## 8.07

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# 8.07 - Electromagnetism II Fall 2012

**Course Administrator:** Prof. Alan Guth

**Recitation Instructors:** Prof. Min Chen

## Announcements:

Announcements will be posted here throughout the semester.

**TUES 12/18/2012: Formula sheet for the final exam is now posted**

The formula sheet for the final exam is now
posted on the course website, under Exams. I'm sorry that it is
so late, but I am doing my best. As with the quizzes, your copy
of the final exam will include a complete copy of this formula
sheet. It is also intended as an aid to studying. If you
understand the meaning of all the formulas on the formula sheet,
you should be in great shape for the final exam.

Best of luck on the final.

— Alan —

**SUN 12/16/2012: Prof. Chen's Review on Waves, Potentials, and Radiation is posted**

The slides from Prof. Chen's presentation at
today's review session, on Waves, Potentials, and Radiation, have
been posted on the website as Lecture Notes #17. (From what
Prof. Chen tells me, due to a computer crash these are not
exactly the slides that he showed today. Instead they are an
earlier version of the same talk.)

I still owe you a formula sheet, which I
understand is very urgent. However, I am still working on
overdue letters of recommendation, which are also very urgent. I
hope to have a formula sheet by tomorrow night. In the meantime,
you should consider the boxed equations on the lecture slides as
the first approximation to a formula sheet for Chapters 9, 10,
and 11, but that doesn't help for Chapters 7 and 8.

Best wishes,

— Alan —

**FRI 12/14/2012: Information about the Final Exam**

As you know, the final exam for this course
will take place on Wednesday, December 19, 1:30 - 4:30 pm, at
Johnson Track (upstairs).

There will be a review session for the final,
led by Prof. Chen and Ahmet Demir, on this Sunday, December 16,
from noon to about 2 pm, in Room 4-153.

A set of Review Problems for the Final Exam
has just been posted on website, under Exams. It consists of 10
problems, all taken from Griffiths' book, from Chapters 9, 10,
and 11. It includes solutions, cut and pasted from the solutions
manual. Since the source material comes entirely from Griffiths,
I am making it available only on presentation of an MIT
certificate. Let me know if you have any problems accessing it.

The final exam will in principle include the
whole course, but will emphasize the material since Quiz 2. This
means that it will focus on Problem Sets 9 and 10, the Review
Problems for the Final Exam, and Chapters 7, 8, 9, 10, and 11.
There are some topics that we skipped completely, that will not
be mentioned on the final exam: Sec. 6.4.2 (ferromagnetism), Secs
9.3.3 through the end of Chapter 9, Sec. 10.2.2 (Jefimenko's
equations), and Sec. 11.2.3 (The Physical Basis of the Radiation
Reaction). I recognize that Chapters 9, 10, and 11 were covered
rapidly. Details were omitted, and you have had on problem sets
only three problems from Chapter 9, and none from Chapters 10 or
11. This material will be covered on the final exam, but the
problems based on this material will be fairly straightforward
ones. For these chapters you are responsible only for material
that was presented in lecture, and which is on the posted lecture
slides. The Review Problems for Final Exam are intended to help
you study this material, and to give you examples of the kinds of
problems that I expect you to be able to solve. (These Review
Problems may not seem much more straightforward than usual, but
in addition I will promise that the exam problems will require
less originality, staying closer than usual to the model of these
sample problems.)

The final exam will include one problem that
is taken verbatim (or at least almost verbatim) from Problem Sets
9 or 10, or from the Review Problems for the Final Exam.

I would suggest that you focus your studying
attention on the Problem Sets and Review Problems, making very
sure that you really understand how the problems are solved, and
how to justify each step. However, if you want to see more
sample problems, you might look at the Final Exams from 2009 and
2010, which are linked to our website via the "Fall 2011 site"
tab. After clicking this tab, choose "Presentations", click that
it is "okay" to view the last day of classes, and then click
"Exam Prep" from the menu at the left. Some of the problems on
these tests make explicit use of special relativity, which would
not be appropriate for our final exam.

Finally, be sure to fill out the online course
evaluations! I really want the feedback. Thanks a lot.

Best of luck on the final exam.

— Alan —

**THURS 12/6/2012: Problet Set 10: Problem 6 is now extra credit**

Since we didn't get as far in lecture on
Wednesday as I had hoped, Problem 6 of Problem Set 10 is no
longer part of the assignment. It can, however, be done for 15
points of extra credit.

