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1.5. The Laws of Motion.

We may summarize the laws of motion for uncharged and charged particles as follows.

Newton’s 1st law essentially provides a recipe for determining whether we are viewing things from an inertial or a non-inertial frame of reference. As such it is universally valid.

Newton’s 2nd law, in the case of uncharged particles (neutrons, atoms, etc.) is the familiar

. (1.5_1)

If a particle is charged, and in particular if such charge is modeled as a spherical shell, then we must add a da/dt term to Eq. 1.5_1:

. (1.5_2)

And, if the particle is a combination of linked mechanical and electromagnetic mass, then we would write

. (1.5_3)

Newton’s 3rd law is generally the same for neutral (uncharged) and charged particles. In both cases the a-induced and any da/dt-induced reaction forces are equal and oppositely directed to F when a distribution’s shape is held constant. In the case of charged particles, both the inertial and radiation reaction forces can be said to be electric forces that the charge experiences in its own electric field. And to the extent every uncharged particle is composed of constituent charged particles, Newton’s equal and oppositely directed inertial reaction force is ultimately always an electric force. In effect "inertia" … something of a mystery in Newton’s day … is seen to be implicit in Maxwell’s equations and the Lorentz force law.

But note that while qE might explain the reaction forces, it is upon the driving agent that these forces always act. To reiterate, the charge can be thought of as the "mechanical hook" whereby the driving agent latches onto and interacts with the electromagnetic field, the two exchanging momentum and energy in the process.