic array (fig. 7) looks like what is shown in this figure, we can figure out why does Casimir force follow inverse cube of attraction strength while gravitation follows inverse square dependency. None of them is quite accurate, but close enough. The shape of a body is as important to the strength to distance attractive force relation as is the composition of an array. (The electro gravity and Van der Walls force are discussed in a follow up paper.)

fig. 7

So, to put it bluntly, the way to understand magnetic force as strictly attractive, disregards orientation of attractors, lies in the comprehension of the composition of the attractors and the way the path of field have to take to join together.

It seems rather obvious that attraction only gravitational force is not an exemption to the rule of attractive and repulsive forces at a distance, but a rule itself. It is the repulsive force of two alike charged bodies, which is the odd man out.

Note:

All above diagrams are a gross simplification of the field structures. It is up to the reader to fill in what is missing as per observable lines of force of magnetic fields. It found it impossible due to the scale and time requirement to do a more detailed job.