Homework 5 Solutions, Electromagnetic Theory II
Dr. Christopher S. Baird, Spring 2014
University of Massachusetts Lowell
Problem 1
Consider a rectangular waveguide that is infinite and uniform along its axis (the z axis) and is situated
so that one corner
Homework 3 Answers, 95.658 Electromagnetic Theory II
Dr. Christopher S. Baird, UMass Lowell
Problem 1
Derive the group velocity and phase velocity for waves propagating in a pure plasma. Calculate these
velocities for the cases of = p , = 2 p , and = (1/2
Lecture 1 Notes, Electromagnetic Theory II
Dr. Christopher S. Baird
University of Massachusetts Lowell
1. Overview of Electrodynamic Theories
SMALL SIZES (atomic)
BIG SIZES
LOW SPEED
HIGH SPEED (close to speed of light)
Classical Electrodynamics
Relativis
Mid-Term Exam: Graduate Electromagnetics II, 95.658
Spring 2009, UMass Lowell, Dr. Baird
Part I: Multiple Choice (60 Points)
Circle only one answer to each question.
1. Where are traveling electromagnetic waves of the form ei(kx t) generally found?
(a) ev
Mid-Term Exam: Graduate Electromagnetics II, 95.658
Spring 2009, UMass Lowell, Dr. Baird
Part I: Multiple Choice (60 Points)
Circle only one answer to each question.
1. Where are traveling electromagnetic waves of the form ei(kx t) generally found?
(a) ev
Lecture 2 Notes, Electromagnetic Theory II
Dr. Christopher S. Baird
University of Massachusetts Lowell
1. Dispersion Introduction
- An electromagnetic wave with an arbitrary wave-shape can be thought of as a superposition of
single-frequency plane waves.
Lecture 6 Notes, Electromagnetic Theory II
Dr. Christopher S. Baird
University of Massachusetts Lowell
1. Radiation Introduction
- We have learned about the propagation of waves, now let us investigate how they are
generated.
- Physically speaking, whenev
Lecture 5 Notes, Electromagnetic Theory II
Dr. Christopher S. Baird
University of Massachusetts Lowell
1. Waveguides Continued
- In the previous lecture we made the assumption that the wave is free in the z dimension but
stays general in the other dimensi
Lecture 4 Notes, Electromagnetic Theory II
Dr. Christopher S. Baird
University of Massachusetts Lowell
1. Introduction to Waveguides
- Electrodynamics is essentially the study of the creation, propagation, and absorption of
electromagnetic waves as they i
Final Exam: Graduate Electromagnetics II, 95.658
Spring 2009, UMass Lowell, Dr. Baird
Part I: Multiple Choice (60 Points)
Circle only one answer to each question.
1. What is the relationship between the polarization vector and the wave vector of a plane w
Homework 5 Answers, 95.658 Electromagnetic Theory II
Dr. Christopher S. Baird, UMass Lowell
Problem 1
Take the general waveguide described in the previous problem where the fields have no dependence on
y. Now consider that this waveguide has perfectly con
Lecture 4 Notes, Electromagnetic Theory II
Dr. Christopher S. Baird
University of Massachusetts Lowell
1. Introduction to Waveguides
- Electrodynamics is essentially the study of the creation, propagation, and absorption of
electromagnetic waves as they i
Lecture 2 Notes, Electromagnetic Theory II
Dr. Christopher S. Baird
University of Massachusetts Lowell
1. Dispersion Introduction
- An electromagnetic wave with an arbitrary wave-shape can be thought of as a superposition of
single-frequency plane waves.
Homework 2 Answers, 95.658 Spring 2010, Electromagnetic Theory II
Dr. Christopher S. Baird, UMass Lowell
Problem 1
Consider the general case where the wave number is complex-valued and the permittivity is complexvalued (but the material is non-magnetic).
Final Exam: Graduate Electromagnetics II, 95.658
Spring 2009, UMass Lowell, Dr. Baird
Part I: Multiple Choice (60 Points)
Circle only one answer to each question.
