## 8.07

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# 8.07 - Electromagnetism II Fall 2014

Lecturer: |
Prof. Alan Guth |

Recitation Instructor: |
Prof. Xiao-Gang Wen |

Teaching Assistant: |
Anton Goloborodko |

## Announcements:

Announcements will be posted here throughout the semester.

**SUN 12/14/2014: Information on the Final Exam**

Dear 8.07 Students,

As you know, the final exam will take place
this coming Wednesday, December 17, from 1:30 - 4:30 pm, in Room
6-120.

The exam will be cumulative, as the subject
matter is, but it will emphasize the material since Quiz 2. That
means that it will emphasize the material from Problem Sets 9,
10, and 11, and correspondingly Chapters 6 (from 6.1.3 onward),
7, 8, 9, 10, and 11. For Chapters 9, 10, and 11, which we rushed
through, you are expected to be able to work problems only at a
fairly basic level. In particular, you are only responsible for
material that was discussed in lecture, as is documented by the
lecture slides, posted as Lecture Notes 7, 8, and 9. Note that
Problem 7 of Problem Set 10 was dropped from the problem set, but
it was included in the problem set solutions. You should treat
this problem as if it were part of Problem Set 11, which means
that you should make sure that you understand the solution.

The formula sheets for the final exam are
posted under the Exams tab of the course website, and they can be
used as a guide to studying. Note that sections indicated by ***
are not really part of the course, but otherwise you should
understand the meaning of these equations. I have enlarged the
formula sheets to include essentially all the mathematical
identities on the inside covers of Griffiths' book. There will
be no questions concerning the derivation of the formulas for the
gradient, divergence, curl, or Laplacian in spherical or
cylindrical coordinates, but you should be able to use these
formulas. The final exam (without solutions) from 2012 is posted
on the OCW version of 8.07, at

http://ocw.mit.edu/courses/physics/8-07-electromagnetism-ii-fall-2012/exams/MIT8_07F12_finalexam.pdf

The final exam will include one problem that
is taken verbatim (or at least almost verbatim) from Problem Sets
9, 10, or 11.

Good luck on the final!

— Alan Guth —

P.S.: Please please please fill out the online
course evaluations!!! You can find them at
http://web.mit.edu/subjectevaluation,
and you have until tomorrow morning at 9:00 am. Comments, as
well as numerical evaluations, are particularly
appreciated!

**SAT 12/13/2014: Quiz 2 and Problem Set 2 Solutions are posted**

Dear 8.07 Students,

Sorry that things have been slow, but I had to
also spend time on a particle theory group grant report, and on
interacting with Pappalardo Fellowship candidates.

In any case, I think I have now finished
everything that you need for studying for the final exam. In
particular, the solutions to Problem Set 10 are now posted, and
so is Quiz 2 and its solutions. Note that the final exam from
2012 (without solutions) is posted on the OCW 8.07 website. And
Prof. Wen's slides from his review session are posted on the
Exams tab of the 8.07 website.

Since you are seeing the solutions to Quiz 2
for the first time, you may have questions about the grading of
your papers. If so, I would be happy to talk to you about it,
and would be glad to change your grade if appropriate. If you
have questions about the grading, it would help a lot if you let
me know by next Thursday evening. (That means it's okay to wait
until after the final. I'll be proctoring, so if you stay until
the end of the final you can ask me questions then.)

Best of luck on the final. If you have
questions about the coverage of the final, or questions about
electromagnetism that may come up while you are studying, send an
email to both Anton (golobor@mit.edu) and me. (Prof. Wen is
traveling, so I don't think he will have time to answer emails.)
If there are a lot of questions we might get overwhelmed, but I
expect that we will be able to get back to you quickly.

— Alan Guth —

P.S.: Please fill out the online course
evaluations!!! You can find them at
http://web.mit.edu/subjectevaluation,
and you have until Monday at 9:00 am. Comments, as well as
numerical evaluations, are particularly appreciated!