Although Problems 4 and 5 also
involve plane waves, I think that you can do them with only the
information we have discussed. Problem 4 depends only on the
relation between the energy and the momentum carried by
electromagnetic fields. Problem 5 can be done by knowing the
form and the meaning of the Maxwell stress tensor, and by knowing
that the relevant electromagnetic wave is described by Eq.
(9.48). Let me know if you have any problems with this.

See you tomorrow,

— Alan Guth —

**TUES 12/4/2012: Quiz 2 Makeup today in Room 32-144**

The Quiz 2 Makeup will be given today (Tuesday 12/4/12),
from 7:30 to 9:30 pm, in Room 32-144 (the same room as our
previous quizzes). If you wish to take it, please come.

— Alan Guth —

**SAT 12/1/2012: Outcome of poll on Quiz 2 Makeup**

[The following email was sent Saturday, and
corrected on Sunday. Please continue to use guth@mit.edu to
reach me.]

Sorry that I was slow about this, but I needed
a lot of time to get my email organized. When the LNS computer
system finally came back after being out for 28 hours due to a
power surge, it delivered just under 200 emails to me (including
over 20 letter of recommendation requests), in a random order,
and some of the attachments were corrupted as well. Now I've
restored it all to the original order, which makes it much easier
to make sense of them.

As for the poll, it turned out that I was
right to suspect that some students felt that they had studied
for the Makeup, and they want to be able to take it to show what
they have learned. There were 17 responses: 13 chose Option A,
and 4 chose Option B. None chose option C or recommended
anything different.

So, the optional Quiz 2 Makeup will take place
on Tuesday evening, December 4, from 7:30 - 9:30 pm. I will
arrange a room and notify you.

The grading policy will be as follows.

If you do not take the makeup, then If you do better on Quiz 2 than on the final exam, then Each quiz will count 20%, the final will count 35%, and the homework 25% (as originally planned). I you do better on the final exam than on Quiz 2, then Quiz 1 will count 20%, Quiz 2 will count 15%, the final will count 40%, and the homework 25%. If you take the makeup, then Your grade will be the highest of the following 3 calculations: 1) 0.20*(Quiz 1)+0.20*(original Quiz 2)+0.35*(final)+0.25*(homework) 2) 0.20*(Quiz 1) +0.20*(Minimum((original Quiz 2 + Quiz 2 Makeup)/2, 75%)) +0.35*(final)+0.25*(homework) 3) 0.20*(Quiz 1)+0.15*(original Quiz 2)+0.40*(final)+0.25*(homework)Note that the grading for students who do not take the Makeup can alternatively be described as the larger of calculations (1) and (3) above. This grading policy is identical to what I proposed in my previous email, but it is described slightly differently. If anything seems unclear, just ask.

While the four students who chose option B were in the minority, I certainly sympathize with their situation. With the postponement of the Makeup into next week, for many of you next week becomes incredibly pressured. The only ideal solution would be to invent a time machine and go back and undo the power failure. So far, the possibility of success on that project does not look good. I would, however, strongly urge the people who chose B to consider switching to C --- i.e., not taking the Makeup. With the 40%/15% weighting option, a low score on Quiz 2 will not be much of a detriment to your final grade.

In any case, best wishes for those who are taking the makeup.

— Alan Guth —

**FRI 11/30/2012: Query about the Quiz 2 Makeup**

In class today we had some discussion about
what to do about the cancellation last night of the Quiz 2
Makeup. I did not want to finalize any decision until I had
given each of you a chance to tell me in private what you would
prefer. In particular, I had the worry that there may be some of
you who studied for the makeup and feel that you deserve to be
rewarded for that study, as promised.

So, if you don't personally care about the
Makeup, you can ignore this email. If you do care, I would like
you to email me today, by 8 pm, to tell me what you think.

It was suggested in class that the final exam
could somehow be used in a way that incorporates the purpose of
the makeup. I said I would think about that, and see if I could
come up with a proposal. Since the final is only three hours,
and the makeup had been planned for two hours, I don't think it
works for the final to contain a subset of problems that are
intended as the Quiz 2 Makeup. The best problems for a final
exam are problems that incorporate a variety of skills from the
term, and I don't want to move too far away from that. So, I
would like it to be the final exam as a whole that has the
possibility of compensating for a low grade on Quiz 2.