1. What is the relationship between the polarization vector and the wave vector of a plane w
Homework 1 Answers, 95.658 Electromagnetic Theory II
Dr. Christopher S. Baird, UMass Lowell
Problem 1
Following the derivation in class, keep the negative-valued dispersion relation instead of the positive
one (this corresponds to meta-materials instead o
Homework 3 Answers, 95.658 Electromagnetic Theory II
Dr. Christopher S. Baird, UMass Lowell
Problem 1
Derive the group velocity and phase velocity for waves propagating in a pure plasma. Calculate these
velocities for the cases of = p , = 2 p , and = (1/2
Homework 2 Answers, 95.658 Electromagnetic Theory II
Dr. Christopher S. Baird, UMass Lowell
Problem 1
For non-magnetic, linear, frequency-dependent dielectric material we found the relationship between
the wave number k of a wave in the material, its freq
Homework 4 Answers, 95.658 Electromagnetic Theory II
Dr. Christopher S. Baird, UMass Lowell
Problem 1
Jackson 8.1: Consider the electric and magnetic fields in the surface region of an excellent conductor in
the approximation of Section 8.1, where the ski
Lecture 3 Notes, Electromagnetic Theory II
Dr. Christopher S. Baird
University of Massachusetts Lowell
1. Superposition of Waves
- Up till now we have only looked at monochromatic waves and how they behave in materials
and hinted at how a frequency-depend
Final Exam: Graduate Electromagnetics II, 95.658
Spring 2011, UMass Lowell, Dr. Baird
Part I: Multiple Choice (45 Points) Circle the one best answer to each question. 1. At very high velocities, what role does a particle's rest mass play in its total ener
Lecture 6 Notes, Electromagnetic Theory II
Dr. Christopher S. Baird
University of Massachusetts Lowell
1. Radiation Introduction
- We have learned about the propagation of waves, now let us investigate how they are
generated.
- Physically speaking, whenev
Mid-Term Exam: Graduate Electromagnetics II, 95.658
Spring 2011, UMass Lowell, Dr. Baird
Part I: Multiple Choice (60 Points) Circle the one best answer to each question. 1. What is the wave E = E0 sin(kx)e-t/e-it? (a) a traveling wave decaying in time (b)
Lecture 4 Notes, Electromagnetic Theory II
Dr. Christopher S. Baird
University of Massachusetts Lowell
1. Introduction to Waveguides
- Electrodynamics is essentially the study of the creation, propagation, and absorption of
electromagnetic waves as they i
Lecture 2 Notes, Electromagnetic Theory II
Dr. Christopher S. Baird
University of Massachusetts Lowell
1. Dispersion Introduction
- An electromagnetic wave with an arbitrary wave-shape can be thought of as a superposition of
single-frequency plane waves.
Mid-Term Exam: Graduate Electromagnetics II, 95.658
Spring 2009, UMass Lowell, Dr. Baird
Part I: Multiple Choice (60 Points)
Circle only one answer to each question.
1. Where are traveling electromagnetic waves of the form ei(kx t) generally found?
(a) ev
Mid-Term Exam: Graduate Electromagnetics II, 95.658
Spring 2009, UMass Lowell, Dr. Baird
Part I: Multiple Choice (60 Points)
Circle only one answer to each question.
1. Where are traveling electromagnetic waves of the form ei(kx t) generally found?
(a) ev
Homework 5 Answers, 95.658 Electromagnetic Theory II
Dr. Christopher S. Baird, UMass Lowell
Problem 1
Take the general waveguide described in the previous problem where the fields have no dependence on
y. Now consider that this waveguide has perfectly con
Final Exam: Graduate Electromagnetics II, 95.658
Spring 2009, UMass Lowell, Dr. Baird
Part I: Multiple Choice (60 Points)
Circle only one answer to each question.
1. What is the relationship between the polarization vector and the wave vector of a plane w
Mid-Term Exam: Graduate Electromagnetics II, 95.658
Spring 2011, UMass Lowell, Dr. Baird
Part I: Multiple Choice (60 Points) Circle the one best answer to each question. 1. What is the wave E = E0 sin(kx)e-t/e-it? (a) a traveling wave decaying in time (b)