**THURS 12/11/2014: Reducing Problem Set 11**

Dear 8.07 Students,

On Problem Set 11, also known as Review
Problems for the Final Exam, the last two problems (9 and 10)
involve material that we never reached in class, and so problems
of that type would not be fair for the final exam. In other
words, as far as the final exam is concerned, you can ignore
Problems 9 and 10. (Of course you still might be interested in
reading them, especially after you are done with your exams.)

— Alan Guth —

**THURS 12/11/2014: The final exam formula sheet is posted**

Dear 8.07 Students,

The formula sheet for the final exam is now
posted on the course website, under the "Exams" tab.

Note that sections marked with ***, which
includes the entire last page, are sections which include
material that will not be covered on the quiz. They are included
in the formula sheet for completeness, and in case you find the
information useful.

— Alan Guth —

**THURS 12/11/2014: Final exam review session today**

Dear 8.07 Students,

As was previously announced, there will be a
review session for the final exam today at 3:00 pm. The new
information is the room number: 4-153.

Anton Goloborodko will review the material
through Chapter 8 of the textbook, and then Prof. Wen will review
the material from Chapters 9 (Electromagnetic Waves), 10
(Potentials and Fields), and 11 (Radiation). Note that these
last three chapters are discussed in slides that were used in
lecture, posted as Lecture Notes 7, 8, and 9.

The formula sheet for the final exam should be
ready later this afternoon. Solutions to Quiz 2, and to Problem
Set 10, should be ready by tomorrow.

— Alan Guth —

**WED 12/10/2014: The lecture slides for today are posted**

Dear 8.07 Students,

The lecture slides for today are posted under
the Lecture Notes tab of the website, as Lecture Notes 9.

— Alan Guth —

**FRI 12/05/2014: Review session next Thursday for the final exam**

Dear 8.07 Students,

Greetings from Heidelberg.

To help you review for the final exam, Anton
Goloborodko and Prof. Wen will jointly be running a review
session, which will take place on Thursday, December 11 (the day
after classes end), from 3:00 pm until about 5:00 pm. This is
the time slot that previously would have included two recitation
sections. The plan is for Anton to review the material through
Chapter 8 of the textbook, and then Prof. Wen will review the
material from Chapters 9 (Electromagnetic Waves), 10 (Potentials
and Fields), and 11 (Radiation). Note that these last three
chapters are discussed in Lecture Notes 7, 8, and 9, of which
Lecture Notes 7 and 8 are now posted. Lecture Notes 9, which
will be discussed during the last lecture on Wednesday, will be
posted shortly.

The room for the review session will be
announced later.

— Alan Guth —

**WED 12/03/2014: Two changes in Problem Set 10**

Dear 8.07 Students,

First, we have not yet gotten far enough for
Problem 7 to be a fair question, so Problem 7 is removed from the
problem set. The problem set now has only 100 points of credit,
plus the option of earning 15 points extra credit.

Second, in Problem 4, you are intended to
consider only rotations about the z axis. In particular, in part
(c) where you are asked to consider a torque tau, the problem
should have specified that tau is in the z direction. Many
thanks to Margaret Pavlovich for raising this issue.

— Alan Guth —

**WED 12/03/2014: Grading of Problem Set 9, Problem 1**

Dear 8.07 Students,

On Problem Set 9, question 1(b) asked you to
sketch plots of the magnitude of B divided by mu_{0} M_{0}, and
the magnitude of H divided by M_{0}.
Anton tells me that before he noticed the absolute value signs in
the question, he took off points on a few papers when students
did not show that inside the cylinder, H points in the opposite
direction from M_{0}. But since the
question asked for the magnitude, the direction of H is not
relevant, and these points should not have been taken off.

In the interest of accurate grading (we try to
do our best!), if points were taken off on your homework for
showing the wrong sign of H, please send an email to Anton (Anton
Goloborodko

**SAT 11/29/2014: Email exchange with David Griffiths about dipole on a circular track**

Dear 8.07 Students,

You probably recall that Problem Set 6
included the paradoxical problem about the dipole on a circular
track, Griffiths Problem 4.31, p. 206. In this problem, a naive
application of the formula for the force on an electic dipole
seemed to lead to a perpetual motion machine. I pointed out that
my understanding of the problem was different from the solution
in the instructor's solution manual. Since then I had an email
exchange about this with David Griffiths, which (with his
permission) I would like to share with you all. I'm pasting
below my email to him, and his reply. The emails also contain
some comments about Sidney Coleman, the late Harvard physics
professor who played a major role in both David's life and mine.
(Sorry that I was slow in posting this --- life has been hectic
this term!)