So, let me offer the following proposal: For
students who do better on Quiz 2 than on the final exam, there
will be no change in policy: each quiz will count 20%, the final
will count 35%, and the homework 25%. But for students who do
better on the final, the final will count 40% and Quiz 2 will
count only 15%.

If the Quiz 2 Makeup is given, which depends
on the feedback I get from you, then the proposal becomes a
little more complicated. For any student who does not take the
Quiz 2 Makeup, the proposal would be as described above. For
students who take the Makeup, their grade would be the higher of
the grades resulting from the original makeup plan, or the
proposal described above (using the original Quiz 2 grade).

I plan to carry out the above proposal, unless
I hear objections from you.

In thinking about this proposal, remember that
I have said all along (see Problem Set 2) that we will push
students above borderlines in selected cases, where students
whose grades have improved significantly during the term, and
students whose average has been pushed down by single low grade,
will be the ones most likely to be boosted. The proposal above
is a quantitative version of the policy announced on Problem Set
2. We would still look at individual cases and make further
adjustments (upwards only) for cases that seem appropriate.

For those of you who want to tell me your
opinions about what we should do about the Quiz 2 Makeup, let me
suggest a few options, that you can name by letter. But you
should also feel free to suggest anything you want.

Option A: I studied for the Makeup Quiz, and I
would like to take it next week, under the original plans.

Option B: Since there are so many things going
on next week, I would like to cancel the Makeup Quiz. However, I
would feel obligated to take it if it were offered.

Option C: I would like the Makeup Quiz to be
cancelled, and if it is offered I would choose not to take it.
Instead I would settle for the proposal described above.

As I said, if you have other suggestions,
please just make them.

If there are any students who choose A, I
think that they are only asking for what they have been promised,
and I would want to carry through on that. I would of course
keep identities private, but I will let the whole class know
whether or not one or more students are taking the Makeup.

Sorry for this complicated mess. (I didn't
cause the power failure!)

IMPORTANT: My regular email address,
guth@ctp.mit.edu, is not currently working. Somehow the
Laboratory for Nuclear Science computer system has not yet
recovered from yesterday's power failure. So, please respond to
guth@mit.edu.

— Alan Guth —

**THURS 11/29/2012: Quiz 2 Makeup postponed**

Due to the power failure in Cambridge, it
seems that we have no choice but to postpone the Quiz 2 Makeup
until next week. I'll get back to you tomorrow to let you know
when and where it will take place.

If any of you want to reach me soon, use
guth@mit.edu instead of guth@ctp.mit.edu, as the latter email
system has been squelched by the power failure.

Enjoy the dark!

— Alan Guth —

**THURS 11/29/2012: Logistics for Quiz 2 Makeup**

Just a reminder that Quiz 2 Makeup will take
place today, Thursday, November 29, from 7:30 to 9:30 pm, in the
same place as the other quizzes, Room 32-144. The coverage of
the quiz will be exactly the same as Quiz 2. If you have a
conflict, you should contact me, and we'll try to arrange for you
to take the quiz on Friday.

On Friday (November 30), there will be lecture
as usual, and I will also have an office hour at the usual time,
4:00 pm.

— Alan Guth —

P.S. The ground rules for the quiz were
described in an email sent 11/20/12:

All students whose grade was less than 75% are invited take the quiz. If your grade on the Makeup is less than your original grade, you keep your original grade. If your grade on the Makeup is higher, then your Quiz 2 grade will be replaced by the average of the two grades, capped at a maximum of 75%. The test itself will be similar to the original Quiz 2, but just a little shorter. The original Quiz 2 was effectively 4 problems (3 + 2 short ones), and the makeup will probably be the equivalent of 3 problems. It will also include one problem that is taken verbatim (or at least almost verbatim) from the problem sets. The goal of the Makeup is to give you motivation to study this material some more, and to give you an opportunity to raise your grades. |

**SAT 11/24/2012: Problem Set 9 is Posted**

Problem Set 9 is now posted.

The good news is that it is not due until
Monday, December 3. I decided that it would be moderately insane
to have the problem set due the day after the Makeup Quiz.

The bad news is that we cannot postpone
Problem Set 10, since the term is ending, so it will be due the
following Friday, December 7.

