By Arnold Sommerfeld, Edward G. Ramberg
Within the 3rd of a six-volume sequence, Sommerfeld offers a distillation of his lecture notes on electrodynamics.
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Extra info for Electrodynamics. Lectures on Theoretical Physics, Vol. 3
1 In this system the pole strength p has, according to (12), the same unsatisfactory dimension as the charge e in the electrical system (8a). Unity pole strength would correspond to a repulsion with a force of 1 dyne of two poles of equal sign and magnitude separated by 1 cm (in air as surrounding medium). C. Rational and Conventional Units We must now deal with the factor 4π in Coulomb's law. It is true that this is much less fundamental than the question of dimensions and bears to the latter only a historical relationship Historically the forms (8) and (12) of Coulomb's law result from an effort to approach as closely as pos sible the customary form of Newton's law.
6) By this definition the energy is localized in the field; a definite electric and magnetic energy content We dr and Wm dr is ascribed to every element of volume dr. This constitutes a first step in the adaptation of the energy concept to the ideas of field theory. The factor 1/2 in the two defining equation (6) evidently points to a con tinuous generation of energy, comparable with the stretching of a spring. In accord with the pattern force X increase in path length = intensity entity X change in quantity entity, we obtain We = f E-dD, which, for a linear relationship between E and D, reverts, in fact, to (6).
6) is evidently a supplementation of Maxwell's theory derived from experiment, which establishes a relationship between the two material constants ε0, μο of vacuum. In the following section we will discuss how the constants are to be determined individually. We now turn to the integration of Eq. (4) specialized for vacuum 4 § = ΔΕ C2 dt2 (8) with the auxiliary condition already made use of div E = 0. (8a) We seek, in particular, solutions of (8) which are independent of y and z. For purely periodic time dependence these represent monochromatic plane waves which advance along the x-axis.