Enjoy the rest of Thanksgiving weekend.

— Alan Guth —

***************************************************************** | |

From: Alan Guth <guth@ctp.mit.edu> | |

To: David Griffiths <griffith@reed.edu> | |

CC: Xiao-Gang Wen <wen@dao.mit.edu>, Anton Goloborodko <golobor@mit.edu>, Ekapob Kulchoakrungsun <ekapob@mit.edu>, Scott Hughes <sahughes@mit.edu> | |

Date: Sun, 2 Nov 2014 20:07:33 -0500 (EST) | |

Subject: A disagreement about dipole-on-a-circular-track problem | |

Attachments: ps06-f14.pdf, sol06-f14.pdf | |

-------------------- | |

Dear Prof. Griffiths, | |

First, let me say that this is the second time that I have lectured MIT's 8.07 course, Electromagnetism II, and both times we have used your "Introduction the Electrodynamics" as a textbook. Last time it was the 3rd edition, now it is the 4th. I think it is an excellent book. | |

Nonetheless, I disagree with the solution in the Instructors Solution Manual to Problem 4.31 (p. 206), so I thought I would write to see if you still think that your solution is correct. You will recall that your solutions manual says that the constraint forces will be larger than the electrostatic forces, and in the opposite direction, tending to slow the dipole down. I believe, and the people I am teaching with here at MIT seem to agree, that the net (tangential) force on the dipole is zero, so in the absence of friction it will continue to circle the track at a constant speed. | |

I am attaching Problem Set 6, and it solutions, where the problem under discussion is Problem 7. (Most of the other problems are also from your book.) | |

There is no hurry of course, but I would appreciate hearing what you think of our solution to this problem. | |

Thanks a lot, | |

— Alan — | |

P.S. I only learned a couple of years ago, when I first taught 8.07, that you were a student of Sidney Coleman's. Sidney also played a tremendous role in my life as a physicist. He was visiting at SLAC in 1979-1980, the same year that I was there, and he became very interested in the idea of inflation, and helped tremendously in making it known to the community. He was really a wonderful person. | |

================================================================= Department of Physics Center for Theoretical Physics V.F. Weisskopf Professor of Physics and MacVicar Faculty Fellow - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Alan H. Guth Center for Theoretical Physics guth@ctp.mit.edu Massachusetts Institute of Technology Phone: 617-253-6265 77 Massachusetts Avenue, Room 6-322 Fax: 617-253-8674 Cambridge, Massachusetts 02139-4307 ================================================================= | |

*************************************************************** | |

From David Griffiths <griffith@reed.edu> | |

To: Alan Guth <guth@ctp.mit.edu> | |

Date: Mon, 3 Nov 2014 01:41:29 -0500 (EST) | |

Subject: Re: A disagreement about dipole-on-a-circular-track problem | |

-------------------- | |

Alan, | |

BEAUTIFUL! I'm embarrassed, but much more than that I am delighted. And your explanation is so wonderful and clear that I would like your permission to quote parts of it (with attribution, of course) when I make the correction to the solution manual. (The only place I would make a change is the 4th line of page 13, where I was confused when I first read it. You have been talking about the constraint imposed by the torque motor, but then you say that "the constraint force acts only on the pivot"---now, of course, you are back to the constraint force that keeps the dipole on the circular track, not the constraint torque that maintains its orientation.) | |

If I can make a feeble response to your final paragraph, I was under the misapprehension that the dipole would accelerate (or actually decelerate), in which case a net torque WOULD be required. But it was, indeed, a silly blunder. What was I thinking? | |

Thank you so much for calling this to my attention, and for sending your solution! (And please convey my apologies to your students. I hope they have learned from my mistake!) | |

Yes, Coleman was a great physicist and an inspired teacher. I wish I had worked more closely with him. In those days he tended to be quite distant from his PhD students; Carl Bender, Tony Zee, and I all worked much more with others than with him. Jeff Mandula and (later) David Politzer were the exceptions. If I were doing it over I would not (I hope) be so timid. | |

