Lorentz Force versus Maxwell's equations, different laws yielding same results.

[Ufopolitics]

Hello to All,

As a discussion was generated on the Transverse Flux Topic, Member Solarlab suggested opening a Topic related to the differences on the great work done about Electromagnetism by James Clerk Maxwell versus the Lorentz Force Law by Hendrik Lorentz...which we were arguing about...so, here it is.
And (how come) both render the same results...

First, I would like to start by bringing on some chronological and Literature data required to start this discussion...

1- In 1831, Faraday discovers the Electromagnetic Induction...He experimented by wrapping two insulated coils of wire around an iron ring. He found that, upon passing a current through one coil, a momentary current was induced in the other coil— mutual induction. If he moved a magnet through a loop of wire, an electric current flowed in that wire.

2- James Clerk Maxwell (1831-1879) is born on 1831 (same year Faraday discovered Induction), He discovered on 1864 (33 years old) that electric and magnetic fields travel through space moving at the same speed of light as waves. Electromagnetic theory: He stated that light is a propagating wave of electric and magnetic field. The theory describes the interaction between the electric field and magnetic field.

Maxwell written books and Papers about Electromagnetism:

1-On Faraday Physical Lines of Force (Paper, 1865)
2-A Dynamical Theory of the Electromagnetic Field (1865)
3-Matter and Motion. (1857)
4-Treatise on Electricity & Magnetism. Volume 1 (1873)
5-Treatise on Electricity & Magnetism. Volume 2 (1875)

As you can see above, there are all known Maxwell Books related to Electromagnetism, except the "Matter and Motion" which defines other parameters as well, however, it is still related.

All cited books above have embedded links to readable PDF Formats online for FREE...

Therefore, I ask you that if you have never even started to read one of his books... please do read them, basically 1, 2, 4 & 5, before commenting here.

The only way to be able to render your comment(s) on Maxwell work, is to know his work, that simple.

And I did not mean to read the ENTIRE Book, but ALL Related Chapters to this Topic Discussion.

It is simple, when you are at the pdf, on Archives Org site (where the 3 main books are), on left press the Search Magnifying lens icon, and type the key words...like Magnetic Field, Single Wire, Coils, Spatial Magnetic Volume, etc.

***********************************

The reason why I cited Faraday first, is simply to understand that majority of Maxwell development is based and inspired on the Faraday Discovery of Induction Laws.

Maxwell work on Magnetism is ALWAYS backed up by SPATIAL GEOMETRIES CALCULATIONS.
Maxwell does include on his books, the analysis of a single wire (Singular) behavior, HOWEVER, after the First Singular Analysis, then Maxwell goes into experiments-based tests of actions-reactions that keep adding this analysis to multiple conductors (wires) ending with COILS EXPERIMENTS as it is known to "All knowledgeable on the Arts", that the ONLY Geometrical Configuration to Generate a FULL Magnetic Field is simply A COIL, not a Single Wire Loop.



And I will still be adding a LOT of Info here...

Ufopolitics

[solarlab]

Ufopolitics,

Thanks for opening this subject; it's my belief there is a lot to be learned by studying, in detail,
their differences and their applications.

From an old post [rather long]:
-------------------------------------
Title: Re: Holcomb Energy Systems:Breakthrough technology to the world
Post by: SolarLab on July 20, 2022, 08:55:32 PM
-------------------------------------
Two Electromagnetic Equations - Yield the Same Results

Of the four laws of electromagnetism, let's consider only Lorentz Force and Faraday's Law of induction.

They both arrive at the same answer; but their mechanisms are different. Some may say Faraday's Law
is associated with Lenz whereas Lorentz is not - Faraday deals with an alternating magnetic field - Lorentz
deals with a sweeping (traveling) magnetic field.

Review the earlier "Asymetric transformers - AAbramovich Discussions" section "Equivalence of induction
according to Lorentz and Faraday" and the information below. Note that the differences between Faraday
and Lorentz were never really resolved - history - seems Einstein got in the way - since he couldn't solve
it, he started a new branch of physics - Special Relativity - and further attempts at a resolution faded. Lots
of reading but worth it!

Four Laws of Electromagnetism

https://www.motioncontroltips.com/four-laws-of-electromagnetism-you-should-know/ (https://www.motioncontroltips.com/four-laws-ofelectromagnetism-you-should-know/)
https://www.vanderbilt.edu/AnS/physics/panvini/p110a/lect37c.html (https://www.vanderbilt.edu/AnS/physics/panvini/p110a/lect37c.html)

Why Faraday's law and Lorentz force create the same electromotive force?

The Faraday's induction formula (flux rule) of electromagnetism says that the electromotive force (emf)
created in a conducting circuit is equal to the rate at which the magnetic flux through the conducting circuit
changes as it is written on a high school text in physics. This emf can be calculated in two ways: either by
using the Lorentz force formula and calculating the force acting on electrons in the moving conductor of the
circuit; or via one of Maxwell's equations (Faraday's law) and calculating the change of the magnetic flux
penetrating through the circuit. The Lorentz force formula and Maxwell's equations are two distinct physical
laws, yet the two methods yield the same results.
https://www.sciencedaily.com/releases/2017/09/170926085958.htm (https://www.sciencedaily.com/releases/2017/09/170926085958.htm)

Includes a bit more "history" - Faraday's Law of Induction:

https://www.dataforth.com/faradays-law-of-induction.aspx (https://www.dataforth.com/faradays-law-of-induction.aspx)
... "This is not exactly what Faraday described but was called Faraday's Law by Oliver Heaviside. It does not
include the movement emf; that is the force effect Faraday found. The magnetic force is called Lorentz force.

