From Newsgroup: sci.physics

The Progressing Electric Field Model
Abstract: Faraday’s law is empirically derived and, as such, may be
subject to limitations. Notably, it appears to violate the law of
conservation of energy in certain contexts. To establish a more robust formulation, it is necessary to derive the law from first principles. In
this article, we theoretically derive Faraday’s law using only
Coulomb’s law and special relativity. We present the first stage of this derivation: the construction of the 'Progressing Electric Field Model.'
This model determines the curl of the electric field produced by moving charges and calculates the electric potential induced in a wire loop
within that field.

Introduction
In electromagnetism, Faraday's law defines the electromotive force (EMF) induced in a wire loop by a varying magnetic field. Although considered a cornerstone of classical electromagnetism, it remains an empirical law; consequently, it may be incomplete regarding phenomena not yet captured by experimental observation. To illustrate this, consider the following experimental setup: suppose two coils, A and B, are positioned side by
side, with coil B connected to a resistor R, as shown in Figure 1.

Let the current in coil A, denoted as Ia, vary as follows: Ia increases linearly from zero to Imax, then decreases linearly back to zero. The
duration of each phase is Δt. According to Faraday's law, voltages are induced in coils A and B, which we label Va and Vb, respectively. Since Ia varies linearly during each phase, Va and Vb remain constant throughout
those intervals. Within resistor R, the voltage Vb generates a current Ib
and dissipates electric power equal to |VbIb|, both of which are constant
in each phase. Consequently, the total work performed in R after both
phases is 2|VbIb|t.

Since Ib is constant, it does not induce a voltage in coil A; therefore,
the value of Va remains unchanged regardless of whether Ib is positive, negative, or zero—just as if coil B were not present. When Ia increases,
the voltage in coil A (Va) is positive, and the electrical work performed
in A is given by ∫_o^Δt▒〖V_a I_a dt〗. Conversely, when Ia
decreases, the voltage in A becomes -Va, and the work equals -∫_o^Δt▒〖V_a I_a 〗 dt. Consequently, the total energy consumption
of coil A after both phases equals zero.

Since the energy consumption in coil A is zero, A does not transfer any
energy to coil B. We therefore encounter a case where B performs work
equal to 2|VbIb|t while receiving no energy from A. This implies that
the system consisting of coils A and B performs work without any energy
input, which violates the law of conservation of energy.

The cause of this violation is that Faraday's law predicts zero voltage in
A when the current in coil B is constant. By theoretically deriving Faraday’s law from more fundamental laws, we can not only resolve this inconsistency but also uncover new phenomena and achieve a deeper understanding of nature.

An example of such a phenomenon is demonstrated in my experiment, which reveals a tangential electromotive force not predicted by Faraday’s law.
You can view the experiment in this video on YouTube: https://www.youtube.com/watch?v=P33Hgj68G9M

To begin the theoretical derivation of Faraday’s law, we must first
examine the electric field of a moving electron.
…

For more detail, please read « A Derivation of Faraday's law from
Coulomb's Law and Relativity / 1.The Progressing Electric Field Model » https://pengkuanem.blogspot.com/2026/01/a-derivation-of-faradays-law-from.html https://www.academia.edu/146009113/A_Derivation_of_Faradays_law_from_Coulombs_Law_and_Relativity_1_The_Progressing_Electric_Field_Model

Discussion
This article presents the first stage of a derivation of Faraday’s law
based solely on Coulomb’s law and special relativity. We demonstrate
that the retarded electric field of a moving electron—which we term the 'Progressing Electric Field'—is a non-conservative vector field. We have derived the mathematical expression for its curl and have found that
several properties of this field are analogous to those of the magnetic
field.

We have derived the electric potential induced in a wire loop by a
progressing electric field, which shares certain properties with the electromotive force defined by Faraday’s law. However, because this potential is not yet proportional to the rate of change of the magnetic
field, it cannot be classified as electromotive force at this stage.
Several additional steps of theoretical derivation are required to fully arrive at Faraday’s law.

