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)?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
(shown in image)
Transcribed Image Text: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)?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 6 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON