02/16/2015 PHY 712 Spring 2015 -- Lecture 14 1 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 14: Start reading Chapter 6 1.Maxwell’s full equations; effects of time varying fields and sources 2.Gauge choices and transformations 3.Green’s function for vector and scalar potentials
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02/16/2015PHY 712 Spring 2015 -- Lecture 141 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 14: Start reading Chapter 6 1.Maxwell’s full.
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PHY 712 Spring 2015 -- Lecture 14 102/16/2015
PHY 712 Electrodynamics9-9:50 AM MWF Olin 103
Plan for Lecture 14:
Start reading Chapter 6
1. Maxwell’s full equations; effects of time varying fields and sources
2. Gauge choices and transformations
3. Green’s function for vector and scalar potentials
PHY 712 Spring 2015 -- Lecture 14 202/16/2015
PHY 712 Spring 2015 -- Lecture 14 302/16/2015
Full electrodynamics with time varying fields and sources
Maxwell’s equations
http://www.clerkmaxwellfoundation.org/
Image of statue of James Clerk-Maxwell in Edinburgh
"From a long view of the history of mankind - seen from, say, ten thousand years from now - there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics"
Formulation of Maxwell’s equations in terms of vector and scalar potentials -- continued
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PHY 712 Spring 2015 -- Lecture 14 1202/16/2015
Solution of Maxwell’s equations in the Lorentz gauge
source , field wave,
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PHY 712 Spring 2015 -- Lecture 14 1302/16/2015
Solution of Maxwell’s equations in the Lorentz gauge -- continued
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PHY 712 Spring 2015 -- Lecture 14 1402/16/2015
Solution of Maxwell’s equations in the Lorentz gauge -- continued
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PHY 712 Spring 2015 -- Lecture 14 1502/16/2015
Solution of Maxwell’s equations in the Lorentz gauge -- continued
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Analysis of the Green's function:
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"Proof" -- Fourier analysis in the time domain -- note that
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PHY 712 Spring 2015 -- Lecture 14 1602/16/2015
Solution of Maxwell’s equations in the Lorentz gauge -- continued
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PHY 712 Spring 2015 -- Lecture 14 1702/16/2015
Solution of Maxwell’s equations in the Lorentz gauge -- continued
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PHY 712 Spring 2015 -- Lecture 14 1802/16/2015
Solution of Maxwell’s equations in the Lorentz gauge -- continued
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PHY 712 Spring 2015 -- Lecture 14 1902/16/2015
Solution of Maxwell’s equations in the Lorentz gauge -- continued
Liènard-Wiechert potentials and fields --Determination of the scalar and vector potentials for a moving point particle (also see Landau and Lifshitz The Classical Theory of Fields, Chapter 8.)
Consider the fields produced by the following source: a point charge q moving on a trajectory Rq(t).