Best, | |

David |

**TUES 11/25/2014: Plans for tomorrow (Wed 11/26/14)**

Dear Students,

Tomorrow is of course the day before
Thanksgiving, and we will have our usual class from 11 am until
noon. However, the schedule would also call for a recitation
from 4-5 pm, and I usually have an office hour from 5-6 pm. I
suspect that there may be no interest in recitation or office
hour, so perhaps we should cancel them both. (There will, of
course, be no recitations for the Thursday classes this week.)

However, if any of you --- even only one ---
is interested in having a recitation class or seeing me during my
office hour, I am happy to do it. (Prof. Wen is still out of
town, so I would be teaching the recitation class.) Just send an
email to let me know. If I receive such an email, then I will
send an email to all of you to let you know that the recitation
and/or office hour is happening. (The identity of the student
who requested it, however, will remain a deep dark secret.)

In any case, I expect to see you tomorrow
morning, and I wish you all a happy Thanksgiving.

— Alan Guth —

**SUN 11/23/2014: Problem Set 10 posted**

Dear 8.07 Students,

Problem Set 10 is now posted. It will be due
on the Friday after Thanksgiving, on December 5.

It has somewhat more reading than previous
problem sets, but I point out 1) these chapters are on the short
side, so it is not as much as it seems; and 2) you have about two
weeks to do it. There are a total of 80 pages to read; for
comparison, Chapter 7 by itself was 49 pages, so the reading per
week is not really more than it has been. During the last half
week I will be asking you to also read Chapter 11, Radiation,
which is 22 pages.

We will be discussing this material in class,
and for this material I will be following the textbook pretty
closely (no more traceless symmetric tensors, or even novel uses
of delta functions). The reading and the lectures should
reinforce each other, and I will try to tell you in lecture
everything that you need to know for the final exam.

— Alan Guth —

**THURS 11/20/2014: Correction to Problem Set 9**

Dear 8.07 Students,

In Problem Set 9, I mistyped the first
equation in Problem 8, so I have posted a corrected version.
(The right-hand side should be the curl of v cross B, and not the
curl of the curl of B.) Thanks to Rudy Garcia and Eric Tomlinson
for pointing this out.

— Alan Guth —

**WED 11/19/2014: Quiz 2 histogram, with
estimated letter grades, is posted**

Dear 8.07 Students,

I have just posted a histogram of the grades
for Quiz , with estimated letter grade equivalents. It is on the
Exams tab of the class website. As it says on the histogram
page,

The grade cuts shown represent my
estimate of what you have earned on this quiz, but they will
not necessarily be the numerical cuts that will be used to
evaluate your final grade. The final grade cuts will be
adjusted to account for the level of difficulty of all the
quizzes and problem sets. |

The class did very well on the quiz, so I am very pleased. The average was 85.6, with a standard deviation of 12.0. The class was very strong at the top, with 8 A+'s: 3 perfect papers, 2 99's, 2 98's, and 1 97. I thought that the quiz was easier than Quiz 1, when the average was 78.7, so I adjusted the cuts upwards a bit. But I also thought that much of the grade improvement relative to Quiz 1 was due to great work on your part, so changes in the cuts did not cancel out the improved grades. The estimated letter grades are somewhat higher for this quiz than for the first.

We have tried to grade as carefully as we can, but grading errors are still possible. If you have any questions about the grading of your quiz, I encourage you to ask about it. I graded problems 1 and 2, and Anton graded problem2 3 and 4, so it might be most efficient for you to start by discussing it with the person who graded the problem in question. But you can discuss the grading with any of the course staff. Both Anton Goloborodko and Prof. Wen are authorized to change grades, as well as me, but any of us might refer the question to the original grader, especially in evaluating partial credit. In any case, if you are unsatisfied with the decision of Anton or Prof. Wen, you should always feel free to come to me, and I will be happy to consider your point of view. In the end, I hope to make sure that the grading in this course is fair, and that hopefully you will all agree that it is fair. Quiz solutions should come out in a few days. You can of course bring up further quesions when the solutions become available.

