Exam 2 post-mortem

I will have the exams graded by Wednesday's class. You can find the exam and partial solutions here. I think we'll probably spend a good deal of that class period going over the exam problems and common misconceptions. It was a hard exam, no question, and we are not in a rush to move on, so we can afford to spend a little time thinking about it.

For now, don't freak out. I'm not going to fail any of you based on a quick glance of the exams, and the partial credit will be generous. It is simply much easier for me to gauge your understanding with very hard problems than very easy ones - if you got everything right, I'd have no way of seeing the limits of what you've learned so far. So, focus on learning something from the exam for now, the grades will be better than you think.

Exam 2

You can bring in one sheet of paper with whatever you want on it to the exam, and I will provide another sheet with all the core formulas, constants, etc. Don't bother memorizing anything.

Exam 2

The coverage for exam 2 on Monday will be:

• potential due to charge distributions
• potential energy of charge distributions (e.g., crystals)
• dc circuits (batteries, resistors; multi-loop circuits)
• capacitors and RC circuits

Nothing on magnetism. I'll give you a formula sheet, no need to memorize anything. No problems involving transistors or op-amps, and no magnetism. Similar to the homework problems, but less involved ("easier") ... more details to follow over the weekend.

The exam will be designed to take an hour, but I'll give you 1hr50m.

Exam 1

EDIT: I probably cannot stress enough that I mean this week.

Just under half of you have scheduled your oral exam so far. If you haven't requested a time yet, you should do it soon ... Here are the times left:

Wed: 2:30-4pm, 5-6:30ish pm
Thurs: pretty well tied up in an all-day meeting.
Fri: 10-10:45, 12:30-1:45, 4-5, 5:30-6, after 6:30 if you really want to

It will not take more than 15-20min for the oral exam. You can use your book for reference (though if you thumb through it too long I may look askance at you). The topics are, by section in the book,

22.2 Electric fields
22.4-7 fields of various charge distributions
22.9 dipoles in electric fields
23.4 Gauss' law
23.7-9 Gauss in various situations

Nothing we'll cover tomorrow (Wed) is on the exam, and nothing from our lab sessions. Additionally, simplified versions of HW problems are fair game. And I do mean simplified - there won't be any complicated integrals to work out. Mainly, you will have to set up the problems and demonstrate to me that you know what you're doing more than actually doing all the calculations in detail. For example, setting up the integral to find the field of a line charge, but not having to perform the integral.

I will have a set of 8-10 problems, all of essentially equal difficulty, and each of you will have to demonstrate knowledge of two of them for me. If you get really stuck at any point, I'll help you along in the problem (though at the cost of a few points).

I'm fairly certain most (all?) of you have not had an oral exam before, but it will be relatively painless, and most of you will do very well. If you understand the material so far and the homework solutions, you'll be fine. Don't get lost in mathematical detail when studying, focus on what is going on in the problems and how to set them up.

Exam 1

As I mentioned in class today, we'll do the first exam as an oral question session. It will take only 15-20 minutes. The format will be more or less that I pose two problems to you, and you discuss them and work them out on the board in my office. Before the examinations start, I will give a list of topics that are 'fair game' and some example problems. They will not be as hard as the homework problems, certainly, more at the level of example problems in the textbook. You will be allowed to use your textbook for reference.

Each of you will need to schedule a 20 minute block with me next week Wednesday or Friday to make this happen. (If this is totally impossible, I can do a couple on Thursday as well.) Here are my free times on Wed and Fri next week:

Wed 7 Sept: 1pm-6pm
Fri 9 Sept: 12-3pm, 4-6pm

When you get a chance, send me an email with a proposed 20 minute block in those windows and I'll let you know if it is taken already. If you cannot make any times within these blocks, let me know your free times on Wed, Thurs, or Fri and we'll see what we can work out.

More details on the exam itself this weekend ...

Christmas comes early

You can skip one problem on the final exam, since it seems to be plenty time-consuming at 7 problems. Which one you skip is up to you, they all carry equal weight.

