## 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.

**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 —