Magnetism

{© 02/12/24}

Magnetism is the converse of electricity, it flows from positive to negative, it accrues between particles, and it is constant (irrespective of temperature).

Coulomb's Constant

Before sorting out today's issues with magnetism, we need to deal with Coulomb's constant, which is not consistent with G, and needs to be corrected.

But first, we need to clarify a couple of facts:
1) Today, we only know how to calculate force using magnetic charge (kg.m/s²). This is because we still haven't grasped the fact that mass and inertia are actually magnetic charge and its field⁽¹⁾.
2) As with Newton's constant 'G', today's units of measurement for 'k' are simply units of convenience, contrived to ensure that force can be derived from the creator's formula;
G; N.m²/kg²,
k; N.m² / kg².C².
The units of measurement for Newton's constant 'G' have at last been resolved, along with its value and its formula, but this is not yet the case for Coulomb's constant 'k'.

Given that mass is magnetic charge, and that electrical charge is its electrical equivalent, for reasons of consistency, we should be able to calculate electrical force using the Coulomb (F; C.m/s²). Therefore; k's units of measurement should also be equivalent to those for 'G' (m³ / C.s²), and not as it is today kg.m³ / C².s². However, this is probably too great a leap for most of us to grasp today, so we are forced to convert Coulombs to kilograms when calculating electrical force..
In order to rectify this problem, we need to multiply 'k' by RC², giving us a revised formula and value for the constant thus:
k' = Rₙ.c²/mₑ = 2.78024810626745E+32 {m³ / kg.s²}
compared with G:
G = aₒ.c²/mᵤ = 6.67359232004333E-11 {m³ / kg.s²}

Two further facts are:
3) the ratio of magnetic and electrical charge forces is the coupling ratio:
Fₘ:Fₑ = Fₘ/Fₑ = φ.
4) magnetism is accrued between magnetic charges (masses) and electricity is shared.

Now the Coulomb must be converted to kilograms;
e = e/RC = 9.1093897E-31 kg
and the force calculations therefore become:
Fₘ = G.mₑ.mₚ/Rₙ² = 1.28051247005732E-38 N
Fₑ = k'.e²/Rₙ² = 29.0535538991261 N
Fₘ:Fₑ = 4.40742111792334E-40 (the coupling ratio)
Moreover, the ratio of constants is now; ξₘ.G/k = φ,
exactly as it should be.

Definitions

Convention today claims;
magnetic flux (Φ) is the equivalent of electrical current (I);
magneto-motive force (mmf) is the equivalent of electro-motive force (emf);
magnetic reluctance (R) is the equivalent of electrical resistance (R).
However;
Φ is measured in units of Weber (J.s/C)
mmf is measured in units of Ampere(-turns) (C/s)
reluctance = magneto-motive force ÷ magnetic flux; R = mmf/Φ
the units of which are; (C/s) ÷ (J.s/C) = C² / s².J
which is not the magnetic equivalent of electrical resistance; J.s/C²,
compare the units in this Table to understand this problem:

magnetism			electricity
label	symbol	units	label	symbol	units
flux	Φ	J.s/C	current	I	C/s
magneto-motive force	mmf	C/s	electro-motive force	emf	J/C
reluctance	R	C² / s².J	resistance	Ω or R	J.s/C²
Equivalent Magnetic & Electrical Properties

When considered together with current belief that the constant 'B' represents a magnetic field, there is something amiss with our understanding of magnetism and the way we treat it, which also means that today's generally accepted definitions are incorrect.
The issue here is that the magnetic equivalent of the Coulomb is the kilogram, which is because we have not yet grasped the fact that mass is magnetic charge⁽¹⁾.
We have sorted this out in our calculations below, and in our definitions page.

The corrected magnetic definitions are listed below:
Magnetic Charge: The non-polar magnetic charge in all atomic particles that we currently refer to as mass (kg),
Magnetic Constant: Joseph Henry's magnetic field generated by the proton-electron pair at its neutronic condition (kg.m/C²),
Magnetic Field: The general formula for Joseph Henry's magnetic field at any radial distance (kg.m/C²),
Magnetic Flux: Magnetic flow rate (kg/s),
Magneto-motive Force: Potential energy per unit magnetic flux {J/kg},
Permeability: The same as magnetic field (kg.m/C²),
Permeance: The reciprocal of reluctance (kg² / J.s),
Reluctance: The resistance to magneto-motive force (J.s/kg²),
that together, give us a genuine relationship (equivalence) between magnetism and electricity, along with a solid basis on which to resolve the issues with the definition and properties of magnetism.