— Alan Guth —

**WED 11/21/2012: Quiz 2 and Solutions Are Posted**

Sorry for the delay, but Quiz 2 and its solutions are now
posted. Problem Set 9 will be posted soon.

— Alan Guth —

**TUES 11/20/2012: Quiz 2 Results, Total Grades, Quiz 2 Makeup**

The Quiz 2 results are now posted on the
Stellar website, and the histogram of grades with estimated grade
cuts is posted on the web.mit.edu 8.07 website, under Exams. The
solutions are not yet ready, but will be soon.

As I told you in class yestereday, the results
of Quiz 2 were very disappointing. The class average was only
55.2, compared to a class average of 73.9 on Quiz 1. The
standard deviation was 23.6, which is unusually large. The
histogram shows a very wide range of grades, from 9 to 100. On
Problem 1, which was taken from Problem Set 8, the average score
was only 61%.

To give you a better idea of how things stand
as of now, I have computed interim total grades for each of you,
which are posted on the Stellar website. There is a histogram of
these grades, with estimated grade cuts, on the web.mit.edu 8.07
website, under Exams. The interim grade was calculated as 0.75
times the quiz average plus 0.25 times the problem set average.
The problem set average is 100 times the total number of points
earned, including extra credit, divided by the total points
possible, not counting extra credit.

Since the grades on Quiz 2 seemed too low to
ignore, we will be offering an optional Quiz 2 Makeup, on
Thursday evening, November 29, 7:30 - 9:30 pm. All students
whose grade was less than 75% are invited take the quiz. If your
grade on the Makeup is less than your original grade, you keep
your original grade. If your grade on the Makeup is higher, then
your Quiz 2 grade will be replaced by the average of the two
grades, capped at a maximum of 75%. The test itself will be
similar to the original Quiz 2, but just a little shorter. The
original Quiz 2 was effectively 4 problems (3 + 2 short ones),
and the makeup will probably be the equivalent of 3 problems. It
will also include one problem that is taken verbatim (or at least
almost verbatim) from the problem sets. The goal of the Makeup
is to give you motivation to study this material some more, and
to give you an opportunity to raise your grades.

Unlike the regular quizzes, the Makeup Quiz
will not cause lecture to be cancelled the following day.

In studying, I would recommend that you make
real sure that you understand the homework problems. I often
tell students that they should imagine that they are sitting next
to the dumbest student in the world, and that it is your job to
patiently explain exactly why each step is done the way it is.

And you should also come to class, and take
full advantage of the staff office hours. I remind you that
Ahmet Demir has office hours 4-5 pm on Tuesdays and Wednesdays,
in Room 8-316; Prof. Chen has office hours from 6-7 pm on
Thursdays, in his office, 24-033D, and I have office hours on
Fridays at 4 pm, in Room 8-308.

— Alan Guth —

**FRI 11/16/2012: No class or office hours today; Problem Set 9**

As we did with the last quiz, we will not have a lecture
today, the day after the quiz. I will also not be holding office
hours today, as I will be grading the quiz (with Ahmet and Prof.
Chen).

Problem Set 9 will appear this weekend. It
will not be due until Friday, November 30, due to the
Thanksgiving break.

Best wishes,

— Alan Guth —

**THURS 11/15/2012: Reminder about Quiz 2 Time and Place**

I just thought that it might help to remind you that Quiz 2
will take place tonight, Thurs November 15, at 7:30 pm - 9:30 pm,
in Room 32-144 (the same room as Quiz 1).

Good luck!

— Alan Guth —

**TUES 11/13/2012: Review session this evening**

There will be a review session for Quiz 2, tonight at 7:00
pm, led by Ahmet Demir.

Unfortunately, I failed to arrange a room! Sorry about
that. So we are going to start with the hope that the room used
last time, 26-310, will be available tonight. If it turns out
not to be, Ahmet will look for a nearby room and put a sign on
26-310 to let you know where to go.

I trust that the review session will go well, and I will see
you in lecture tomorrow.

— Alan Guth —

**MON 11/12/2012: Formula Sheet and Practice Problems are posted**

I have finally finished the formula sheet(s), now up to 10
pages. They are posted on the 8.07 website under "Exams". I
have also posted a set of practice problems and solutions from
Fall 2003, when Prof. Bertschinger was in charge of the course.

