p09fl40 - Lecture 40: Electrodynamics II (7 Dec 09) A....

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Unformatted text preview: Lecture 40: Electrodynamics II (7 Dec 09) A. Review Electrodynamics 1. Recall: 4-vector transforms as A * = X a A and that x = ( ct, r ) is a 4-vector. 2. Lorentz invariance of scalar products of two 4-vectors: ( A ,B ) g A B ; g =- 1 ,g 1 = g 2 = g 3 = 1 3. gradient as a 4-vector: 2 = g x and ( 2 , 2 ) is the wave equation operator. 4. 4-velocity using proper time dt = d : u = ( u , u ); u = d r d = ( v ) v ; u = cdt d = ( v ) c and then to the energy-momentum 4-vector p = ( E/c,m u ) 5. 4-vectors in electrodynamics: current density j = ( c, ~ j ) and vector potential A = ( /c, ~ A ), with ( 2 ,j ) = 0 (equation of continuity) and ( 2 ,A ) = 0 (Lorentz gauge) and the Maxwell source equations 2 2 A =- j . 6. Dynamics using the Lorentz force: d~ p dt = q ( ~ E + ~v ~ B ); dE dt = q~v ~ E dp d = F with a 4-vector force F = q X g u ( 2 A - 2...
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This note was uploaded on 12/14/2009 for the course PHYS 711 taught by Professor Bruch during the Fall '09 term at Wisconsin.

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p09fl40 - Lecture 40: Electrodynamics II (7 Dec 09) A....

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