Magnets

Fig 1. Bar Magnet

Permanent magnets, such as bar-magnets (Fig 1), are blocks of metallic elements that will generate a fixed magnetic field without outside help. Their magnetism cannot be switched on and off.
Electro-magnets (Fig 2), are coils of [generally] copper wire, that will generate a variable magnetic field whilst energised with an electrical current. Their magnetism can be switched on and off.

Bar magnets attract and repel by aligning their proton-electron pairs, and therefore, their magnetic fields, to act unidirectionally. A few elements are better at this than most.
Despite the statement below regarding temperature, the properties of any and all bar magnets can and will deteriorate with prolonged exposure to high temperature (and magnetic fields) simply due to changes in their lattice structures and crystallinity.
Some elements, such as; Neodymium, Cobalt, Gadolinium, Terbium, Dysprosium, etc., all of which are hcp, are naturally magnetic.
Iron, which is bcc, for example, can have its atoms aligned permanently if treated with a lodestone. But iron will lose its magnetic strength with time, if its atomic alignment is not periodically maintained.

Fig 2. Electro-Magnet

Electro-magnets generate magnetic fields simply by passing an electrical current along a conductor. The resultant magnetic field is naturally generated around the conductor normal to the electrical current; according to the right-hand rule. If the conductor is wound into a tight coil (adjacent wires are very close; Fig 2), it will act as a bar magnet (Fig 1), generating a magnetic field that will vary with the applied current.

A solenoid is a simple combination of the bar and electro magnets, the bar magnet being the central plunger and the coil acting as the surrounding energiser. The relative North-South pole positions will determine which direction the plunger is pushed; identical poles repel.

A transformer uses a non-magnetic iron core that will instantly magnetise when the surrounding coil is energised, and demagnetise the instant it is de-energised.
Magnetism in iron will become permanent if the coil remains energised for long periods which would render an iron core useless in AC transformers, in which its constant reversal (frequency) prevents the magnetisation from becoming permanent.

Calculations

The field of attraction between celestial bodies is due to the non-polar magnetic charge in their atomic particles (protons (mₚ), electrons (mₑ) and neutrons (mₙ)). It is what we today call gravity. This potential [gravitational] force is calculated as defined above; Fₘ = G.mₑ.mₚ/R² {kg.m/s² = N}

Why does magnetism not vary with temperature?

Man-made magnets come in the form of bar-magnets and electro-magnets, but their attraction and repulsion is due to the magnetic field generated by their atom's proton-electron pairs, which is constant, irrespective of temperature.
But why is it constant?

Magnetic force at any distance (d) is calculated thus:
F = μ.I² = (mₑ.R/e²) x (e.2π.ƒ)² x (4π.R² / 4π.d²)
R is the electron orbital radius, and ƒ is the electron orbital frequency
remove the constants and we get:
factor = R.ƒ².R² = R³.ƒ² = 6.41524280848628 {m³/s²}⁽²⁾
which is the reciprocal of Isaac Newton's constant of proportionality for the proton-electron pair:
K = tₙ²/Rₙ³ = 0.15587874533403 s²/m³ = 1/factor
i.e. a constant!
irrespective of temperature.

... yet further vindication of the Newton-Coulomb atom, as if more was needed (Episode 52; Gravity & Episode 100; Verification).

Magnetic Field

The term 'field' when used for magnetism relates to the remote attraction and/or repulsion between particles that are not in physical contact.
Joseph Henry gave us a formula and a constant we can use today to define the strength of this field:
formula; μ = mₑ.R/e² {kg.m/C²}
where; 'R' is the orbital radius of the proton-electron pair generating the field.
constant; μ = mₑ.Rₙ/e² = 1.00000000000E-07 {kg.m/C²}.
The force associated with this field is calculated thus:
Fₘ = μ.I²
where; I is the internal current of a proton-electron pair; I = e.ƒ; ƒ = v/R; v = electron orbital velocity; R = electron orbital radius.
Hendrik Lorentz also gave us formulas for the potential force of magnetic field;
dynamic: Fₘ = e/RC . v²/R {N},
static: Fₘ = e/RC . a {N}.

