Physics PHYS 354
Electricity and Magnetism II
Spring Semester 2016
4 Credit Hours
Syllabus
Instructor:
Office Hours:
Schedule:
Brandon Hoffman
Description:
An examination of the important role of special relativity in electromagnetic
phenomena. Maxwell's equations are introduced in a relativistic manner, and
used to investigate the properties of electromagnetic waves. Also included are
mathematical techniques for solving the equations of Laplace and Poisson in
electrostatics. Prerequisite: PHYS 353.
Objectives:
In this class you will become familiar with the basic concepts and formalism of
special relativity, and their application to the theory of electricity and
magnetism developed last semester. In addition, it is my hope that you will
begin to appreciate the elegant and unexpected manner in which God has
designed the universe.
Learning
outcomes:
The objectives listed above I hope will be evidenced by the following
outcomes:
1. The ability to solve electrostatic boundary-value problems using the
method of images.
2. The ability to solve Laplace’s equation for rectangular, cylindrical
and spherical symmetry using separation of variables.
3. Familiarity dealing with 3-vectors and tensors using index notion
rather than traditional vector notation.
4. The ability to explain the difficulties posed to classical mechanics by
the fact that Maxwell’s equations are not invariant under Galilean
transformations, and how this problem was solved.
5. Familiarity 4-vectors and tensors and their properties.
6. The ability to solve relativistic problems in mechanics using invariant
quantities and 4-vectors.
7. The ability to derive the relativistic transformation of electric and
magnetic fields, and to calculate them in various reference frames.
8. The ability to use the stress tensor to examine the conservation of
energy and momentum in electric and magnetic fields.
9. An understanding of the behavior of electromagnetic waves in
various media.
10. An increased level of mathematical sophistication in your thinking
and writing.
11. The ability to appreciate God’s creation in a way you could not prior
to this course.
Lecture
MTWTF
MWF
Rm. P107
10:00-11:00 AM
11:55-1:00 PM
567-9235
Rm. P-107
Rm. P-204
Text:
Introduction to Electrodynamics (Third Edition) by D. J. Griffiths, Prentice
Hall, Englewood Cliffs, New Jersey, 1999.
Attendance:
Excessive absence from class will have a detrimental effect on assigned
grades. The instructor will decide on a case-by-case basis whether tests can
be made-up.
Homework:
Problem Sets are generally to be turned in on before 5:00 PM on the due
date.
Late homework will not be accepted.
I plan to be very particular about the format of the homework. Sloppy
or disorganized work will not be accepted. I will expect the following rules
to be followed:
1. Use only one side of your paper.
2. Each new problem is to begin on a new sheet.
3. Copy the problem, in its entirety, at the top of the page, before you begin
the solution.
4. Use words to describe each step in the solution.
5. Leave space - do not crowd your work into a tiny area on the page.
Exams:
Grades:
There will be a take-home midterm examination Feb 12-19, 2016. There
will also be a comprehensive take-home final examination, which will be
due during the regularly scheduled final exam period.
A grading rubric for activities in this course can be found at:
http://www.houghton.edu/physics/physics-grading-rubric/
The final grade will represent a weighted average of the scores on the
homework, mid-term, and the final exam. The weighting factors will be
50%, 25%, and 25% respectively.
Expected
Minimum
Time
Required:
Learning activity
Additional
comments
Class time
65 minutes per
class
37 classes
Assigned reading
181 pages
Homework
9 Problem Sets
Take-Home Exams
Typical minimum Total time
in minutes
time on task
2,405
Textbook reading
without quizzes
5 minutes per page
905
Work a selection of
example problems
10 hours per
problem set
5,400
20 hours per exam
2,400
Midterm and Final
TOTAL
11,110
Lecture Schedule (tentative)
Wednesday, Jan. 13
Topic:
Friday, Jan. 15
Topic:
Review of electro- and magnetostatics.
Assignment: Problem Set #1
Monday, Jan. 18
Topic:
Example: “The big slab of charge!”
Wednesday, Jan. 20
Topic:
Read:
Method of images.
Griffiths, p. 110-126
Friday, Jan. 22
Topic:
Example: Point charge outside a grounded sphere
Due:
Problem Set #1
Assignment: Problem Set #2
Monday, Jan. 25
Topic:
Read:
Laplace's equation in rectangular coordinates.
