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Maxwell's equations VS. Lorentz & Coulomb force equations 
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#1
Mar1210, 08:59 PM

P: 64

I find Maxwell's equations insufficient and superfluous having the Lorentz & Coulomb's force equations. As far as I see magnetic (Lorentz force) and electric (Coulomb's force) interaction is best defined by these two equations themselves, and although Maxwell's equations can describe quite a few electromagnetic interactions, by not having Lorentz force incorporated in any equation nor included as separate one, Maxwell's equations are automatically doomed to fail to describe any interaction due to this very, very important force. Did I miss something?
Why describe electric interaction with any other but with 'Electric force' equation? Why describe magnetic interaction with any other but with 'Magnetic force' equation? *** Electric interaction Step 1: Electric field potential given by Coulomb's law Step 2: Electric force (acceleration vector) given by Coulomb's law *** Magnetic interaction Step 3: Magnetic field potential given by BiotSavart law Step 4: Magnetic force (acceleration vector) given by Lorentz force ==================================================== As far as I see that's all what is necessary to solve any em interaction, no? 1. Gauss's law  This is obviously about Coulomb's law/electric potential, so why would this equation be "more suitable"? 2. Gauss's law for magnetism  divB = 0, what in the world? Instead of to describe magnetic potentials or force, to put here BiotSavart law, or Lorentz force equation or Ampere's force law, they included some equation that has result already calculated in advance? No monopoles? That's as useful as stating "there is no other intelligent life in the Universe". 3. Faraday's law of induction  Is there anything here we can not calculate with the time integral of four steps given above? How is this induction supposed to accurately describe complete interaction if it is oblivious to Lorentz force? 4. Ampère's circuital law  Is there anything here we can not calculate with the time integral of four steps given above? This is the best candidate to be saying something about Lorentz force, if it only included "Ampere's force law" too. I suppose the explanation why these equations are in this form is because that is the most suitable for practical application and experimental setups, but still, my greatest concern is how any of that can accurately work without incorporating Lorentz force and BiotSavart law in the same fashion as Coulomb's law and electric potential/force. 


#2
Mar1210, 09:59 PM

Mentor
P: 17,330

You do need all four of Maxwell's equations and the Lorentz equation. BiotSavart is only an approximation to Maxwell.



#3
Mar1310, 12:00 AM

Sci Advisor
PF Gold
P: 1,777




#4
Mar1310, 01:49 PM

P: 192

Maxwell's equations VS. Lorentz & Coulomb force equations
You can think of maxwells equations as equations of motion for the field, and the lorentz force as EOM for the currents. If you are looking for a single equation, it is the EM lagrangian, which will get you to all the equations of motion for the field and currents.



#5
Mar1310, 01:58 PM

P: 836

The knowledge that radiowaves, infrared, visible light, xrays and gamma rays all are the same phenomenon but with different energies, the prediction of the speed of light and probably the theory of relativity are thanks to Maxwell's equations. 


#6
Mar1310, 02:02 PM

Sci Advisor
P: 1,395

How are you gonna get them accelerated electrons to emit EM radiation using your 4 step program above? Maxwell's equations and the Lorentz equation accurately describe *all* classical physical phenomena involving electricity and magnetism .. any proposed "substitute" would also need to do that, at the very least.



#7
Mar1310, 03:28 PM

P: 64

Electric and magnetic fields do not sustain each other. According to Coulomb's law, Lorentz force and BiotSavart law, electric field is intrinsic property of any single electron (charge), while magnetic fields forms proportionally to velocity, there is no creation of any other fields here, there will always be electric field whose potential magnitude will be independent of everything, and the magnitude potential of the magnetic field of moving charge will vary according to velocity vector. Magnetic field is EFFECT of charge motion, it is not the CAUSE for it, however since all moving electrons can interact with this magnetic field, what it can do is to cause electron displacement, i.e. it can cause electric CURRENT, but that does not mean it can be the CAUSE or CREATE any new electrostatic potential. 


#8
Mar1310, 03:37 PM

P: 64

I really have no idea how Maxwell's equations do it, what are you referring to? 