The force of attraction (or repulsion) between particles - magnetic and electrical - does not vary with distance; it is constant throughout the universe.
However, as the distance varies between bodies, this force is distributed over the spherical area (4πR²) at that distance, exactly as heat and light are so distributed.
The general formula for the force of attraction (or repulsion) between particles is calculated thus: F = K.C₁.C₂/R²
where K is an arbitrary constant, and C₁ and C₂ are arbitrary variables
Because this condition applies to all fields (magnetic, electrical, and electro-magnetic), constants 'G' & 'k' should be multiplied by 4π, and the /R² in each force formula should be replaced with /4πR² in order to reflect this spherical distribution. It will not change the resultant forces, but it does reflect the true nature of the potential force as it varies with distance.
Joseph Henry's magnetic field force generates exactly the same force as Newton & Coulomb, so the condition 4π should only be applied to his force formula (μ.I²) (not his field variable μ #) for comparison purposes with Newton, Coulomb and Lorentz.

Magnetic field strength constants are today variously defined thus:
Newton: G = aₒ.c²/mᵤ = 6.67359232004333E-11 {m³ / kg.s²}
Coulomb: k = mₑ.Rₙ.(c/e)² = 8.98755184732666E+09 {kg.m³ / C².s²}
Henry: μ = mₑ.Rₙ/e² = 1.00000000000E-07 {kg.m/C²}
Lorentz: B = 1/RC = 5.685634367312130E-12 {kg/C}

This variation in the constants means that their definitions of force each require different calculation methods, which will only be correct if they all generate identical results:
e.g. a proton-electron pair @ temperature 300K:
v = √[Ṯ/X] = 207982.67075397 m/s
R = Xᴿ/Ṯ = 5.854887216934510E-09 m
g = v²/R = 7.38815108322488E+18 m/s²
ƒ = g/v = 3.55229166759022000E+13 /s
m = e/RC = 9.10938970E-31 kg
μ = mₑ.R/e² = 0.207772041572393 kg.m/C²
I = e.ƒ = 5.69139818666179E-06 C/s #
Newton: Fₘ = G/φ . mₑ.mₚ/R² = 6.73015473795726E-12 N
Coulomb: Fₑ = kꞌ.m²/R² = 6.73015473795726E-12 N
Lorentz: Fₘ = e/RC . v²/R = 6.73015473795726E-12 N
Henry: Fₘ = μ.I² = 6.73015473795726E-12 N
all of which are indeed identical.

Note: #
because electrical current is defined as ...
I = e.ƒ {C/s}
where;
ƒ = g/v {/s}
g = v²/R
ƒ = v/R
I² = (e.v)²/R²
R = orbital radius of the electron.
... 4π can only be applied to the force formula if it is also applied to the current-squared (I² = (e.v)² / 4πR²) in your calculation. As you can see above; 4π has not been applied to any of the comparison calculations, yet they all generate the same result.
It is safer, therefore, never to apply 4π to Henry's μ unless you know exactly why you need it.

Force vs Destance

Magnetic fields are radiated by both magnetic charge and magnetic induction.

The strength of the field from magnetic charge is defined thus:
F = G.m₁.m₂/d²
which tells us that its strength varies with the square of the distance.

But the field strength from bar and electro-magnets are defined like this:
Power {J/s} is constant for a given current and Voltage (P = V.I),
Potential energy {J} is also constant (PE = P/ƒ),
Force {N} must vary with distance (F = PE/d),
which tells us that for any given power, the force of attraction (or repulsion) varies linearly, it does not vary with the square of the distance.

The variation in magnetic charge, is due to the distribution of force over the spherical area (4πd²) at distance (d), because its field is radiated uniformly in all directions. Therefore, when calculating the effect of force at a distance, you must multiply the datum force (in the proton-electron pair) by factor; K = 4πR²/4πd².
But this is not the case for the field radiated by bar and electro magnets, because they act unidirectionally (d). The multiplication factor in this case is; K = R/d.
Where R is the electron orbital radius.

Example Calculations

Input Data (iron):

Assume only shell-1 electrons in each atom are magnetically active⁽³⁾, the number of aligned shells per atom will be; N = 2
separation (centres of mass): d = 1.5 m
magnet mass: m = 1 kg
atomic mass: mₐ = 9.34617738165495E-26 kg
aligned proton-electron pairs: N° = N.m/mₐ = 2.1399123067423E+25
shell-1 electron orbital performance:
radius: R₁ = Xᴿ/Ṯ = 5.854887217E-09 m
velocity: v₁ = √[Ṯ/X] = 207982.67075397 m/s
frequency: ƒ₁ = v₁/R₁ = 3.55229166759022E+13 /s
force: Fₘ = 6.73015473795726E-12 N (per proton-electron pair)

