Is this formula for interaction of 2 electrons OK?

[Lazarus]

Question: Is this a satisfactory formula for the electrical interaction of 2 electrons at speeds << c?

 

K cos(X) Vv/r^2 – Q^2/r^2

 

Where V is the velocity of the causing electron

v is the velocity of the effected electron

r is the distance between them

Q is the charge of the electrons

X is the angle between the direction of v and the

plane of the direction of the cause electron and

the position of the effect electron. (The alignment with the flux)

K is the constant to make the units come out right.

I will answer it myself.

 

NO.

 

It at least needs another cosine for the lag behind a perpendecular to a V vector.

[timo]

You might want to put a little more effort into explaining what you are talking about and what the reasoning behind your conclusion is (but please start with the first part, reading reasoning without knowing the context is pointless). Labelling all terms appearing in an expression is a good thing. But while it could be considered necessary it is certainly not sufficient.

[swansont]

It doesn't look to be Lorentz invariant (two frames where the interaction is zero), so even without context it looks to be unsatisfactory.

[timo]

I would expect that it is normal for non-relativistic equations to not be Lorentz invariant (interpreting v<<c as "non-relativistic", here). In fact, you don't even know what the term is supposed to represent in the first place. It might be a force with non-force dimensions. But that's just a semi-random guess. I considered quite a lot of possible criticism on the OP. But in the end it boiled down to "it's not even criticizable".

Edited June 17, 2014 by timo

[Lazarus]

Please excuse my pathetic attempt to find the interaction of 2 electrons. I have to do calculations a half a dozen time to get the same result twice. That certainly lowers the probability that it is correct.

 

It's just that since we can describe the gravitational interaction of 2 planets it seems that we should be able to describe the interaction of 2 electrons.

[ajb]

I guess we could take the force on each charged particle to be the Lorentz force and take each charged particle to be the source of the fields. You maybe able to take some Galilean limit c-> infinity and make sense of that, I don't know. I have not looked at this in any detail.

[swansont]

I would expect that it is normal for non-relativistic equations to not be Lorentz invariant (interpreting v<<c as "non-relativistic", here). In fact, you don't even know what the term is supposed to represent in the first place. It might be a force with non-force dimensions. But that's just a semi-random guess. I considered quite a lot of possible criticism on the OP. But in the end it boiled down to "it's not even criticizable".

 

 

My objection is that in the rest frame of either particle (v=0 or V=0) there is no interaction, but in any other frame there would be. That seems unphysical.

[Lazarus]

Swansont said:

My objection is that in the rest frame of either particle (v=0 or V=0) there is no interaction, but in any other frame there would be. That seems unphysical.

 

To paraphrase Swansont:

My objection is that in the rest frame of either PLANET (v=0 or V=0) there is no interaction, but in any other frame there would be. That seems unphysical.

[Strange]

Huh? Planets aren't electrons and aren't even charged...

[timo]

Swansont said:

My objection is that in the rest frame of either particle (v=0 or V=0) there is no interaction, but in any other frame there would be. That seems unphysical.

 

To paraphrase Swansont:

My objection is that in the rest frame of either PLANET (v=0 or V=0) there is no interaction, but in any other frame there would be. That seems unphysical.

I still recommend focussing on trying to make sense rather than focussing on maxing out cynism. Not expecting this to happen, judging from what I have seen in this thread so far, I am out of this.

Huh? Planets aren't electrons and aren't even charged...

It is not uncommon to consider mass as the charge in newtonian gravity.

[Mordred]

Judging from what I've read so far and I could be off on this he is looking for the dipole to dipole interactions of 2 charged particles. Might help if the OP can clarify which interaction specifically he is trying to define.

 

probably not the best article but it has some of the basics

http://chemwiki.ucdavis.edu/Physical_Chemistry/Quantum_Mechanics/Atomic_Theory/Intermolecular_Forces/Dipole-Dipole_Interactions

 

problem is I'm not sure if he is looking for it in the more classical mathematics vs the QED metrics. His reference to Coulombs law makes me think he is looking for the former

Edited June 18, 2014 by Mordred

[Lazarus]

I don't think any of the comments are meant to be obnoxious. Only trying to make their point strongly.

 

The vector equation:

 

F = q(E + v x B)

 

describes the effect of one electron on another but how to determine B seems to be a problem.

