Motion of two oppositely charged particles

Joel Franklin
April 11, 2013

The "opposites" attract force law of electrostatics is arguably the most familiar force, both in the classroom and in our everyday experience. It is somewhat surprising, then, that its complete formulation, in the simplest possible case, leads to an ill-posed physical (and mathematical) problem. We will explore the various layers of this problem, working from low to high energy,  and exploring the motion in its complete formulation, in which both special relativistic dynamics and the retarded time evaluation of the forces must be included.