ABSTRACT
This chapter discusses the motion in a vacuum of a point charge under the influence of an electromagnetic field. The inclusion of the "self-force" presents quite fundamental difficulties because of the infinities associated with the concept of a point charge. Consider first a charged particle moving in a purely magnetostatic field. The field is non-uniform, but its space variation is assumed so slight that a picture of the particle proceeding along the field lines and at the same time encircling them at the local gyro-frequency is in some sense a valid approximation. The requisite restriction on the variation of the magnetic field is that throughout the duration of a local gyro period the field at the particle shall not have changed appreciably; that is to say, the change of direction of the field, in radians, and the ratio of the change of magnitude to the magnitude, both remain small.