Actual hints (I)

I really think exams should be a learning experience. With normal exams, this should be so: you get to see the solutions and discuss. With finals, not so much. This is one more reason I like the take-home final: I can try to teach you a few last things, and I don't feel bad coaching you a little along the way, since most of the problems are brand-new for you. I'll be around campus until Thursday afternoon if you want to drop by. Anyway, some hints:

#1. Use the integral form of Faraday's law to get the first correction to the E field. Take a square contour which (looking from the sides) runs down the center, parallel to the plates, up the right side, and back to the center.

The original field E will have no contribution to the integral of E.dl around the line contour. The new contribution will. If the new contribution is due to time variation in B, you know its symmetry ... so all but one side of the square will give zero to the integral. Put another way, the flux of B only contributes to the new correction to the E field, so you can find the correction directly. After the exam, I'll tell you where I found this; brilliant discussion.

More massive hints to follow on this one later in the week; it is subtle.

#2. Build it out of rings. You know the field from a ring.

#3. If the network is infinite, one more element makes no difference at all. Terminate it at some arbitrary place, and the rest of the network continuing on can be represented by some Req. That Req has to be the same wherever you terminate, so pick some easy places: after just one instance of R1 and R2, and after none. The two have to give the same Req.

Next, imagine you're in the middle of the network somewhere. Now you can have a single R1 and R2 terminated on *both* sides by Req if it is an infinite network. Now you have a simple 4 resistor circuit; find the voltages. If the ratio holds for two arbitrary nodes like this, it holds for all.

#4. Download the final again so you get the correct equations without typos. Apply the curl equations for E & B in free space ... that's about it. Apply the divergence equations as a trivial sanity check. w/k should be the velocity of propagation, right? Energy density can be had from the field amplitudes.

#5. Just work it in one dimension until part c, it makes no difference really. Two dimensions if you like, one component of E is important, the other just gives a torque. For the last part, generalizing to three dimensions should not be too hard if you're careful.

#6. The chain rule thing is key: d(fg) = f*dg + df*g. Also note that at certain points you'll want to write v in terms of gamma (to simplify the final result) and gamma in terms of v (to do an integral).

#7. Force is the gradient of the potential energy (with a minus sign). Write the energy of the capacitor for fixed charge ...

#8. See previous post. You may neglect atmospheric refraction, as it is essentially the same at the top and bottom of the cherry picker.

Clarifications

There were a couple of typos on number four: the argument of the sin functions should have a + sign, not a - sign, and the B_z component should be divided by c. The posted version of the exam has been corrected.

Here are some clarifications I sent one of you by email, for all to see:

In the formulas for problem 1, what does the i term indicate? Also, I
think the little e is Euler's number, and just wanted to check and
make sure.

It is good to be certain before you start. The "e" is indeed Euler's number, the base of the natural logarithms. The "i" is the imaginary unit, so the formula for E is just writing a sine wave in complex exponential notation. Check the chapter in Griffiths on EM waves for similar notation & problems.

On problem 4, I'm not sure what the k and x stand for in the wave
equations. Also, I think you left out the units you wanted the energy
density in.

Here k is the wavevector, which relates to the spatial periodicity of the wave (k = 2pi/lambda). Omega is the angular frequency. You can basically treat them as constants. Since these are wave equations, you can guess that omega/k should give the velocity of the wave ... The energy density should be in joules per cubic meter, or energy per unit volume.

For problem 5, are we supposed to assume the dipole is in a specific
orientation for the first two parts? It seems as though you meant for
it to be perpendicular to the z axis. I'm assuming total force for
part (a) is not the same as net force, because that would depend on
the direction of the field. Also, I'm not sure to what distance the
distance d in part (b) refers.

First, the distance d is the separation of the two charges, I should have noted that.

You can assume that the dipole is along the z axis, so the two charges are sitting on the z axis with the origin at the center of the two charges. You can also let the E field be along the z axis if you like. It isn't perfectly general then, but close enough; just work the first parts of the problem as if it is one dimensional, and generalizing for the last part is not hard.

There need not necessarily be a net force for the first part ... For the second part, you are to pretend that the E field is slightly different at one charge than the next. For instance, say E is a little bit bigger at the positive charge sitting at z=(d/2) than at the negative charge at z=(-d/2). You could say then that the field at the negative charge is just Eo, and the field at the positive charge is roughly that plus the gradient of the field times the separation distance: E = Eo + (dE/dz)*(d). If the separation distance d is small enough, it is pretty good to approximate the variation in the field as a constant plus distance times a gradient.