The essential steps of the derivation presented in this article are as follows:
Propagation at the speed of light: In accordance with special relativity,
the electric field propagates at the speed of light, c.
Iso-intensity circles: The electric field of a moving electron radiates
in 'iso-intensity circles.' The centers of these circles correspond to the retarded positions of the electron.
Application of Coulomb’s law: The intensity of the electric field on an
iso-intensity circle is defined by Coulomb’s law relative to the
circle's center.
Non-conservative nature: The 'Progressing Electric Field' is a deformation of the static electric field and is inherently
non-conservative.
Instantaneous curl calculation: The Progressing Electric Field is analyzed within a single temporal snapshot, allowing its curl to be
computed using instantaneous values.
Superposition of charges: The curl of the Progressing Electric Field for
a steady current is derived by integrating the fields of individual moving charges.
Induction and Lenz’s Law: The Progressing Electric Field induces an electric field within a wire loop; the calculated average value of this
field is shown to be consistent with Lenz’s law.

We have constructed our theory upon the Progressing Electric Field, a
concept that may initially appear to lack direct experimental
verification. One might ask: what if this field is merely a theoretical construct? In reality, experimental evidence for its existence already
exists; however, it has historically been overlooked or reinterpreted
through the lens of well-established theories.

By applying the 'Progressing Electric Field Model,' we will provide a new
and comprehensive explanation for this experimental evidence in a
forthcoming article.

In summary, the 'Progressing Electric Field Model' demonstrates that the induction phenomena traditionally attributed to Faraday's law can be
derived from the relativistic motion of electric charges. By accounting
for the propagation delay of the field at speed c, we establish that the resulting electric field is non-conservative and possesses a non-zero
curl. While this initial stage of the derivation produces results
consistent with Lenz’s law, further refinement is required to achieve
full mathematical proportionality with the rate of change of magnetic
flux. This theoretical framework not only aligns with the principle of
energy conservation but also opens the door to predicting electromagnetic phenomena beyond the reach of classical empirical laws.

For more detail, please read « A Derivation of Faraday's law from
Coulomb's Law and Relativity / 1.The Progressing Electric Field Model » https://pengkuanem.blogspot.com/2026/01/a-derivation-of-faradays-law-from.html https://www.academia.edu/146009113/A_Derivation_of_Faradays_law_from_Coulombs_Law_and_Relativity_1_The_Progressing_Electric_Field_Model

1. Introduction 1
2. The Electric Field of a Moving Electron 2
a) The Static Case: The Immobile Electron 2
b) The Dynamic Case: The Moving Electron and the Progressing Field 3
3. Geometry of the Wire Loop and Iso-intensity Circles 1
a) Partitioning the Wire Loop into Sectors 4
b) Determining the Lengths of Segments AB and CD 5
c) Calculation of the Surface Area of Sector S 6
4. Potential within the Progressing Electric Field 4
a) Definition of Potential 7
b) Calculation of Potential around the Boundary of a Sector 7
c) Demonstration of Null Potential Variation on Arcs 8
d) Resultant Potential Variation for a Complete Sector 9
5. Potential and Field within the Wire Loop 7
a) Summation of Individual Sector Influences 11
b) Characterization of the Electric Field in the Wire Loop 12
c) Application of Stokes' Theorem to the Induced Field 13
6. The Influence of Electric Current 13
7. The Curl of the Progressing Electric Field 13
a) Calculation of the Curl for a Single Moving Charge 15
b) Calculation of the Curl due to a Macroscopic Current 16
c) Connection to the Biot–Savart Law 17
d) Connection to the Lorentz Force 17
8. Implications for a Theoretical Faraday's Law 18
9. Discussion 19
Letter to the Readers 20


For more detail, please read « A Derivation of Faraday's law from
Coulomb's Law and Relativity / 1.The Progressing Electric Field Model » https://pengkuanem.blogspot.com/2026/01/a-derivation-of-faradays-law-from.html https://www.academia.edu/146009113/A_Derivation_of_Faradays_law_from_Coulombs_Law_and_Relativity_1_The_Progressing_Electric_Field_Model

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From Newsgroup: sci.physics

Kuan Peng wrote:

The Progressing Electric Field Model
[...] https://pengkuanem.blogspot.com/2026/01/a-derivation-of-faradays-law-from.html

[blogspot.com, where many crackpots are self-publishing.]