The same issues apply to problem set grades. If you have any questions about the grading of your paper(s), going back to the beginning of the term, I encourage you to ask about it. For the homework it would probably be most efficient for you to first talk to Anton, but I am very much available to consider any points of disagreement.

Best wishes,

— Alan Guth —

**SUN 11/16/2014: Problem Set 9 posted**

Dear Students,

I'm sorry that it is a little late, but
Problem Set 9 is now posted. It will be due this coming Friday.

— Alan Guth —

**THURS 11/13/2014: Revised Problem Set 6 Solutions**

Dear 8.07 Students,

In the solution to Problem 1 in the Problem
Set 6 Solutions, Eqs. (1.2a) and (1.2b) were mistyped. I have
just posted a corrected version of these solutions.

— Alan Guth —

**THURS 11/13/2014: Quiz problem to be taken from the problem sets**

Dear 8.07 Students,

I was asked during my office hour whether the
problem that will be taken verbatim (or at least almost verbatim)
from the problem sets might be one of the extra credit problems.
It will not. It will be taken from one of the regular, required
problems on Problem Sets 5 through 8.

By the way, the problem taken from the problem
sets should be an easy 100%, I would think, but that was not the
outcome when I did the same thing on Quiz 2, 8.07 Fall 2012. On
that quiz the first problem was taken from the problem sets, and
I was very disappointed that the class average on Problem 1 was
only 61%. You folks will do much better, right? If you know how
to do the problems on the problem sets, we will all be very
happy.

— Alan Guth —

**WED 11/12/2014: Location for the review session and quiz**

Dear 8.07 Students,

The review session tonight, run by Anton
Goloborodko, will start at 7:30 pm in the TEAL Room, 26-152. It
will be somewhat open-ended, but you can of course leave whenever
you feel that your questions have been answered. The quiz
tomorrow will also be in the TEAL Room, 26-152, also starting at
7:30 pm. The quiz will end at 9:30 pm.

— Alan Guth —

**TUES 11/11/2014: Information on Quiz 2**

Dear 8.07 Students,

Quiz 2 will take place this coming Thursday,
November 13, 7:30 - 9:30 pm, in the TEAL Room, 26-152. You will
have two hours to do the quiz, although it will be intended as a
one-hour quiz. Prof. Wen will be proctoring.

There will be a review session for the quiz,
led by Anton Goloborodko, tomorrow (Wednesday) evening at 7:30
pm. The room is not yet known, but I expect to email you and
post it on the website tomorrow morning.

I also want to let you know that the solutions
to all the problem sets have now been posted.

The quiz will in principle be cumulative, as
the subject matter is, but it will emphasize the material since
the last quiz. That means it will focus on Problem Sets 5, 6, 7,
and 8, and correspondingly Chapters 4, 5, and the very beginning
of 6. We are skipping the polarizability tensor mentioned on pp.
162-163, and in Chapter 6 you will only be responsible on this
quiz for Secs. 6.1.1 and 6.1.2. Problem Set 5 included some
problems that came from Chapter 3, but which were more
sophisticated than the problems that came earlier. Such problems
are fair game for Quiz 2, so you might want to review Chapter 3.

The formula sheets, which are posted, are also
a guide to the material that you are expected to understand. If
you understand the meaning of the formulas on these 10 pages, and
are prepared to use them when appropriate, then you are in great
shape for the quiz.

This time I will be putting one problem on the
quiz that will be taken verbatim (or at least almost verbatim)
from Problem Sets 5, 6, 7, or 8. This will encourage you to
study the problem sets carefully, which I think is a good idea;
the other problems will test your creativity.

On the Exams tab of the archived Fall 2012
website, http://web.mit.edu/8.07/fall12/index.html, you will find
Quiz 2 Practice Problems from 2003, with solutions, Quiz 2 from
2012, with solutions, and Quiz 2 Makeup from 2012, without
solutions. (The Quiz 2 Makeup, by the way, was given because
Quiz 2 turned out to be too hard, with many low grades. I will
try to make sure that doesn't happen this year.)