For the practice problems, I might mention that I consider
the wording of Problem 5 to be ambiguous. Where it says "Charges
are flowing in the e_y direction," I would say "Charged particles
are moving in the e_y direction."

The formula sheet is intended as a summary or checklist of
what you are expected to have learned. So, I recommend that you
look it over carefully and brush up on any topics that don't seem
clear to you.

Best wishes,

— Alan Guth —

**MON 11/12/2012: Information concerning Quiz 2**

As you probably know, Quiz 2 will take place this coming
Thursday, November 15, 7:30 - 9:30 pm, in Room 32-144, the same
place as last time.

There will be a review session for the quiz, led by Ahmet
Demir, tomorrow (Tuesday) evening at 7:00 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 Problem
Set 8 were posted this morning.
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 6, 7, and 8, and
correspondingly Chapters 4, 5, and 6. We are skipping the
polarizability tensor mentioned on pp. 162-163, and in Chapter 6
we have not yet talked about Sec. 6.4.2, Ferromagnetism.
This time I will be putting one problem on the quiz that
will be taken verbatim (or at least almost verbatim) from
Problem Sets 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.
I am still working on the formula sheet, which should be out
later today. I have also located a quiz from a prior year that
makes a good practice quiz for us, but I am still trying to
contact the instructor to get permission to post it.
Good luck on the quiz. I will see you on Wednesday.
— Alan Guth —
**

**TUES 11/6/2012: Problem Set 7 Solutions;
Comment on Problem 5, Problem Set 8**

First, I want to point out that the Problem
Set 7 Solutions have now been posted.

Second, I have a comment about Problem 5,
Problem Set 8. The problem has 4 parts, which are all related.
The best order in which to do them depends on the method you
choose to use, so you should not feel obligated to answer them in
the order given. (As far as this course is concerned, you should
never feel obligated to answer questions in the order in which
they are given.) In this case, I would probably do part (c)
first, but there are different ways to attack the problem.

— Alan Guth —

**SUN 11/4/2012: Problem Set 8 posted**

I just wanted to let you know that Problem Set 8 is now
posted. It will be due next Friday at 6:00 pm, as usual.

— Alan Guth —

**FRI 11/2/2012: On Problem Set 7 due
today, skip Problem 6 **

I announced this in class on Wednesday, but I
forgot to also put it into an email. If you have already done
Problem 6, there is no harm in submitting it with Problem Set 7,
but it will not be graded. Please save a copy that you can turn in
next week with Problem Set 8.

Have a good weekend.

— Alan Guth —

**TUES 10/30/2012: Revised version of Problem Set 7**

I have just posted a revised version of
Problem Set 7, fixing two misprints, both in Problem 7. In
Eq. (7.8), in the second term of the second line, the argument of
phi should be the zero vector, and not the r-vector. Also, after
Eq. (7.11), the equation d^3x = r^2 dr sin theta d theta d phi
was mistyped.

See you tomorrow,

— Alan Guth —

**MON 10/29/2012: Problem Set 6 Solutions and Class Contact List posted**

I wanted to let you know that Problem Set 6 Solutions have
been posted, in case you want some reading during our hurricane
day off. I really do recommend that you read the solutions, by
the way, even if you already know how to do the problems. We've
put a lot of work into trying to make them clear and useful. I
should warn you that the posting is perhaps premature --- for
some reason my staff has been slow in getting back to me to
confirm that they like the solutions. But I wanted you to have
access to them today. There is even a chance that when I discuss
the grading with the grader, we might change the spot-grading
choices. I'll of course let you know if that happens.

I also wanted to let you know that the class
contact list is posted, and students in the class should be able
to access it with their MIT certificates. I would urge all of
you to put yourselves onto the list --- why hide from your
classmates? For your convenience, I'll paste below a copy of the
contact list questionnaire.

And enjoy our unexpected break!

— Alan Guth —

*****************************************************************

QUESTIONNAIRE:

Name:

Email:

Phone (leave blank if you never answer it):

Living Group:

Comments:

Do you have any objections to my posting your
photo with the class contact list? Yes or No?

(If you give me your permission, I believe
that I have photos of all of you from the registrar. If you
would prefer that I post a different photo, or if you are
not officially registered, then feel free to attach a photo
to your email.

