By Francis E. Low
The writer makes use of a special procedure which emphasizes the sector theoretic elements of gravitation and the robust analogies among gravitation and the opposite components which are studied in physics. The theory-centered textual content starts with the easiest experimental evidence then proceeds to the corresponding differential equations, theoretical constructs reminiscent of strength, momentum and tension and several other functions. End-of-chapter difficulties supply scholars with a chance to check their realizing, function an creation to and a evaluation of fabric now not integrated within the e-book and will be used to enhance examples, extensions and generalizations of the cloth offered.
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Extra info for Classical Field Theory: Electromagnetism and Gravitation
The outer conductor h carries a charge Q and is electrically connected to the inner conductor. (a) Calculate the chargc S Q induced o n the inner conductor if the force law is derivcd from a potential where L >> b. Note that this form of potential would result from n theory with massive photons. 38 Electrostatics (b) Same as (a) but with (c) with ( E ( << 1. Same as (a) and (b) but with with (€1 << 1 and -1 < p < 1. 8. Two conducting plates make an angle of 90" with each other. ' = yo > 0, z = 0.
10) where Eo is the field produced by the macroscopic charge density p and E,, the field produced by the polarization charge density p,, = -V . P. The electrostatic energy change produced by introducing the dielectric medium is 'I AW = - dr(E D - Ec) 87T = 87T L(r[(E + E,,) . 12) where P is the polarization density. 12) vanishes after an integration by parts, since V . 13) which is a linear functional of the microscopic polarization and bilinear only in the applied field. 13) also holds in the presence of conductors, although the proof is more complicated.
17) and hold microscopically, that is, at the atomic level. 2) where we use lowercase letters to denote microscopic fields. The symbol e and p,,, will fluctuate over atomic scale distances. We eliminate these fluctuations by considering average fields and charge densities, where we average over a region containing many atoms. We then try t o obtain equations for the averaged fields. A subtle issue arises here: Can a description of the interaction of fields and matter that docs not make use of quantum mechanics be correct?