Good luck on the quiz. I will see you
tomorrow morning, and I will have my usual office hour tomorrow
at 5 pm. There will be no class on Friday.

— Alan Guth —

**WED 10/29/2014: Holding over problems 6 and 7 of Problem Set 7**

Dear 8.07 Students,

Since we have not yet talked about magnetic
dipoles, the last two problems on Problem Set 7 --- i.e.,
Problems 6 and 7 --- are not yet appropriate. So, we will hold
them over until Problem Set 8. Problem Set 7 is now redefined to
consist only of Problems 1 through 5, worth a total of 70
points.

— Alan Guth —

**FRI 10/24/2014: Quiz 1 histogram, with estimated letter grades, is posted**

Dear 8.07 Students,

I have just posted a histogram of the grades
for Quiz 1, with estimated letter grade equivalents. It is on
the Exams tab of the class website. As it says on the histogram
page,

The grade cuts shown represent my
estimate of what you have earned on this quiz, but they will
not necessarily be the numerical cuts that will be used to
evaluate your final grade. The final grade cuts will be
adjusted to account for the level of difficulty of all the
quizzes and problem sets. |

We have tried to grade as carefully as we can, but grading errors are still possible. If you have any questions about the grading of your quiz, I encourage you to ask about it. I graded problems 2 and 3, and Anton graded problem 1, so it might be most efficient for you to start by discussing it with the person who graded the problem in question. But you can discuss the grading with any of the course staff. Both Anton Goloborodko and Prof. Wen are authorized to change grades, as well as me, but any of us might refer the question to the original grader, especially in evaluating partial credit. In any case, if you are unsatisfied with the decision of Anton or Prof. Wen, you should always feel free to come to me, and I will be happy to consider your point of view. In the end, I hope to make sure that the grading in this course is fair, and that hopefully you will all agree that it is fair.

The same issues apply to problem set grades. If you have any questions about the grading of your paper(s), going back to the beginning of the term, I encourage you to ask about it. For the homework it would probably be most efficient for you to first talk to Anton, but I am very much available to consider any points of disagreement.

Best wishes,

— Alan Guth —

**FRI 10/24/2014: Fringing fields: correction to Wed 10/22 lecture**

Dear 8.07 Students,

There was an item that I intended to mention in lecture
today, but forgot. This past Wed (10/22/14), I drew on the
blackboard a diagram of a capacitor that was initially filled
with a dielectric slab, but the dielectric was pulled part way
out. Where the dielectic is sticking out of the capacitor
plates, the nearly uniform E-field inside the capacitor changes
smoothly into the very small field outside of the capacitor, and
that leads to a fringing field pattern. I showed that
(qualitatively) correctly in my diagram. At the other end of the
dielectric, however, where the edge of the dielectric slab is
well within the capacitor, the diagram I drew in lecture was not
accurate. I showed fringing fields here, too, but that is not
correct. Since the potential difference between the two
capacitor plates is constant throughout the capacitor, the
electric field need not have any discontinuity at the edge of the
dielectric. As long as the edges of the capacitor are far away,
there is a solution in which the E-field is completely uniform
between the capacitor plates, pointing perpendicular to the
plates (just as inside a vacuum-filled capacitor). This
satisfies div D = 0 and curl E = 0 inside each region, as it
must. At the edge of the dielectric it satisfies the right
boundary conditions: E-parallel is continuous across the
boundary, since E is uniform; and D_perp is continuous, since it
is zero on both sides of the boundary. Thus this configuration
satisfies all the requirements, and therefore is the unique
solution to the problem.

A good diagram of this situation can be found at

http://teacher.pas.rochester.edu/PHY217/LectureNotes/Chapter4/LectureNotesChapter4.html#Heading712

in Figures 4.13 and 4.14.

Sorry for the previous confusion, and I hope
that this email straightens things out.

— Alan Guth —

**WED 10/08/2014: Problem Set 4 Solutions are posted**

Dear 8.07 Students,

The solutions to Problem Set 4 are now posted, on the
Problem Sets tab of the course web page.

— Alan Guth —

**TUES 10/07/2014: Rooms for Review Session and Quiz**

Dear 8.07 Students,

The Review Session for Quiz 1 will take place
at 7:30 pm on Wednesday evening, October 8, in Room 26-310. It
will be run by Anton Goloborodko.