*****************************************************************

**SAT 10/27/2012: Problem Set 7 posted**

I just wanted to let you know that Problem Set 7 is now
posted. It will be due next Friday at 6:00 pm, as usual.

— Alan Guth —

**THURS 10/25/2012: Class contact list**

As I mentioned in class a few weeks ago, I
would like to set up a class contact list. (Sorry for the delay,
but I have been a bit overwhelmed this term.) I think that
classes are more fun and productive when students know each other
and work together. To make it easier for this to happen, I have
found it useful to set up a class contact list on the web. The
goal is simply to make it easier for you to find each other.
This could lead to regular meetings to work on homework in
groups, or maybe just to occasional conversations. Don't feel
that you have to be interested in a homework group to sign up.
If you want other students to know who you are, that's reason
enough. If you are interested, please enter the information that
you would like posted on the form below, and email it back to me.
The web page will be visible only to other students in the class.
Participation is completely voluntary, so you can skip this if
you want, but I would encourage you to put yourself on the
contact list.

There is a place for comments, which may seem
a bit vague. You can put whatever you want, including nothing at
all. You might indicate whether you are looking for a study
group, or just looking for occasional contact when the problems
are difficult. You might be inspired by some samples from the
past:

"I start psets early, available most evenings from 4pm, also 1 to 2:30pm on T,Th. Like ice cream." | |

"I'd like to start problem sets at least a little early. I live in Boston, but I have a car." | |

"Usually like to do pset for 8.07 on wed or thurs." |

**I might add that if you send something and then don't like the way it looks, you should feel free to send me corrections, or ask me to take it down altogether. I will act on your requests as quickly as I can.**

Best wishes,

— Alan Guth — *****************************************************************

QUESTIONNAIRE:

Name:

Email:

Phone (leave blank if you never answer it):

Living Group:

Comments:

Do you have any objections to my posting your photo with the class contact list? Yes or No?

(If you give me your permission, I believe that I have photos of all of you from the registrar. If you would prefer that I post a different photo, or if you are not officially registered, then feel free to attach a photo to your email.

*****************************************************************

Best wishes,

— Alan Guth — *****************************************************************

QUESTIONNAIRE:

Name:

Email:

Phone (leave blank if you never answer it):

Living Group:

Comments:

Do you have any objections to my posting your photo with the class contact list? Yes or No?

(If you give me your permission, I believe that I have photos of all of you from the registrar. If you would prefer that I post a different photo, or if you are not officially registered, then feel free to attach a photo to your email.

*****************************************************************

**THURS 10/25/2012: 8.07: Grade histogram for Quiz 1; grading errors grading policy**

Last evening I posted a histogram of the Quiz
1 results, so that you can see where you stand. On the histogram
I marked an estimated letter grade scale. As it says in the PDF
file, "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."
I don't grade with any fixed distribution of A's, B's, etc.,
since I want to allow for the possibility that everyone deserves
an A. So I have to rely on my own estimates, with advice from
Prof. Chen and Ahmet Demir, about how hard the quiz actually
was.

We have tried to grade carefully,
consistently, and fairly, but I will always admit that there are
possible errors. So if you feel that your paper was misgraded,
we will be happy to reconsider and try to straighten it out.
Prof. Chen graded problems 1(c) and 2, Ahmet Demir graded
problems 1(a), 1(b), and 3, and I graded problem 4. If you are
not sure about why points were taken off on your quiz, feel free
to ask me, or Prof. Chen or Ahmet. Prof. Chen, Ahmet, and I all
have the authority to raise your grade for any of the problems if
we think it is justified. If it is a matter of deciding how much
partial credit an answer is worth, we will very likely refer you
to the original grader, since consistency is an important issue
for such questions. If you speak to Prof. Chen or Ahmet and are
still not satisfied that your grade is fair, you should not
hesitate to talk to me. I am ultimately responsible for grading
in 8.07, and I want to make sure your grades have been fairly
assigned, and that you agree that they have been fairly
assigned.

What I said above about grading applies also
to the grading of problem sets. I should have said this earlier,
but if you feel that there may have been grading errors on any of
your problem sets, you can talk to Prof. Chen, Ahmet, or me. And
if you are not satisfied with the outcome of any such
conversation, please bring it up with me.