For problem 8, I have a certain vision for how this date would ideally
play out, and want to check that it is appropriate. I imagine that
the couple starts on the level of the earth, then, at the moment the
top of the sun disappears over the horizon, the cherry picker lifts
them until the bottom of the sun is level with the horizon. Also,
should we take into account diffraction due to the atmosphere?

You are correct, they wait until the sun is level with the horizon and then rise up until they are again level with the sun & the horizon. You can ignore the atmospheric refraction, since we already did a problem on that. You can also assume that the cherry picker is sitting in a little hole, so they start out exactly at the ground level.

Ok, go ahead and look here if you like, but your solution should be a bit more thorough and elegant.

I didn't recognize this until I got into the problem. On problem 3,
to which nodes exactly does "successive nodes" refer? Is it nodes
across the top, from top to bottom, across the bottom, or something a
bit more specific?

If you move from left to right, it is probably easiest to say that a node starts at the left of an R1, and the next node starts after the R2 to its right. It doesn't matter too much, so long as you are consistent and move from left to right (along the top) as the figure is drawn. More hints on this one later. As an aside, this sort of circuit is useful for quick & dirty digital-analog conversion. Think about that: power of 2 ratio of voltages at every node ... just meant for binary.

Final Exam

Ok, a couple of days later than planned, but here it is. You probably will not like it. Do not delay in starting, it is not something you can bang out in a couple of hours over coffee.

I will post hints over the next days on various problems, with increasing helpfulness as the deadline gets closer. Feel free to ask for clarification if you aren't sure how to get started. They are not easy problems, but I think you can handle them. The final exam is due back to me by 5pm next Thursday, 10 Dec 2009.

You're allowed to use your textbook and notes (which includes posted solutions/notes from this page), and I would consider Wikipedia fair game, but random googling for answers is not. You will need to sign your exam, stating that you've played by the rules. A bit much, I know, but those are the breaks when you get a take-home exam ... anyway, with most of these problems you would not have much luck googling anyway.

Also, HW8 solutions are out. Exam III solutions should follow this weekend, since they might be of some utility for the final.

Also.

Next homework

Here's the exam you just took. It is also your next homework, due 20 Nov 2009.

Recall that you have an outstanding homework at the moment. It is OK if you turn that in on Monday.

Exam formula sheet

Here it is. Subject to some proofreading ...

Friday's exam

You're ready. Get some sleep.

If you don't believe me, and want to cram anyway, I'd spend some time on Ch. 7, sections 2&3 in Griffiths, and then probably review the sections on Maxwell's equations (sans vector potential).

You will be rewarded if you can quickly recognize what to do with Maxwell's equations when (for instance) given an E field. You will also be rewarded if you have subjugated div, grad, and curl in spherical coordinates (formulas given).

Finally, you will be rewarded with bonus points if you remember what I said about tensors on Wednesday. Specifically, conductivity tensors.

PS - If you are unsure what a question means, or how to go about it tomorrow, don't hesitate to ask. More than likely, I will be willing to clarify the problem a bit or give you a hint to get you started. Also, show and turn in all your work, even if you think it illegible or unimportant. Partial credit is key.

Exam III

As you are probably aware, exam III is this Friday. There will be five problems, you must solve any two. The topics are

• ac circuits
• relativity
• induction
• Maxwell's equations / EM waves

Obviously, one of these sections will have two problems, the others a single problem. Here's what you might want to study/reread before the exam:

• ac circuits - my PH102 notes
• relativity - PH102 notes, Griffiths 12.1 (all) and 12.3.1-2
• induction - PH102 notes, Griffiths 7.2
• Maxwell - Griffiths 7.3, 8.1, 9.2.1

The corresponding example problems in Griffiths and end-of-chapter problems in my PH102 notes are particularly worth reading through.

This is assuming that you have already read the relevant homework solutions on these topics, which are also helpful. The exam problems will not be as difficult as the usual homework problems, however.