On page 6, you write:

| Because v/c ≪ 1, (l/r_e)^2 is neglected in (4).

ISTM that that is precisely what you MUST NOT do if you want to arrive at a proper relativistic formulation of electromagnetism.

Incidentally, though, that train has already left the station; that ship has already sailed: Quantum electrodynamics is the best special-relativistic formulation of electrodynamics that we have to date; its predictions agreed with experiment to 10 decimal places in 2014 (probably more now). It is how you can even write this and post this as modern computer technology is based
on it.

Since the rest of your work is apparently based on this approximation, unfortunately it is useless (*iff* correct, it does NOT show anything
*new*) as it does NOT consider special-relativistic effects.

| In physics, we can use the sign "=" when a really small quantity is
| neglected.

That is just not true. Physics is an *exact* science. What you can do is
an approximation using the symbol "≈", or, more precisely, make a Maclaurin series approximation and signify the minimum degree of polynomials using the O-notation and then declare that one can neglect them if the variable of the polynomial is close to 0. (Einstein did that with the actual kinetic energy
to derive "E_0 = m c^2".)


https://www.academia.edu/146009113/A_Derivation_of_Faradays_law_from_Coulombs_Law_and_Relativity_1_The_Progressing_Electric_Field_Model

academia."edu", where most crackpots are self-publishing.

| In 1997, I discovered that the Lorentz force occurs because the density of
| a moving electric charge increases due to length contraction.

Yeah, well, it doesn't. The idea of a point-like object that somehow
carries an electric charge does not really work especially when one
considers special relativity; which is why we need quantum field theory to describe it properly.

But you can derive the Lorentz force law from the principle of stationary action in Minkowski space if you only consider the spatial components of the four-vectors; if I had time, I would post it here (it would be not my idea,
but from our Classical Field Theory lecture notes; maybe I will do it later).

See also: <https://en.wikipedia.org/wiki/Crackpot_index>
--
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
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From Newsgroup: sci.physics

On 1/15/26 00:20, Thomas 'PointedEars' Lahn wrote:

Kuan Peng wrote:

The Progressing Electric Field Model
[...]
https://pengkuanem.blogspot.com/2026/01/a-derivation-of-faradays-law-from.html

[blogspot.com, where many crackpots are self-publishing.]

On page 6, you write:

| Because v/c ≪ 1, (l/r_e)^2 is neglected in (4).

ISTM that that is precisely what you MUST NOT do if you want to arrive at a proper relativistic formulation of electromagnetism.

Incidentally, though, that train has already left the station; that ship has already sailed: Quantum electrodynamics is the best special-relativistic formulation of electrodynamics that we have to date; its predictions agreed with experiment to 10 decimal places in 2014 (probably more now). It is how you can even write this and post this as modern computer technology is based on it.

Since the rest of your work is apparently based on this approximation, unfortunately it is useless (*iff* correct, it does NOT show anything
*new*) as it does NOT consider special-relativistic effects.

| In physics, we can use the sign "=" when a really small quantity is
| neglected.

That is just not true. Physics is an *exact* science.

There is something called 'experiment', and it is difficult
to say if that can be 'exact'.

I suggest that one consult with another alien
called the 'Rael'.

I am thinking that 'real' in French is something like 'reel'.
But I am thinking that the 'Rael' is called the 'Rael' because
they consider that the 'Rael' has the right to interchange
the 'ae' with an 'ea' in English. You are utterly disconnected
from 'reality' unless you get approval from the 'Rael'. Your
pointy ears mean nothing.