For those of you on the left side of the
histogram, work harder but do not give up hope. This quiz counts
20% of your grade, with homework counting 25%, with 20% for the
second quiz and 35% for the final exam. So there is plenty of
opportunity to bring up your grade. Furthermore, I don't grade
strictly by the averages. No student will get a grade lower than
the numerical average implies, but, as I described in the Problem
Set 2 Solutions, at the end of the term Prof. Chen, Ahmet, and I
will look at each student's grades individually, and we might
decide to give a higher grade to some students who are slightly
below a borderline. Students whose grades have improved
significantly during the term, and students whose average has
been pushed down by single low grade, will be the ones most
likely to be boosted. So, if you did badly on Quiz 1 but plan to
do better for the rest of the course, you will be a prime
candidate to have your grade boosted if it is close to a
borderline.

Finally, for those who did badly on the quiz,
I have a few platitudes, that maybe are worthwhile. The problem
sets are a good tool for making sure that you really understand
things. Work hard on the problem sets before you hand them in,
and when the solutions come out, go over them carefully. We have
put a lot of work into making these solutions useful, even if you
have already found the right answer. Make sure that you
understand not only what procedure is used to solve each problem,
but also how one justifies that procedure. I often urge students
to go over problems while imagining that you are sitting next to
the dumbest student in the world, and that it's your job to
explain to this student exactly why each step is done the way
it's done. And of course, if you have trouble figuring out these
things yourself, take advantage of office hours! Ahmet Demir has
office hours on Tuesdays and Wednesdays, 4:00-5:00 pm, in Room
8-316. Prof. Chen holds office hours from 6:00-7:00 pm on
Thursdays in his office, Room 24-033D. My office hours are on
Friday 4:00-5:00 pm, in Room 8-308. And if you can work with
somebody else in the class, or a small group, that can be a big
help.

Best wishes,

— Alan Guth —

**WED 10/24/2012: Revised version of Problem Set 6**

I have just posted a revised version of
Problem Set 6, fixing two misprints. In Problem 1, I inserted a
preposition ``to,'' which was missing in the original October 21,
2012 version. In Problem 6, the phrase ``with side larger than
$2a$'' was replaced by ``with side larger than $2R$.''

Sorry for any confusion.

— Alan Guth —

**THURS 10/18/2012: Quiz 1 and Solutions are posted**

Quiz 1 and the Quiz 1 Solutions are now posted
in the Exams tab of the website. Your grades should get posted
to Stellar tomorrow evening some time, and you will get your
papers back at the recitation sections this week.

— Alan Guth —

**SUN 10/21/2012: Problem Set 6 is posted**

I just wanted to let you know that Problem Set
6 is posted, and will be due this Friday at 6:00 pm.

I hope to have solutions to the quiz posted
later today, and solutions by tomorrow.

— Alan Guth —

**THURS 10/18/2012: Formula Sheet is posted**

The formula sheet for the quiz is now posted.
A copy of the formula sheet will be printed as part of the quiz.
I know that there is not much time left, but I tried to make the
formula sheet pretty thorough, so that you could use it as a
checklist of topics that you should understand. So, if possible,
try to go over the formula sheet before the quiz.

Best of luck for the quiz.

— Alan Guth —

**WED 10/17/2012: Final Lecture Notes 9 finally posted**

Finished the final version of Lecture Notes 9,
"Traceless Symmetric Tensor Approach to Legendre Polynomials and
Spherical Harmonics," and they are posted on the Lecture Notes
tab of the website.

Formula sheet coming.

— Alan Guth —

**TUES 10/16/2012: Test from 2001 is posted; Review Session reminder**

This morning I posted the first 8.07 test from 2001 (when
the class was taught by Barton Zwiebach) with the solutions, on
our website under "Exams". The test had four questions, three of
which (#1, #2, and #4) are relevant to our upcoming quiz. The
fourth is about magnetic fields. The 2001 test was given at the
end of October, so it is natural that it includes a little more
material.

I also want to remind you about tonight's review session
with Ahmet Demir, from 7pm until about 9pm, in Room 26-310.

I'm still working on the extension of the notes on traceless
symmetric tensors, and then I will also put together a formula
sheet.

