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.


*

*A charge can feel external fields.

*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?
 A: 
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.
A: 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.
