Classical electromagnetism (or classical electrodynamics) is a branch of theoretical physics that studies consequences of the electromagnetic forces between electric charges and currents. It provides an excellent description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible (see quantum electrodynamics). Fundamental physical aspects of classical electrodynamics are presented e.g. by Feynman, Leighton and Sands,[1] Panofsky and Phillips,[2] and Jackson.[3]
The theory of electromagnetism was developed over the course of the 19th century, most prominently by James Clerk Maxwell. For a detailed historical account, consult Pauli,[4] Whittaker,[5] and Pais.[6]
See also: History of optics, History of electromagnetism, Magnetism, Electromagnetism, and Maxwell's equationsRibarič and Šušteršič[7] considered a dozen open questions in the current understanding of classical electrodynamics; to this end they studied and cited about 240 references from 1903 to 1989. The outstanding problem with classical electrodynamics, as stated by Jackson[3], is that we are able to obtain and study relevant solutions of its basic equations only in two limiting cases: »... one in which the sources of charges and currents are specified and the resulting electromagnetic fields are calculated, and the other in which external electromagnetic fields are specified and the motion of charged particles or currents is calculated... Occasionally, ..., the two problems are combined. But the treatment is a stepwise one -- first the motion of the charged particle in the external field is determined, neglecting the emission of radiation; then the radiation is calculated from the trajectory as a given source distribution. It is evident that this manner of handling problems in electrodynamics can be of only approximative validity.« As a consequence, we do not yet have physical understanding of those electromechanical systems where we cannot neglect the mutual interaction between electric charges and currents, and the electromagnetic field emitted by them. Despite of a century long effort, there is as yet no generally accepted classical equation of motion for charged particles, as well as no pertinent experimental data, cf.[8]
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