Griffiths, p. 127-136
Wednesday, Jan. 27
Topic:
Example: Infinitely long rectangular box.
Friday, Jan. 29
Topic:
Read:
Due:
Assignment:
Laplace's equation in spherical coordinates.
Griffiths, p. 137-145
Problem Set #2
Problem Set #3
Monday, Feb. 1
Topic:
Laplace's equation in spherical coordinates (continued).
Wednesday, Feb. 3
Topic:
Example: Hemispheres at constant potential.
Friday, Feb. 5
Topic:
Example: Hemispheres at constant potential (continued).
Monday, Feb. 8
Topic:
Read:
Boundary value problems with linear dielectrics.
Griffiths, p. 186-190
Wednesday, Feb. 10
Topic:
Poisson’s equation for electric fields
Friday, Feb. 12
Topic:
Due:
Handout:
Example: Electric field in an atomic nucleus.
Problem Set #3
Take-Home Midterm Exam
Monday, Feb. 15
Wednesday, Feb. 17
Friday, Feb. 19
Introduction
Review of electro- and magnetostatics
MIDTERM EXAM (NO CLASS)
Monday, Feb. 22
Wednesday, Feb. 24
Friday, Feb. 26
February Break
Monday, Feb. 29
Topic:
Read:
Wednesday, Mar. 2
Topic:
Some simple examples using index notation.
Assignment: Problem Set #4
Friday, Mar. 4
Topic:
A more difficult example: multipole expansion.
Monday, Mar. 7
Topic:
Read:
Review of special relativity
Griffiths, p. 477-499
Wednesday, Mar. 9
Topic:
Read:
Due:
Assignment:
The Galilean and Lorentz transformations.
Griffiths, p. 500-506
Problem Set #4
Problem Set #5
Friday, Mar. 11
Topic:
The Galilean and Lorentz transformations (continued).
Monday, Mar. 14
Topic:
Read:
Geometry in four dimensions
Handout, pages 14-27.
Wednesday, Mar. 16
Topic:
Read:
Due:
Assignment:
Some special four vectors.
Griffiths, p. 507-511
Problem Set #5
Problem Set #6
Friday, Mar. 18
Topic:
Read:
Example problems using four vectors.
Griffiths, p. 511-516
Monday, Mar. 21
Wednesday, Mar. 23
Friday, Mar. 25
Monday, Mar. 28
Geometry in three dimensions.
Handout, pages 1-14.
Easter Break
Wednesday, Mar. 30
Topic:
Read:
Gauge transformations.
Griffiths, p. 416-422
Friday, Apr. 1
Topic:
Read:
Electromagnetic field tensor.
Griffiths, p. 523-537
Monday, Apr. 4
Topic:
Read:
Due:
Assignment:
Electromagnetic field tensor (continued).
Griffiths, p. 537-543
Problem Set #6
Problem Set #7
Wednesday, Apr. 6
Topic:
Relativistic transformation of fields.
Friday, Apr.8
Topic:
Relativistic transformation of fields (continued).
Monday, Apr. 11
Topic:
Field due to a moving charge.
Wednesday, Apr. 13
Topic:
Field due to a moving charge (continued).
Due:
Problem Set #7
Assignment: Problem Set #8
Friday, Apr. 15
Topic:
Read:
Energy and momentum conservation.
Griffiths, p. 517-522, 349-360
Monday, Apr. 18
Topic:
Energy and momentum conservation (continued).
Wednesday, Apr. 20
Topic:
Read:
Due:
Assignment:
Plane electromagnetic waves in vacuum.
Griffiths, p. 364-380
Problem Set #8
Problem Set #9
Friday, Apr. 22
Topic:
Read:
Electromagnetic waves in media
Griffiths, p. 382-384
Monday, Apr. 25
Topic:
Read:
Electromagnetic waves in conductors
Griffiths, p. 392-396
Wednesday, Apr. 27
Topic:
Electromagnetic waves in conductors (continued)
Due:
Handout:
Wave generation
Problem Set #9
Take-Home Final Exam
Friday, Apr. 29
Monday, May 2
Wednesday, May 4
Friday, May 6
Work on final examination.
Due:
Final Exam