If An Instantaneous Force Causes A Charged Particle To Briefly Accelerate, Does Self-inductance Decelerate It?

Question

Consider the following example:

A charged particle initially at rest briefly accelerates in the forward direction due to an initial force. At this point the particle is carried forward only by inertia, creating a constant velocity, and a constant magnetic field. The brief change in the magnetic field will cause a brief change in the electric field, which I think by Lenz’ law will be in the opposite direction of the particle’s velocity, slowing the particle down.

I am skeptical about this, and I do not seem to understand Maxwell’s Equations as well as I thought, so although I have qualitative reasoning, I do not have the mathematics necessary to come to a definite result.

Could someone enlighten me?

Mathematics Preferred. Please stay in Vector Calculus or lower. For all major steps, specify which equations you are using. No PDEs or PDE solving.

Answer 1

From Wikipedia

Lenz's law states that: The current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux and to exert a mechanical force which opposes the motion

The key point you're missing here is that the change in magnetic field here is not accompanied by an apparent change in magnetic flux. If said charged particle were to be accelerated inside a conductive loop, then the change in magnetic field would result in a change in magnetic flux through the loop that would in turn result in an opposing electromotive force through the wire.

So if I understand correctly, and the particle is accelerated in free space, Lenz's law does not apply here

Answer 2

The brief change in the magnetic field will cause a brief change in the electric field, which I think by Lenz’ law will be in the opposite direction of the particle’s velocity, slowing the particle down.

If the particle's charge is distributed in space in non-zero volume, then yes, this is effect of the induced electric field of the accelerated charge acting back on itself, and since it is proportional to particle's acceleration in magnitude, and opposite to it in direction, its effect is an increase of the effective inertial mass of the particle. In other words, this is how the positive electromagnetic mass of charged system of particles comes about.

If the charged particle is a point, then self-action and electromagnetic mass is very problematic concept, because it leads to inconsistencies (runaways, pre-accelerations due to the Lorentz-Abraham-Dirac self-force, or energy inconsistencies of the Landau-Lifshitz force).

Answer 3

The case of an accelerated charge gives rise to a disturbance in the field around that charge; that disturbance generates photons, called 'synchrotron radiation' because it is a major energy loss only for those electronic devices...

The momentum of emitted photons ought by symmetry to have a bias in the acceleration direction, which means that emission acts like a retarding force (an addition to the accelerating impulse) on the charge. I'm not certain about 'self inductance' as a label for this retarding force, because it is wrong to characterize an electron ( or any elementary particle) as acting on itself.