Consider a plane polarized electromagnetic wave in the vacuum described by the vector and scalar potentials, A(r, t) Ae(kr-wt) D(r, t) = Poe(kr-wt) where the orientation of the vector Ao is arbitrary. a) Using Maxwell's equations, find the relationship that must hold between Ao and po b) Using the principal of gauge invariance, show that one can transform to a new but physically equivalent vector potential which is transversely polarized, i.e. Ao k-0. Explicitly find the gauge transformation function x that does this. c) What is the scalar potential p(r, t) in the gauge of part (b)?

Consider a plane polarized electromagnetic wave in the vacuum described by the vector and scalar potentials, A(r, t) Ae(kr-wt) D(r, t) = Poe(kr-wt) where the orientation of the vector Ao is arbitrary. a) Using Maxwell's equations, find the relationship that must hold between Ao and po b) Using the principal of gauge invariance, show that one can transform to a new but physically equivalent vector potential which is transversely polarized, i.e. Ao k-0. Explicitly find the gauge transformation function x that does this. c) What is the scalar potential p(r, t) in the gauge of part (b)?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter34: Maxwell’s Equations And Electromagnetic Waves

Section: Chapter Questions

Problem 38PQ

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