# Does a point charge exert force on itself?

Can a point charge feel the force of its own electric field?

In various texts it is always mentioned about the force on a point charge in an external electric field. I think the particle does feel its own field, because it's not that the field of other charges are painted in visible color and that of its own are ultraviolet that it can't see itself.

Consider the two statements, both for electrostatic conditions.

1. A charge can feel external fields.
2. A charge can feel any electric field (contribution of external plus self)

Both the above statements are consistent if we consider force on a charge in electrostatic field. Statement #1 is what is found in texts . Statement #2 is also consistent in the sense that when there is no electric field its own field (which is also the total field) are symmetrical radially out and hence no net force on the point charge. Also when there is another charge in the vicinity, then the net field no longer remains symmetrical and hence the point charge experiences force.

Which of the statements above is more correct if we take other physical quantities and phenomena into account, not only the force experienced?

• All charged particles have an electric field. Saying they can feel external fields and the asymmetric portion of their own field is (because the superposition principle lets the particle's field always be symmetric) fundamentally exactly the same as saying they only feel external fields. Nothing changes; there's not really any point in making a distinction. – Jim Jul 9 '15 at 16:14

Can a point charge feel the force of its own electric field?

Mathematically, that is impossible. Electric field of point particle is defined everywhere except the point where the particle is. It is not clear what magnitude and direction should the action take at this point.

People have tried and failed to introduce such self-force for charged point particle - search Lorentz-Abraham force. It leads to pathological equation of motion with unphysical solutions. Best not to introduce self-force at all. It is not really needed for any experiment and it only brings problems.

• That people failed in the past doesn't mean that they were wrong to try, the problems have been solved recently. – Count Iblis Jul 9 '15 at 19:09
• @CountIblis, I think they were right to try under the assumptions they made (that self-force is needed to explain observation of radiation damping), but they were wrong in the assumption. – Ján Lalinský Jul 9 '15 at 21:09
• @CountIblis, the paper you reference is valuable, but it did not "solve the problems". They derive, perhaps more rigorously, approximate equations of motion for extended bodies, not point particles, and make interesting but unphysical limit where size, mass and charge go to zero. Electrons, ubiquitous case where equations of motion for point particle would be applied, have non-zero charge and mass. – Ján Lalinský Jul 9 '15 at 21:14

Statement 2 is the correct statement. For a charge to only feel the fields generated by other charges would require the field to carry additional information about its origin, there is obviously no evidence that this is the case.

It's not true that both positions are operationally identical, so you actually cannot always pretend that charges only feel the effect of other charges without that leading to errors. Only when charges are moving at uniform velocities relative to each other, will the self-force cancel. When you consider accelerating charges, the self-force will no longer cancel out. This effect leads to electromagnetic radiation being emitted, the self-force can be interpreted as the backreaction of the emitted electromagnetic radiation.

Now, because treating the self-force is obviously a mathematically difficult issue due to the singular behavior of the fields of point charges, this has traditionally been done in an ad hoc way for treating the emission of electromagnetic radiation. Only recently has this problem been treated in a rigorous way, see here.

• It's worth keeping in mind that the Wald/Gralla paper linked here is derived within the mathematical framework of general relativity. In this context, the electric field of a particle causes curvature in the surrounding spacetime, which contributes to the force acting on the particle. I'm not sure if there are similar results for classical electromagnetism in a flat spacetime, but I'd be curious to see how they work. – user35736 Jul 9 '15 at 16:32
• "For a charge to only feel the fields generated by other charges would require the field to carry additional information about its origin" that is not necessary. EM field is a mathematical construct based on experience with EM action of one body on another. When Lorentz formula is used for point particles in EM field, the E,B in the formula belong to external field only. This was never falsified. No self-action of electron on itself was ever directly measured, nor found necessary to explain its motion. – Ján Lalinský Jul 9 '15 at 18:41
• @user35736 The paper uses the formalism of GR for technical reasons, it's not that gravitational effects are relevant here. – Count Iblis Jul 9 '15 at 19:04
• @JánLalinský It is falsified when considering accelerating charges. A charge that is accelerated in an external field will emit radiation, this radiation has a net momentum, the charge thus accelerates at a different acceleration than what you get when inserting the external electric field in the Lorentz force formula. – Count Iblis Jul 9 '15 at 19:07
• @Count Iblis, there is no conclusive evidence that radiation of single isolated particle carries away momentum from the particle. Experiments done in particle accelerators involve billions of mutually interacting charged particles in so-called bunches. For such bunches, the self-force is evident from the experiments, but it is explicable as a result of mutual interparticle forces; no self-force is needed for point particles. – Ján Lalinský Jul 9 '15 at 20:08