See you tomorrow,

— Alan Guth —

**MON 10/15/2012: New postings and review session**

Tonight I posted the Problem Set 5 Solutions, and also a
preliminary set of lecture notes (Lecture Notes #9) on the
"Traceless Symmetric Tensor Approach to Legendre Polynomials and
Spherical Harmonics." I intend to enlarge these notes, hopefully
by Tuesday morning, but maybe not until Wed. I will also be
posting a formula sheet for the exam.

Sample quizzes are hard to come by, especially since in
recent years Prof. Belcher has been lecturing this course with a
rather different ordering of the material. I did, however, find
a test from 2001, when Prof. Zwiebach was teaching the course,
which I will post later today under Exams. The test has 4
questions, one of which is on magnetic fields, which you should
ignore. But there are three problems on electrostatics which
look interesting. I will post the solutions as well, but I
recommend that you try the problems before looking at the
solutions.

On Tuesday evening Ahmet Demir will hold a review session
for the quiz, from 7 pm until about 9 pm, in Room 26-310.

Quiz 1 will be on Thursday evening, from 7:30 - 9:30 pm, in
Room 32-144.

See you later.

— Alan Guth —

**THURS 10/11/2012: Recommended: session tonight on Higgs Boson**

I just wanted to make a recommendation that you might be
interested in the session tonight, at 8:00 pm in 26-100, about
"The Discovery of the Higgs Boson: The Final Missing Piece?".

The speakers are Professors Edward Farhi, Jesse Thaler,
Christoph Paus, and Markus Klute, and the description is as
follows:

What is this "Higgs Boson?" What does it mean? Come and find out about this elusive particle and what its apparent confirmation means to science and future research. Postulated in the 60s and included in the Standard Model of particle physics, the Higgs Boson particle remained the last unknown in the set of predicted particles that includes quarks and leptons. Learn about the 40-year search from those in the forefront of the discovery and understand the implications of this breakthrough. |

— Alan Guth —

**THURS 10/11/2012: Problem Set 4 Solutions and Lecture Notes 8 are posted**

I just want to let you know that Problem Set 4
Solutions are now posted on the website, and I also posted
Lecture Notes 8. These are a write-up of the part of the lecture
that I did not get to yesterday, about the traceless symmetric
tensor expansion and how to relate the terms to the standard
spherical harmonics.

— Alan Guth —

**THURS 10/11/2012: Typo and clarification for Problem Set 5**

Yu-An Chen pointed out to me that I misprinted
the factor that appears on the right-hand side of Eq. (4.12) on
Problem Set 5, in Problem 4(c). The correct factor is the
inverse of the one that originally appeared. I have posted a
revised version. Thanks, Yu-An!

I was planning to send a message in any case,
to indicate some flexibility in the answers to Problem 4. I
would like you to learn how to use traceless symmetric tensors to
describe angular functions. If you are starting from scratch, I
think that this is the easiest approach. If you already know
spherical harmonics, I think that you will find that the
traceless symmetric tensor approach is a useful addition to your
body of available techniques. However, I generally hate the idea
of insisting that anyone use some particular method for solving
problems. So, in Problem 4, where you are asked to use the
traceless symmetric tensor method to find Y_{31}, Y_{ll}, and
P_4, I will ask the grader to accept any valid answer, whether it
uses the traceless symmetric tensor method or not. Of course
looking up the answer in a book is not sufficient for credit, nor
is it sufficient to name a method and then write the answer ---
you have to show the calculation in full. But it is okay to
start with any general formula for the spherical harmonics and/or
the Legendre polynomials, and then to calculate the special cases
that are requested. I still recommend that you use the traceless
symmetric tensor method, but I'll accept the principle that it is
a free country.

— Alan Guth —

**WED 10/10/2012: Update on office hours, review session, and the quiz **

I want to make sure that everyone knows that we will have
our first quiz on Thursday, October 18, a week
from tomorrow, from 7:30 to 9:30 pm, in Room 32-144 in the Stata
Center. There will be no class on Friday, October 19.

Ahmet Demir will be holding a review session on Tuesday
evening, October 16, from 7:00 pm to
approximately 9:00 pm, in a room that is still to be found.

As a reminder, Ahmet Demir has office
hours on Tuesdays and Wednesdays, 4:00-5:00 pm, in Room 8-316.
Prof. Chen holds office hours from 6:00-7:00 pm on Thursdays in
his office, Room 24-033D. My office hours are on Friday
4:00-5:00 pm, in Room 8-308.

— Alan Guth —