[Mordred]

evidently my guess is off lol

Edited June 18, 2014 by Mordred

[swansont]

Swansont said:

My objection is that in the rest frame of either particle (v=0 or V=0) there is no interaction, but in any other frame there would be. That seems unphysical.

 

To paraphrase Swansont:

My objection is that in the rest frame of either PLANET (v=0 or V=0) there is no interaction, but in any other frame there would be. That seems unphysical.

 

 

Planet? How did we get there from your mention of an electrical equation? What equation that would apply to planets are you thinking of?

I don't think any of the comments are meant to be obnoxious. Only trying to make their point strongly.

 

The vector equation:

 

F = q(E + v x B)

 

describes the effect of one electron on another but how to determine B seems to be a problem.

 

Problem for whom, and how is your equation related to this? And what happened to the planets?

[Lazarus]

Swansont said:

Problem for whom, and how is your equation related to this? And what happened to the planets?

 

 

A problem for me, at least. I would like to know what the value of the magnetic field from one of the electrons would be perpendicular to its velocity and also, how to calculate the field as the other electron is a distance from the perpendicular.

The skew is accounted for in the equation so B is the needed value.

 

Two electrons traveling at different velocities resulting in them being in different frames making it impossible to calculate their interactions implies that the interaction of 2 planets can not be calculated.

[Mordred]

I don't think any of the comments are meant to be obnoxious. Only trying to make their point strongly.

 

The vector equation:

 

F = q(E + v x B)

 

describes the effect of one electron on another but how to determine B seems to be a problem.

 

Alright you have the Lorentz force equation here, now you want to calculate B the equation for B is on page 10 magnetic dipole, However there is different equations for B depending on the various factors in this article. So your going to have to define your problem with a lot more clarity

 

http://www.ece.msstate.edu/~donohoe/ece3313notes8.pdf

 

I still have no idea what the relation is to planets considering the motion of planets has nothing to do with electromagnetism.

Edited June 19, 2014 by Mordred

[swansont]

It's usually best to do it in the rest frame of one of the particles. It's magnetic field is trivial, since the magnetic moment is almost exactly one Bohr magneton.

 

 

Two electrons traveling at different velocities resulting in them being in different frames making it impossible to calculate their interactions implies that the interaction of 2 planets can not be calculated.

 

Newtonian gravity is not speed dependent.

[Lazarus]

Swansont said:

Newtonian gravity is not speed dependent.

 

 

I see what you are saying. The difference is that the motion of one electron affects the other one, whereas with planets the only consideration is position of the planets.

 

------------------

 

Swansont said:

It's usually best to do it in the rest frame of one of the particles. It's magnetic field is trivial, since the magnetic moment is almost exactly one Bohr magneton.

 

The magneton is a good clue. If i can relate that to the magnetiic field, B, that gives the answer for the case where the effect electron is on a line from the other electron that is perpendicular to it's velocity vector. Then the problem is to determine the rate that the mangetic field drops away from the perpendicular.

[swansont]

 

The magneton is a good clue. If i can relate that to the magnetiic field, B, that gives the answer for the case where the effect electron is on a line from the other electron that is perpendicular to it's velocity vector. Then the problem is to determine the rate that the mangetic field drops away from the perpendicular.

 

It's a dipole. I believe Mordred gave a link to the equation.

[Lazarus]

Dr Benjamin Crowell pointed out another difficulty in formulating a relationship for the interaction of two electrons. The magnetic field is shaped something like the bow wave of a ship because of the time it takes for the information to travel from one to another.

 

The velocity of the information from a particle is assumed to be the speed of light for electrostatic, electromagnetic and gravitational fields. Those velocities should be independent from the speed of radiation.

 

Astronomers have to use the current position of masses rather than their position when light would have left to get correct answers. Is there experimental verification of any of the 3 velocities of information?

[swansont]

Dr Benjamin Crowell pointed out another difficulty in formulating a relationship for the interaction of two electrons. The magnetic field is shaped something like the bow wave of a ship because of the time it takes for the information to travel from one to another.

 

Yes, several have written books about the details of such a calculation. The standard is JD Jackson's book on Electrodynamics.

 

It would be helpful if you'd stick to one topic instead of jumping around like this. The magnetic field of an electron is a fairly easy calculation. The interaction between two electrons where there is relative motion is a more difficult problem.

 

Still nothing to do with planets, though, nor does it give the equation in the OP any validity.