Quiz 1 will take place at 7:30 pm on Thursday
evening, October 9, in the TEAL Room, 26-152. You will have two
hours to do the quiz, although it will be intended as a one-hour
quiz.

Best wishes for the quiz,

— Alan Guth —

**SAT 10/04/2014: Problem Set 3 Solutions are posted**

Dear 8.07 Students,

The solutions to Problem Set 3 are now posted, on the
Problem Sets tab of the course web page.

— Alan Guth —

**THURS 10/02/2014: Lecture Notes 4 are posted**

Dear 8.07 Students,

I just posted a set of lecture notes, Lecture
Notes 4, on the "Traceless Symmetric Tensor Approach to Legendre
Polynomials and Spherical Harmonics". They are based on Lecture
Notes 9 of 2012, but I made a few improvements in the editing.
In particular, the equation that is now Eq. (4.32) has been
corrected.

— Alan Guth —

**SAT 09/20/2014: Lecture Notes 3 posted (addendum to Wed's lecture)**

Dear 8.07 Students,

When I ran out of time in lecture last
Wednesday (9/17/14), there were two topics that I did not have
time to discuss. Since these topics are relevant to Problem Set
2, and are not discussed in Griffiths' textbook, I wrote Lecture
Notes 3 to fill in the gaps. You can access them on the Lecture
Notes tab on the course website.

You will probably find these notes useful in
completing Problem Set 2.

Best wishes,

— Alan Guth —

**MON 09/15/2014: Problem Set 1 Solutions are posted**

Dear 8.07 Students,

The solutions to Problem Set 1 are now posted, on the
Problem Sets tab of the course web page,

http://web.mit.edu/8.07/www

— Alan Guth —

**SAT 09/13/2014: Problem Set 2 is posted**

Dear 8.07 Students,

Hi from San Francisco.

Problem Set 2 is posted, so you can start whenever you find
the time. Since Friday Sept 19 is a student holiday, the due
date for the problem set is postponed until the following Monday,
Sept 22.

Best wishes,

— Alan Guth —

**WED 09/10/2014: Lecture Notes 1 and 2 are posted**

Dear 8.07 Students,

Hi from Oslo.

I just wanted to let you know that Lecture Notes 1 and 2
have been posted, on the Lecture Notes tab of the course website.
These are notes on "Vector Analysis," and "Rotations in Index
Notation," which you may find useful in doing this week's
homework.

Best wishes,

— Alan Guth —

**THU 09/04/2014: Course Information Sheet is posted**

Dear 8.07 Students,

An information sheet describing 8.07 is now
posted, on the General Info tab. Let me know if you have any
questions that are not answered in this handout.

— Alan Guth —

**WED 09/03/2014: Problem Set 1 is posted**

Dear 8.07 Students,

I just thought that I would let you know that
Problem Set 1 is now posted on the course website. The home page
is at

http://web.mit.edu/8.07/www

from which you can click on "Problem Sets".

As I mentioned in lecture, it will be due on Friday,
September 12, at 5:00 pm. You should turn in the problem sets at
the Physics Department homework boxes, which are at the
intersection of buildings 8 and 16, on the third floor of bldg. 8
and the 4th floor of bldg. 16.

— Alan Guth —

**TUES 09/02/2014: Welcome to 8.07!!!**

Welcome to 8.07, for fall 2014. This web page
is not set up yet, but the course this fall will strongly
resemble the course I taught two years ago, which is archived on
OCW at

http://ocw.mit.edu/courses/physics/8-07-electromagnetism-ii-fall-2012/

Prof. Xiao-Gang Wen will be teaching the recitations this fall,
and Anton Goloborodko will be the teaching assistant. The
lectures will take place from 11:05 am to 11:55 am on Mondays,
Wednesdays, and Fridays in 6-120. The recitations will take
place on Wednesdays at 4:05 pm and on Thursdays at 3:05 and 4:05
pm. The recitations will all be in 26-310, and will each be 50
minutes long.

I look forward to seeing you.

— Alan Guth —