Lecture 22 Lecture Notes

Lecture 22 Lecture Notes - Jackson 2nd Ed. ch. 9.1-9.2...

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7.3.2 Causality Structure of Electrodynamics and depend only on source in back light cone 7.3 Application to Electrodynamics 7.3.1 Formal solution Solutions: Lorentz Gauge Note: If gauge condition is fulfilled initially, it is also fulfilled at later times. Lec 22 - 4. Mar March 04 09 9:54 PM Lecture Notes Page 1
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Signal: non-analytic change in at point y at time at position can be influenced only at time later! More precisely: are affected at precisely time later. signal velocity ( Front velocity ) is always exactly ! three velocities: in practise: signal travelling with front velocity c is weak! ==> hard to utilize effect =>strong signal travels typically with slower velocity, e.g. group velocity see books by: R. U. Sexl, H.K. Urbantke, Relativity, Groups, Particles: special relativity and relativistic symmetry in field and particle physics - L. Brillouin, Wave propagation and group velocity - other expression of same truth So we expect in all structures 7. 4 Reduction mechanism: oscillating sources and
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Unformatted text preview: Jackson 2nd Ed. ch. 9.1-9.2 Griffith 11.1, especially 11.1.4 multi-pole expansion 7.4.1 Reduction to oscillating time dependency So far we have: Lecture Notes Page 2 Decompose sources in oscillatory terms via Fourier Transform similarly: The fields can be decomposed as so that we find the relations for the Fourier components: outside of source area Remarks: 1) general solution can be found by considering each contributing frequency component separately! Lecture Notes Page 3 => from now on we concentrate on a single frequency component Though note: here positive and negative frequency components are treated separately: physical oscillation with has in general two contributing Fourier frequencies 2) outside of the source area fields can be found from vector potential alone: => as we are mainly interested in solution outside source area, we can concentrate on the vector potential alone, ignoring the scalar potential. Lecture Notes Page 4...
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This note was uploaded on 07/28/2009 for the course PHYS 441B taught by Professor Norbertlutkenhaus during the Winter '09 term at Waterloo.

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Lecture 22 Lecture Notes - Jackson 2nd Ed. ch. 9.1-9.2...

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