#9
Mar1310, 06:07 PM

P: 836

Note that it skips a step. Instead of showing the final wave equations using the permeability and permittivity constants the author immediately substitutes them. Compare with this to see that Maxwell's equations, using constants measures from electrostatics and magnetostatics, really does predict the wave nature and speed of electromagnetic waves. Wave equation Note that this was before quantum physics and thus the model was later exanded to account for the particle nature of light. 


#10
Mar1310, 06:24 PM

Mentor
P: 17,330

1) no way to calculate the magnetic field 2) no waves 3) no interaction between magnetic field and electric field 4) infinite speed of a propagating electric field 


#11
Mar1310, 09:00 PM

P: 64

1) no way to calculate the magnetic field Step 3. F= q(E + v x B); E here refers to Coulomb's Law, and B to BiotSavart law, or at least I'll define it like that, so that basically unrolls to these four: *** Electric interaction Step 1: electric field potential given by Coulomb's law Step 2: Electric force (acceleration vector) given by Coulomb's law *** Magnetic interaction Step 3: Magnetic field potential given by BiotSavart law Step 4: Magnetic force (acceleration vector) given by Lorentz force ====================================================  How Maxwell's equations calculate magnetic field? 2) no waves  I'll make them just like they did. What do you think E and B stand for in Maxwell's equations? 3) no interaction between magnetic field and electric field  Magnetic and electric fields DO NOT interact. 4) infinite speed of a propagating electric field  What is propagation speed of E and B fields in Maxwell's equations? What is the expression for E and B? 


#12
Mar1310, 09:06 PM

P: 64

 "To obtain the electromagnetic wave equation in a vacuum using the modern method, we begin with the modern 'Heaviside' form of Maxwell's equations. In a vacuum and charge free space, these equations are: Taking the curl of the curl equations gives:  What in the world curl of E and B fields, and even the curlofthecurl, is supposed to have with the speed of light? What are they trying to do here, how did anyone ever figure out they should combine curls to get any information about any speed?  How can we talk about any velocity if we are not calculating FORCES, how can field potentials and their shape tell us anything about any velocity without calculating the FORCE and ACCELERATION first? I need to understand what and WHY they did so I can do the same thing with "my" equations. Is this it, the beginning of it? As a time integral my equations are already in similar form like this, can you help me make a 'wave equation' out of it? 


#13
Mar1310, 09:47 PM

Sci Advisor
P: 2,850

How would you explain all of EM radiation if you assert that electric fields and magnetic fields don't interact? I would like to know this. 


#14
Mar1310, 10:45 PM

Sci Advisor
PF Gold
P: 1,777

Again, you are using static equations for timevarying situations. This will not work. 


#15
Mar1310, 11:18 PM

Mentor
P: 17,330




#16
Mar1410, 04:32 AM

P: 64

Please show me that equation where I can see how E and B interact.  Can E and B interact, do we add magnetic and electric vectors, do we superimpose them, or do electric only interact with electric and magnetic with magnetic fields? This the whole point behind my arguments, thanks for that. 1.) Maxwell's equation are about em field potentials  Coulomb's law and BiotSavart law, but approximated in relation to currents and charge densities. 2.) Lorentz force equation is about em fields and forces  Coulomb's law, BiotSavart law, Coulomb and Lorentz force, but in relation to point charges, no approximations. These two deal with the same E and B fields, all the same constants are there, all the relations, divergence, curl, flux or whatever is there. There is nothing in 1. that is not in 2, but there are things in 2. that are not in 1. Were approximations for charge densities and current potentials in Maxwell's equations derived from the point particle equations or was it the other way around? 


#17
Mar1410, 05:59 AM

Sci Advisor
PF Gold
P: 1,777

1. What are the total fields produced by an electron that is moving in a circle of constant radius R and at some constant speed v? We will let v vary as we see fit. This can easily be done by assuming a constant B field applied normally to the plane of oscillation. 2. What are the total fields at some point (X, 0, 0) as a function of time produced by an electron located at the origin that starts at rest from t=\infty to t = 0 and starts oscillating along the zaxis. The oscillations can be modeled as a harmonic oscillator of magnitude A and angular frequency \omega. 


#18
Mar1410, 06:27 AM

P: 836

B: Mag. Gauss and Ampere 


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