Exam II

Here's the exam you took today. Note that two of the magnetism problems are example problems from Griffiths (Ex. 5.9), the third is from Purcell. Two of the circuit problems are from Purcell, the third is based on a Serway problem (ph106 textbook).

I hope to have solutions out on Wednesday, and you will get your graded exams back during Wednesday's class if all goes well. So far, it seems the results will be very good. The exam was much easier than the homework, and your performance seems to be commensurate ...

Exam II

Seriously:

• field due to a bunch of straight or circular wires (e.g., #8 here)
• dc circuits with batteries and resistors (e.g., #9 here)

Monday's exam

The exam will be low-key, and you should have plenty of time. Here's the basic format:

• six questions total
• three questions on circuits (dc; resistors and batteries only)
• three questions on the magnetic field from wires (straight or circular; superposition)
• answer any three of the six

I'll provide a full formula sheet, you're free to bring in one sheet of your own paper just as last time.

I think you can probably solve three problems and be done in less than 90 minutes, some of you certainly in about 60 minutes. They are not hard problems compared to the homework, and a few of them are drawn from PH102 homework in fact.

If you're cramming now, I would suggest reviewing the solution to the field from a finite segment of current-carrying wire, and the battery charging problem from Hw4. HW4 partial solutions will be out in a couple of minutes.

Today's circuit slides / oral exam

Here's what I presented today, along with some stuff we'll get to next time. Powerpoint format, I'll try and make a PDF later today just in case.

Also: good work on the circuit today. I was very happy that everyone got it to work within the allotted time! Wednesday, we'll try to add an amplifier to the output stage (i.e., the voltage on the resistor you probed with the scope) to make the thing more sensitive.

Lastly, if you want to schedule an oral exam to improve your Exam I score, here are some time blocks that are good for me. I can meet you in Gallalee or Bevill, whichever is easier, but I'll list my preference.

Tues: 12-5 (Bevill preferred)
Wed: 1-2:30 (Gallalee preferred)
Thurs: 12-5 (Bevill preferred)
Fri: 10-11, 12-1 (Gallalee preferred)

If possible, I would like to do the oral exams this week, or this coming Monday at the latest.

Exam I full solutions available.

Here they are. Let me know if you find any typos, or anything which could use further clarification.

You'll get your graded exams back on Monday.

Exam I and its (partial) solution

Find them here. I have solutions for problems 1 and 2, and the first two parts of 4.

I should have full solutions for 3 & 4 this evening, and you will get your exams back on Monday.

More last minute thoughts on the exam

UPDATE: I made corrections & additions to the HW3 solutions today, might be worth a last-minute check.

So I've actually made it now, and I think you will be fine. I am going to do the problems again myself just to be sure the timing is somewhat reasonable. A few of random thoughts:

• As promised, the exam has 4 problems, you can solve any 2.
  
• There are no terrible integrals involved. Just polynomials and so forth, no weird arctans or anything.
• For most of the problems, there are at least two straightforward methods of attack. This is on purpose, with the hope that you'll see one of them quickly.
• Two problems will favor those of you that remember the basics of mechanics, two problems will favor those of you that like the math.
• The binomial approximation is just about the coolest thing ever. Know when you can get away with it.
• There are no numbers on the exam (except things like pi and 2, possibly a 3). A calculator is not useful unless it happens to do symbolic math.
• It is fine with me if you bring an complex calculator that does symbolic math. The basic rules are no pc's, no cellphone calculators, no PDAs that have wireless communication capabilities.

Anyway: if you've been able to follow the homework so far, the exam problems will seem almost laughably easy. The only real issue is time pressure: you get about 20 minutes per problem, so

• Use your time wisely, and watch the clock.
• Don't get stuck on anything - if you find yourself stuck, see if you can make a simplifying assumption to move on (this might entail some lost points, but many less than not finishing the problem at all), or pick another problem
• In spite of the time pressure, spend a few minutes reading and thinking about all the problems before starting. Make sure you really know what is being asked, and have a physical picture in your mind before moving on. If you can't at least see the 'flavor' of the answer, math is probably not going to help.
• Please, please make sure you read the problems you choose to answer a second time, there are multiple parts to some of the problems.
  

I'll be up another couple of hours if you have questions.