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First, I have shamelessly plagiarized the title of this chapter. I have stolen the title from that of one of the most famous physics research papers of the twentieth century – Zur Elektrodynamik Bewegter Körper, the paper in which Einstein described the Special Theory of Relativity in 1905. I shall be describing the motion of charged particles in electric and magnetic fields, but, unlike Einstein, I shall (unless I state otherwise – which will happen from time to time) be restricting the considerations of this chapter mostly to nonrelativistic speeds – that is to say speeds such that $$v^2/c^2$$ is much smaller than the level of precision one is interested in or can conveniently measure. Some relativistic aspects of electrodynamics are touched upon briefly in Chapter 15 of the Classical Mechanics notes in this series, but, apart from the fact that this chapter and Einstein's paper both deal with the motions of charged bodies in electric and magnetic fields, there will be little else in common.