# I How can a point charge exert force on itself?

1. Apr 5, 2016

### maline

An accelerated charge emits radiation and so must lose energy. This implies that it feels a "reaction force" in the direction opposite the motion. Since EM interactions conserve energy/momentum, it must be possible to describe the reaction force in terms of EM fields acting on the charge. These fields must be generated by the charge itself- we may assume that any external fields are uniform.
Now, we know that the fields at any point can be found by integrating a function of the charges & currents along the past (or future) light-cone of that point- the "retarded time" integral. But our particles world-line is of course timelike, so it never intersects the light-cone of any point on the path!
So how can the particle produce a force on itself?

2. Apr 5, 2016

Staff Emeritus
It doesn't.

3. Apr 6, 2016

### maline

Care to actually answer the question?

4. Apr 6, 2016

### BvU

Question has been answered. What you want to hear is where your reasoning fails, right ?

5. Apr 6, 2016

### maline

Yes, obviously. Pardon me for being annoyed, but no response at all is clearly better that a response that clearly won't help me.

6. Apr 6, 2016

### BvU

Well, perhaps V50 will help us out. I've grown accustomed to the idea that there's no point in wanting to know about the self-energy of a point charge (renormalization and all that), but maybe there's a better story to be told !
At least your slight sarcasm demonstrates you care !

7. Apr 6, 2016

### maline

Just to clarify, I am asking about the classical version of the problem. I know there is an ODE for the reaction force in terms of the derivative of the acceleration, but it seems that consistency requires a formulation in terms of the self-field, hence my question: it seems the self-field at the particle's position cannot depend on the history, (and certainly not the third derivative of the position), because the world-line does not intersect the past light-cone.

8. Apr 6, 2016

### vanhees71

This is a very tough issue, which is not completely solved and in my opinion hardly ever completely solvable, because classical point particles are ill-defined in relativistic field theories. My favorite paper on the topic at the moment is

http://arxiv.org/abs/physics/0508031

9. Apr 12, 2016

### tech99

Sorry, I am just an amateur scientist, so probably wrong, but my simple perception was that the charge has lines of electric force radiating out in all directions, and all pulling outwards so that the total force is zero. If the charge is suddenly accelerated, the lines are distorted. This is because the new information propagates outward at a finite speed of c. The distortion of the lines is such that they are now pulling back, against the acceleration. Like a ball hitting a net. So we end up doing work against the attraction of the field lines and this energy is lost as radiation. Maybe someone can correct my picture in a simple way?

10. Apr 12, 2016

### phyzguy

I recommend reading The Feynman Lectures on Physics, Vol 2, Chapter 28 for an excellent summary of the classical attempts to deal with these questions.

11. Apr 12, 2016

### maline

As you said, the lines are radiating out at speed c. So the particle can't possibly catch up with them!
If the particle has a finite radius, then one side can be slowed down by the field of the other side. The question is what happens when or if we let the radius go to zero...

12. Apr 12, 2016

### tech99

Under static conditions, my picture was that the electric field lines just extend out like radial strings and are not moving outward. When acceleration occurs, some of the strings are bent, so that they are at an angle to the charge and no longer apply a balanced pull on the charge. Maxwell's vision of the lines of force was of elastic strings under tension.

13. Apr 12, 2016

### maline

Of course, electric fields never actually move. They are just vector-valued functions of position & time, that describe the force on a test particle. "Lines of force" is just a descriptive way of saying "curves that are tangent to the field at each point". But as you mentioned, the influence of charges & currents on the field propagates at speed c. Technically this is true even in the the static case: the field around a charge is kq1q2/R2 "because" the charge was in its position R/c seconds ago, not because it's there now.
As for "elastic strings under tension", I don't see at all what might have been intended by that, so I can't tell you definitively that it's wrong. What I can tell you is that it bears no reseblence to the way fields are normally spoken about & understood, and if you want to study EM you will probably need to drop that idea.

14. Apr 12, 2016

### David Lewis

I don't think the point charge can exert force on itself, and I don't see how it could interact with empty space*, so the only thing left is radiation being emitted by other point charges. If we have a retarded wave (arrives after it leaves the source) then there should also be an advanced wave coming from somewhere else (arriving before it leaves the source).

*There would have to be at least one other electron in the universe to absorb the radiation.

15. Apr 13, 2016

### tech99

I have shown a demonstration of a mechanical analogue of radiation. The Slinky represents a conductor, and I have sent a longitudinal wave of compression along it. The string which is hanging represents a static field line from an electron. As the wave on the wire passes, it accelerates the electron, and a transverse ripple is sent out on the static field line, representing radiation. Although this energy leaves the wire at the speed of propagation on the string, the electron still feels a force opposing its acceleration, against which the generator must do work.
https://www.flickr.com/photos/58337586@N08/26137254760/in/dateposted-public/

16. Apr 14, 2016

### marcusl

Just because you constructed a mechanical model of EM fields doesn't make it correct. Field lines are not strings.

17. Apr 16, 2016

### tech99

It is meant to portray classical physics, such as the views of J J Thompson (who suggested acceleration of a charge as a mechanism of radiation) and Joseph Larmor. The formula which Larmor produced for radiation seems still correct today.

18. Apr 17, 2016

### marcusl

I don't follow. To my knowledge, neither Thomson (no 'p') nor Larmor proposed an elastic string model of EM fields.

19. Apr 19, 2016

### David Lewis

In this thread, the model only needs to be realistic enough to answer the OP's question.

20. Apr 24, 2016

### tech99

The basis of my model is the book "Electromagnetic Vibrations, Waves and Radiation", by Bekefi and Barrett of MIT. Lines of force must be elastic because if two opposite charges move apart the string does not break.