I am thinking the article is OK if they just delete the words 'and Relativity'.How do you contact the 'Rael' to see if you are living in 'reality'? I do not know. Here is a link.

https://en.wikipedia.org/w/index.php?title=Claude_Maurice_Marcel_Vorilhon


What you can do is

an approximation using the symbol "≈", or, more precisely, make a Maclaurin series approximation and signify the minimum degree of polynomials using the O-notation and then declare that one can neglect them if the variable of the polynomial is close to 0. (Einstein did that with the actual kinetic energy to derive "E_0 = m c^2".)

https://www.academia.edu/146009113/A_Derivation_of_Faradays_law_from_Coulombs_Law_and_Relativity_1_The_Progressing_Electric_Field_Model

academia."edu", where most crackpots are self-publishing.

| In 1997, I discovered that the Lorentz force occurs because the density of | a moving electric charge increases due to length contraction.

Yeah, well, it doesn't. The idea of a point-like object that somehow
carries an electric charge does not really work especially when one
considers special relativity; which is why we need quantum field theory to describe it properly.

But you can derive the Lorentz force law from the principle of stationary action in Minkowski space if you only consider the spatial components of the four-vectors; if I had time, I would post it here (it would be not my idea, but from our Classical Field Theory lecture notes; maybe I will do it later).

See also: <https://en.wikipedia.org/wiki/Crackpot_index>

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From Newsgroup: sci.physics

Thank you for reading my paper and commenting.

What do you think about the violation of the law of conservation of energy
by Faraday’s law?

Kuan Peng

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From Newsgroup: sci.physics

Kuan Peng wrote:

Thank you for reading my paper and commenting.

You are welcome.

What do you think about the violation of the law of conservation of energy by Faraday’s law?

There are several (at least 3) Faraday's laws. I presume you mean Faraday's law _of induction_:

<https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction>

If so, why do you think that the law of the conservation of _total_ energy would be violated by it?
--
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.
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From Newsgroup: sci.physics

I have explained this violation of the law of conservation of energy in
the introduction.

To illustrate this, consider the following experimental setup: suppose two coils, A and B, are positioned side by side, with coil B connected to a resistor R, as shown in Figure 1.

Let the current in coil A, denoted as Ia, vary as follows: Ia increases linearly from zero to Imax, then decreases linearly back to zero. The
duration of each phase is Δt. According to Faraday's law, voltages are induced in coils A and B, which we label Va and Vb, respectively. Since Ia varies linearly during each phase, Va and Vb remain constant throughout
those intervals. Within resistor R, the voltage Vb generates a current Ib
and dissipates electric power equal to |VbIb|, both of which are constant
in each phase. Consequently, the total work performed in R after both
phases is 2|VbIb|t.

Since Ib is constant, it does not induce a voltage in coil A; therefore,
the value of Va remains unchanged regardless of whether Ib is positive, negative, or zero—just as if coil B were not present. When Ia increases,
the voltage in coil A (Va) is positive, and the electrical work performed
in A is given by the integral of VaIa . Conversely, when Ia decreases, the voltage in A becomes -Va, and the work equals the integral of -VaIa . Consequently, the total energy consumption of coil A after both phases
equals zero.

Since the energy consumption in coil A is zero, A does not transfer any
energy to coil B. We therefore encounter a case where B performs work
equal to 2|VbIb|t while receiving no energy from A. This implies that
the system consisting of coils A and B performs work without any energy
input, which violates the law of conservation of energy.

The cause of this violation is that Faraday's law predicts zero voltage in
A when the current in coil B is constant.

Kuan Peng

16/01/2026 à 08:22, Thomas 'PointedEars' Lahn a écrit :

Kuan Peng wrote:

Thank you for reading my paper and commenting.

You are welcome.

What do you think about the violation of the law of conservation of energy >> by Faraday’s law?

There are several (at least 3) Faraday's laws. I presume you mean Faraday's law _of induction_:

<https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction>

If so, why do you think that the law of the conservation of _total_ energy would be violated by it?

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From Newsgroup: sci.physics

Den 16.01.2026 12:50, skrev Kuan Peng:

I have explained this violation of the law of conservation of energy in
the introduction.

https://pengkuanem.blogspot.com/2026/01/a-derivation-of-faradays-law-from.html

To illustrate this, consider the following experimental setup: suppose
two coils, A and B, are positioned side by side, with coil B connected
to a resistor R, as shown in Figure 1.
Let the current in coil A, denoted as Ia, vary as follows: Ia increases linearly from zero to Imax, then decreases linearly back to zero. The duration of each phase is Δt. According to Faraday's law, voltages are induced in coils A and B, which we label Va and Vb, respectively. Since
Ia varies linearly during each phase, Va and Vb remain constant
throughout those intervals.

