# Accleration of charged particle

1. Oct 19, 2010

### arul_k

I came across an article on the net which stated that in 1881 J.J. Thomson realized that a charged particle was more resistant to accleration than an identical neutral particle.

I would like to know how Thomson came to this conclusion, was it determined by experiment or mathematically, also any further references to this observation are also welcome.

2. Jul 8, 2012

### Simon Bridge

Last edited: Jul 8, 2012
3. Jul 8, 2012

### Staff: Mentor

Looks like a proof by reference to inaccessible literature.
Acceleration by what? What happens to momentum conservation?

Anyway, this thread is from 2010.

4. Jul 8, 2012

### Simon Bridge

Yeah - or at least a hoped inaccessible text.
I was trying to get a handle on arul_k's thought processes so I could better assist in another thread when I saw this one and thought "eh?" and decided to look it up.
Hence the resurrection.

There's an email address on the paper - and contact details - presumably one could just ask Petkov? But this may not be the author of "the article on the net" that arul_k "came across".

I like to encourage people to state their sources when they been reading around. It's OK to ask about statements in dodgy sources ... just say something like: "I think this is a dodgy source but I'm unclear about what this is about..." or something. Examining pseudo and plain junk science can be a good exercise in learning the real science and you never know - it may not be all that dodgy after all. Either way it provides a context for useful answers.

BTW: At first I thought that it was talking about effective mass as in Solid State Physics where charge carriers can be modeled as particles in a vacuum but with a different mass. But Petkovs paper appears to be trying to exploit space-time anisotropy in an accelerating reference frame to get the effect ... he's also got a book - review: Petkov ALMOST gets things right in his treatment of the Sagnac effect when he correctly points out that the local light speed is isotropic, even in accelerated frames. Then, he proceeds with a huge blunder by attributing the terms in $\pm \omega r/c$ to the "acceleration" of the frame, when , in reality, these terms are the contribution of the "closing" part. Petkov misunderstands closing (coordinate) speed for proper speed (in an accelerated frame). Don't waste your money on such crackpottery. :)

But this may not be what OP is thinking of ...

Last edited: Jul 8, 2012
5. Jul 9, 2012

### K^2

The effect is well known. It's the contribution to the mass of a charged particle. As the charged particle accelerates, the electric fields "bunch together", increasing the total energy of the electric field. Therefore, it requires more energy to accelerate a charged particle than a neutral one. The "mass" the particle picks up this way, however, is exactly equal to the total energy of electric field. So you can think of it as being the mass of the field the particle carries with it.

Let me see if I can find an article on this, at least on Wiki, so you can trace the references further.

Edit: Here we go. Electromagnetic Mass (Wikipedia).

And yes, J.J. Thomson is the person who first derived this.

6. Jul 9, 2012

### Staff: Mentor

In this case, the "identical" particle would not be identical, but a particle with lower mass.
Well, that just a question of wording.

7. Jul 9, 2012

### vanhees71

This is a highly non-trivial issue, mostly because you posted it into the classical-physics forum.

Qualitatively the issue is the following: As you can show using Maxwell's equations and apply it to charged point particles (classical electron theory invented and worked out by H. A. Lorentz in the 1910s after the discovery of the electron and the experimental hints of being a charged point particle by J.J. Thomson), such a particle radiates electromagnetic waves, which carry energy and momentum. Since the total energy and momentum are conserved (due to space-time translation invariance in the special-relativistic framework of Minkowski space), the particle must lose this part of irradiated energy and momentum. This means it must be decelerated due to this energy-momentum loss, and this in turn means that there must be a force that it caused by its own electromagnetic field.

As Lorentz very quickly figured out, there's a lot of trouble in working out this thought mathematically. First of all the self-energy and self-momentum of the electron's own em. field diverges. Even for a point particle at rest, the total energy of its own Coulomb field diverges.

Lorentz cured this by assuming a small but finite extension of the electron. He invented a kind of perturbation theory by first calculating the electromagnetic waves from the accelerated motion of the particle as we all have learned it in our E+M theory lecture (retarded potentials, Lienard-Wiechert fields etc.). Then he considered the backreaction force from the radiation to the particle. He found that part of the force could be lumped into the particle mass. This is quite natural from the point of view of special relativity since any form of energy contributes to the inertia of the particle, and thus also its own em. field does so. This contribution is divergent, when putting the extension of the particle to 0 (i.e., in the limit of a point particle), and Lorentz thus was the first to apply "renormalization", i.e., he put the "bare mass" + "electromagnetic mass" together as the finite physical mass of the electron. The residual force is known as Abraham-Lorentz force (since also Abraham had the same thoughts around the same time).

The trouble with the Abraham Lorentz model is however that one has self-accelerating solutions, which have to be excluded by hand by assuming certain boundary conditions on the solution.

A fully complete self-consistent classical equation of motion for charged point particles is still not found. A very good source on these issues is

Fritz Rohrlich, Classical Charged Particles, World Scientific

Of course, in quantum electrodynamics, this problem is solved to a more satisfactory level, because in the perturbative sense QED is renormalizable, and thus one can calculate the self-energy of the electron to any order of perturbation theory by renormalizing the infinities by lumping them into the unobservable bare mass and wave-function normalization and using the physical values of these quantities (dependent on the renormalization scale and running according to renormalization-group equations), while for the classical theory this is not possible.

8. Jul 9, 2012

### K^2

If two particles have different charge, they are already not identical. The closest you'll probably be able to get are pions which are "almost identical" to within an isospin. The charged ones are heavier by a few MeV. If you take cutoff at classical radius and compute the energy of electric field, it comes down to 1.5MeV. The mass difference is a bit higher, but it's the right order of magnitude, so the idea is not entirely stupid.

Same could be said about neutron/proton, but here you immediately run into trouble with neutron being heavier. Of course, the mass of nucleons is primarily due to sea quarks, so it should not be a surprise that such a naive approach fails.

9. Jul 9, 2012

### Simon Bridge

@K^2: Surely the point of the question is to inquire about the effect of charge on acceleration and not wether the particles are literally identical. I think we can cut OP a bit of slack here.

I'm sure you are capable of reformulating the question in terms of classical bodies with the same mass but different charge?

Thank you vanhees71. I suspect that has actually answered OPs question.
Remains only to hear from arul_k.

10. Jul 10, 2012

### K^2

I'm just trying to answer mfd's query. If masses of two classical charged objects are the same, then you will experience the identical resistance trying to accelerate them, since electromagnetic mass is already factored into the total mass. Conversely, if you take two objects that are identical initially and charge one of them, their masses will no longer be identical.

11. Jul 10, 2012

### Simon Bridge

Oh excuse me. I took your statements too generally.