Current flowing in a wire in the presence of a magnetic field will experience a force and move if not restrained.
In this case, magnetic energy is released kinetically." ...
" The previous mention of the relative motion of magnetic field and electric circuit has had considerable thought by many, well-known physicists. Richard Feynman stated: (1)

So the "flux rule" that the emf in a circuit is equal to the rate of change of the magnetic flux through the circuit
applies whether the flux changes because the field changes or because the circuit moves (or both) ...

Yet in our explanation for the rule we have used two completely distinct laws for the two cases Faraday's Law
equation (both vector quantities: -v x B) for "circuit moves" and Faraday's Law equation (vector: V x E = -dtB)
for "field changes".

We know of no other place in physics where such a simple and accurate general principle requires for its real
understanding an analysis in terms of two different phenomena.

Richard P. Feynman, The Feynman Lectures on Physics
---------------------------------------------------------------
Lorentz Force 3d view animation video (Lorentz is near the end, 6:26)
https://www.youtube.com/watch?v=YZ9YRWYv2cY (https://www.youtube.com/watch?v=YZ9YRWYv2cY)

------------- Food for thought ---------

Professor Eric Laithwaite: Magnetic River 1975
https://www.youtube.com/watch?v=OI_HFnNTfyU (https://www.youtube.com/watch?v=OI_HFnNTfyU)

Professor Eric Laithwaite: Motors Big and Small - 1971
https://www.youtube.com/watch?v=oWiYsRi2Dss (https://www.youtube.com/watch?v=oWiYsRi2Dss)

SL

[solarlab]

All,

If you're really into this "EM Stuff" here's the "Feynman Letures on Physics Volume II"
from Caltech.edu (free - read-on-line). Ties a lot of the physics together. 

Table of Contents:

https://www.feynmanlectures.caltech.edu/II_toc.html

Be aware, however, this is heavy-duty Physics - mainly "Electromagnetism and Matter
as presented by Feynman!" [There's a lot there - I think it was a full semester or two.]
Original ~ 1964, Revised ~ 2006 & ~ 2013...

SL

[Ufopolitics]

Hello,

I will try to put it as simple as I can...

The reason why I have opened this Topic is NOT just to know why both Laws yield the same results...the answer is very obvious to many reading here.

Lorentz Law (Lorentz Force) is just a 'compacted modern version' of Maxwell's 'Magnetism Universe'; therefore, it contains the 'extract' which must derive on the same results.

But only If you get to read Maxwell Books, then you would understand the differences between the Lorentz Compact Extraction versus the vast Maxwellian Geometries of Magnetism.

Because to understand Lorentz Force it may take you just a few minutes, one single wire, one single particle, passing through one single Magnetic Field.

The maximum expression you will get on Lorentz Force Law is a looped wire, of a single turn within a magnetic field, then apply a current:

This is it...and yes, you can easily understand that both forces Fup & Fdown, on each side of the loop, will result in a Half Rotation (180º)
Until this single loop reverses, to fall back on the same scenario at start.

So-you think- you fully understand how 'a motor works or rotates'...just by looking at above image...
And yes, you also get on the same 'package' the "Right Hand Rule" as a rudimentary way to know how to apply it (how to set your fingers while sticking two on the direction that your hand muscles allow to stretch) wherever you find this 'situation'...

Only thing I find awkward here, are the relation between B-Field and the Two Forces that must be on a 90º set UP & DOWN?...then ask ourselves, why Forces do not also manifest on the back part of the wire loop?

If they are following the same current flow?

I will answer (according to Lorentz): No, because you MUST use all Three (3) Parameters involved, that is IL & B!!
So, the back wire on the loop is not following the Perpendicular direction of B-Field, but is Parallel to it...so it is 'neglected'...no force.

And here comes our "Right Hand Rule Assistant" as a 'holy savior' that would get us all out of any doubts, right?

As you all have noticed, the Force Formula (F=I.L.B) is identical for a Motor, as for a Single wire inside a magnetic field 'B'...

So, this is it, all we need to know related to a current carrying single wire within a magnetic field...

That is Lorentz Force...

Now, how long it took you to understand this?...10, 20, 30 minutes?

Great!!

Next, let's analyze same 'scenario' but with Maxwell Magnetism.

Ufopolitics

[Ufopolitics]

Hello again,

Unfortunately, the REALITY does not 'Apply' to Lorentz Force...

Or have ANY ONE of you, ever seen a Motor or a Generator, where there is just a Single Loop of wire within its Armature/Rotor for any Motor or a Rotary Field on a Generator having just one single wire?

So, to make it easier, I have made a short video...using my links above to Maxwell Books, basically the Three Main Books He wrote...and searching the word "coil".

This would give you an idea that the work of Maxwell is purely based on a Coil Behavior and Analysis, and Test in many Experiments that He performed.

You could verify it yourself...doing the same thing I did on video above, but, going on detail on every page that mentions the word "coil".

Regards

Ufopolitics