Let us first consider coil A only. Let its inductance be L.

(Just summing up, I expect you to agree)

When the current increases from zero to Imax,
the voltage on the current source is:
Va = L⋅dI/dt = L⋅(Imax/Δt)
Note that both Va and Ia are positive.

The energy W stored in the magnetic field
at the time when the current is Imax is:
Wa = L⋅(Imax)²/2

When the current decreases from Imax to zero,
the voltage on the current source is:
Va = L⋅dI/dt = - L⋅(Imax/Δt)
Note that Va is negative while Ia is positive.

That means that energy is delivered back to
the current source.

The energy W released from in the magnetic field
at the time when the current is zero is:
W = - L⋅(Imax)²/2 = -Wa

While the current is increasing, the current source will
deliver energy to the magnetic field,
when the current is decreasing, the magnetic field
will deliver the stored energy back to the current source.

(If the resistance in the coil is different from zero,
some energy will be lost as heat. Some energy will also
be lost as em-radiation. This will be strongly dependent
on Δt. We ignore these losses.)

Now let us consider what will happen in coil B.

Within resistor R, the voltage Vb generates
a current Ib and dissipates electric power equal to |VbIb|, both of
which are constant in each phase. Consequently, the total work performed
in R after both phases is 2|VbIb|t.

This is correct.

When the current in A is increasing, the voltage over
the resistor R will be constant Vb and the current Ib = Vb/R.

When the current in A is decreasing, the voltage over
the resistor R will be constant -Vb and the current -Vb/R = -Ib.
Energy loss Wb = 2|VbIb|⋅Δt

Now let us consider how this will affect coil A.

Since Ib is constant, it does not induce a voltage in coil A; therefore,
the value of Va remains unchanged regardless of whether Ib is positive, negative, or zero—just as if coil B were not present. When Ia increases, the voltage in coil A (Va) is positive, and the electrical work
performed in A is given by the integral of VaIa . Conversely, when Ia decreases, the voltage in A becomes -Va, and the work equals the
integral of -VaIa . Consequently, the total energy consumption of coil A after both phases equals zero.

Let's take it from the beginning:

When the current in A is increasing, the magnetic field in A
will be increasing. Part of this field will go through B,
so there will be an increasing flux through B. This will induce
a constant voltage Vb and current Ib in B. This will give a
constant magnetic flux through B. Part of this flux go through A
and will have the opposite direction of the flux in A.
The result is that the flux in A will increase slower, and the
energy stored in the magnetic field at the time when the current
is Imax will be less than Wa = L⋅(Imax)²/2 . Let's call it Wa'.

When the current in A is decreasing, the magnetic field in A
will be decreasing. Part of this field will go through B,
so there will be an decreasing flux through B. This will induce
a constant voltage -Vb and current -Ib in B. This will give a
constant magnetic flux through B. Part of this flux go through A
and will have the same direction of the flux in A.
The result is that the flux in A will decrease slower, and the
energy stored in the magnetic field at the time when the current
is zero will be W = 0.

The net result is that the stored energy in A will increase from
zero to Wa', and then decrease back to zero.

This means that the current source has delivered the energy Wa
to the field, but has only got Wa' back.

Wa-Wa' = Wb

Since the energy consumption in coil A is zero, A does not transfer any energy to coil B.

Strange conclusion.

The energy consumption in coil A is zero.
A transfers energy to B.
This energy is supplied by the the current source in A.

We therefore encounter a case where B performs work
equal to 2|VbIb|t while receiving no energy from A. This implies that
the system consisting of coils A and B performs work without any energy input, which violates the law of conservation of energy.

The cause of this violation is that Faraday's law predicts zero voltage
in A when the current in coil B is constant.

--
Paul

https://paulba.no/
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