Charge

The potential force (Fₘ) between a proton-electron pair in shell-1 (R₁) at 300K is calculated above.
To find the force between a proton-electron pair in shell-46 (e.g. the uranium atom) you simply multiply Fₘ by factor; K = (R₁/R₄₆)²;
R₄₆ = R₁ . 46 = 5.85488721693451E-09 x 46 = 2.69324811978988E-07 m
K = (5.85488721693451E-09 ÷ 2.69324811978988E-07)² = 4.7258979206049E-04
Fₘ₄₆ = K.Fₘ₁ = 4.7258979206049E-04 x 6.73015473795726E-12 = 3.18060242814614E-15 N
which in this example is also; Fₘ₄₆ = Fₘ₁/46²

An alternative example for massive bodies:
The magnetic field force between the earth and our sun may be calculated using any of the above force-formulas because we now know that they all produce the same result. But because we are calculating the magnetic charge (not electrical charge) with Newton's formula, we must dispense with the coupling ratio:
The magnetic charge (mass) of our sun is; m₁ = 1.9885E+30 kg
The magnetic charge (mass) of the earth is; m₂ = 5.95786303763713E+24 kg
The earth's perigee radius is; Rᴾ = 1.47095E+11 m
The force between them is; Fₘ = G.m₁.m₂/Rᴾ² = 3.65409608E+22 N

The above is all you need to define the magnetic force between magnetic charges (masses); remember, the unit of measurement 'kilogram' actually refers to magnetic charge.

Field

The field force from a bar magnet is dependent upon the number of aligned proton-electron pairs which is at least 2 ⁽³⁾.
Its theoretical strength may therefore be calculated using Henry's field, like this:

magnetic permeability: μ₁ = mₑ.R₁/e² = 0.207772041572393 kg.m/C²
atomic current: I = e.ƒ₁ = 5.69139818666179E-06 C/s
atomic force @ R₁: Fₐ = μ₁.I² = 6.73015473795726E-12 N
atomic force @ d: Fₘ = Fₐ.(R₁/d)² = 1.02536761984608E-28 N
total force @ d: F = Fₘ.N° = 0.00219419678864369 N
The field force induced by an iron magnet at 1.5m from its centre of mass will be; F = Fₘ.(R₁/d)².N° = 0.002194196789 N
and the same force at 50mm is; 1.974777109779 N.

But you must bear in mind that actual (practical) strength will vary with the efficiency of your lodestone⁽⁴⁾ treatment and the material thickness. The thicker your magnet, the more time and effort will be required to achieve 100% alignment. Therefore, the above force @ 'd' will be a maximum.

Today, we calculate the force induced by an electro-magnet like this:
F = (N°.I)² . (4π.μₙ) . (A / 2.d²)
where:
N°: number of turns (1000)
I: current (10 C/s)
A: coil cross sectional area (0.5 m)
d: distance (1.5 m)
F = (1000 x 10) . (4π x 1E-07) . (0.5 / 2/1.5) = 13.96263402 N

But if we calculate this force using Henry's formula for the proton-electron pair (μ) and the current in the wire; ignoring the coil altogether:
F = μ.I²/d = 13.851469438 N

The problem with today's calculation method is that it takes no account of the different coil diameters, and 4π has been incorrectly applied.

Useful Formulas:
coil properties: wire length: L = π.ℓ.(R²-r²)/Ø²
Joseph Henry's magnetic field formula: μ = mₑ.R₁/e² = 0.207772041572393 kg.m/C²
where:
coil length: ℓ
wire diameter: Ø
coil outside radius: R
core inside radius: r
shell-1 electron orbital radius (@ 300K): R₁ = Xᴿ/Ṯ = 5.85488721693451E-09 m

Notes

If we fully understood the concepts of electricity and magnetism, both of which comprise charge and field, and together their charges generate EME, we would realise that the units of measurement for their respective forces and their equivalence should be as follows:
magnetic force (accrues): Fₘ = G.m₁.m₂/R² {kg.m/s²}
electrical force (shared): Fₑ = k.e²/R² {C.m/s²}
equivalence Fₘ:Fₑ = Fₘ/Fₑ = φ (the coupling ratio).
When the reciprocal of this factor (1/K) is divided by the mass of an electron, we get Coulomb's modified constant; k' = 4π² / K.mₑ = 2.78024810626745E+32 {m³/s² / kg}.
The highest energy electron shells will dominate the reaction in magnetism and lodestone alignment. This means that shell-1 proton-electron pairs will define magnetic strength, and every atom (except hydrogen) must have at least two aligned electron shells, because two proton-electron pairs always occupy shell-1.
Lodestones are not the only method of creating permanent magnetism in a bar-magnet, you can also put it inside an energised electro-magnetic coil. But the thicker the bar, the more time and current (in the electro-magnetic coil) will be required to maximise its strength.