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

Today, Coulomb's force constant has been manipulated in order to generate Newtons from Coulombs, and whilst his force formula is identical to Newton's and Gilbert's force formulas, Coulomb's constant does not have compatible units. As we understand it today, force is based upon kilograms (kg.m/s²), yet Coulomb's formula appears to generate this same force from electrical charge.
In order to rationalise Coulomb's constant 'k' with Newton's constant 'G', we must ensure that their units are identical. And to do this, we must incorporate electrical charge within his constant, such that we can use mass in his force formula.

The units for Newton's gravitational constant (G) have at last been finalised, along with its formula and its value; {m³ / kg.s²}
and using this constant, the potential force in a proton-electron pair at the neutronic state can be calculated like this;
Fₘ = G.ξₘ.(mₑ/Rₙ)²
Fₘ = 6.67359232004333E-11 x 1836.15115053207 x (9.1093897E-31 ÷ 2.81793795383896E-15)²
Fₘ = 1.28051247005732E-38 {kg.m/s²}
his potential energy at the neutronic state may be calculated like this;
PEₘ = Fₘ.Rₙ = 3.60840468973861E-53 {kg.m²/s²}

Coulomb's formula and units for 'k' are currently:
k = c².mₑ.Rₙ/e²
k = 8.98755184732666E+09 {kg.m³ / C².s²}
but because we are trying to calculate force (kg.m/s²), it should be; m³ / kg.s² as defined by Newton above.
We can correct it by incorporating the relative charge capacity (RC) and modifying his formula thus;
k' = k.RC² = e²/mₑ² . c².mₑ.Rₙ/e² = Rₙ.c²/mₑ
k' = 2.78024810626745E+32 {m³ / kg.s²}
Coulomb's potential force at the neutronic state becomes;
Fₑ = k'.mₑ²/Rₙ² = 2.78024810626745E+32 x (9.1093897E-31 ÷ 2.81793795383896E-15)²
Fₑ = 29.0535538991261 {kg.m/s²}
and his potential energy at the neutronic state becomes;
PEₑ = Fₑ.Rₙ = PEₙ = 8.18711122262533E-14 {kg.m²/s²}
the electrical charge is now included within Coulomb's constant.

The coupling ratio;
φ = Fₘ/Fₑ = PEₘ/PEₑ = 4.40742111792334E-40

Because magnetic charge forces accrue and electrical charge forces are shared; the coupling ratio becomes;
φ = (G.mₑ.mₚ/R²) / (k'.mₑ²/R²) = (G.ξₘ.mₑ²/R²) / (k'.mₑ²/R²) = G.ξₘ / k'
φ = 6.67359232004333E-11 x 1836.15115053207 ÷ 2.78024810626745E+32
φ = 4.40742111792334E-40
but now we are no longer trying to generate Newtons from Coulombs and the units of both constants are identical, what's more the coupling ratio becomes ...
φ = G.ξₘ / k' ...perfect
in which 'ξₘ' emphasises the converse between accrued magnetic charge force and shared electrical charge force.

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⁾.
CalQlata has 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 . (2π)² = (mₑ.R/e²) x (e.ƒ.2π)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 variable and a constant we can use today to define the strength of this field:
variable; μ = m.R/e² {kg.m/C²}
where; 'R' is the orbital radius of the proton-electron pair generating the field.
His variable becomes a constant for a proton-electron pair at the neutronic condition;
constant; μₒ = mₑ.Rₙ/e² = 1.00000000000E-07 {kg.m/C²}
The force associated with this field is calculated thus:
Fₘ = μ.I² . (2π)²
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}.

Magnetic and electrical charge force of attraction (and repulsion) between particles 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 between any two bodies as the distance between them varies.
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 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 / 2π.v = v / 2π.R = 1/t = 5.65364778201136E+12 /s
m = e/RC = 9.1093897E-31 kg
t = 2πR/v (orbital period) = 1.76876954235065E-13 s
μ = mₑ.R/e² = 0.207772041572393 kg.m/C²
I = e.ƒ = 9.05814154511474E-07 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 . (2π)² = 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 / 2π.v {/s}
g = v²/R
I² = (e.v)²/(2π.R)²
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 Distance

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

Below we provide a pair of magnetic force calculation methods for both a bar magnet and a solenoid.

Bar Magnet:

The strength of a bar magnet can be calculated using Henry's magnetic charge;
F = N° . μ₁.I₁² . (2π)² . (R₁/d)²
or the modified version of Coulomb's constant;
F = N° . k'.ξₘ.mₑ²/d²
Force 'F' in these formulas is a maximum value; it only applies if all of the shell-1 proton-electron pairs are aligned.

where;
d = magnet-target spacing
m = magnet mass
μ₁ = shell-1 proton-electron pair magnetic field (μ = mₚ.R₁/e²)
R₁ = shell-1 proton-electron pair orbital radius (R₁ = Xᴿ/Ṯ)
I₁ = shell-1 proton-electron pair current (I₁ = e.ƒ₁)
ƒ₁ = shell-1 proton-electron pair orbital frequency (ƒ₁ = (Ṯ/Ṯₙ)¹˙⁵ / tₙ)
N° = the number of proton-electron pairs in the magnet (N° = Z/RAM . m/mₐ)
mₐ = atomic mass

For example, an iron bar magnet;
m = 0.1 kg
d = 0.25 m
μ₁ = 381.500873181541 kg.m/C²
N° = 4.98126309159847E+23
gives a force of;
F = 3.37621432901708 N (both of the above calculation methods give exactly the same results)
This force does not vary with a change in temperature in bar magnets.

Solenoid:

The strength of an electro-magnet can be calculated using Henry's magnetic charge;
F = μ₁.I² . π . A/d²
or the modified version of Coulomb's constant;
F = k'.m_q²/R₁² . A/(4π.d²)

where;
A = cross-sectional area of the solenoid winding
d = magnet-target spacing
I = applied current
μ₁ = shell-1 proton-electron pair magnetic field (μ = mₑ.R₁/e²)
R₁ = shell-1 proton-electron pair orbital radius (R₁ = Xᴿ/Ṯ)
m_q = mass equivalent for electrical charge (m_q = I / ƒ₁.RC)
ƒ₁ = shell-1 proton-electron pair orbital frequency (ƒ₁ = (Ṯ/Ṯₙ)¹˙⁵ / tₙ)

For example, an iron bar magnet;
A = 0.5 m²
d = 1.5 m
I = 10 C/s
μ₁ = 0.20777204157239 kg.m/C²
m_q = 1.00565768978436E-23 kg
gives a force of;
F = 14.505224876115 N (both of the above calculation methods give exactly the same results)
This force varies with a change in temperature due to its effect on electrical resistance.

A typical calculation method today is:
F = (N.I)² . 2π . μₒ . A/d²
where; N = number of turns
F = 13.9626340159546 N

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.