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Unformatted text preview: Here, B is the flux of the B field through the loop. The LHS is evaluated as A E d S = [ E y ( x + dx )- E y ( x )] dy = E y x dx dy . The RHS is- d B dt =- B z t dx dy , so that E y x =- B z t . (8) By differentiating Eqs. (7) and (8) and eliminating mixed second derivative terms, one can obtain wave equations. With the identification c 2 := 1 / ( ) these equations lead to 2 E y t 2- c 2 2 E y x 2 = 0 and 2 B z t 2- c 2 2 B z x 2 = 0 . We find two wave equations for the E y and B z fields, each propagating with the speed c . When calculating its magnitude from the experimentally measured values of and , we find c to experimentally equal the speed of light in vacuum. Notice that both the permit- tivity and the permeability are known from static experiments, not experiments involving dynamics or radiation! Maxwell inferred from the equality of the speed of electromagnetic waves to the speed of light that light is a form of an electromagnetic wave. By doing so Maxwell unified the field of electromagnetism (in itself a unification of the former sciences of electricity and of magnetism) with the hitherto independent field of optics. The paradigm of unification is currently very popular in theoretical physics, with attempts to unify the four fundamental interactions of nature, e.g., research into superstring theory. The first to unify disparate magesteria was perhaps Isaac Newton, who unified terrestrial physics with celestial physics. The magnitudes of the E , B fields : Consider an infinite planar current sheet, carrying current density j =- j y . A current sheet is a two dimensional surface carrying current, and can be approximated by a large number of wires, all carrying current in the same direction, so that the total current per unit length (perpendicularly to the wires) is j = i/ , where i is the total current included in the length . Current sheets are a very useful model in....
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- Spring '09