HW7 miscellanea

Since we don't have class on Friday, I thought I'd post some HW hints. Keep in mind that the HW is due Mon 31 Oct at midnight, so we still have Monday's class to discuss the problems, i.e., I have not necessarily ruined your long weekend :-)

HW6 solutions

Here are some proposed solutions to HW6. The circuit construction questions have many possible solutions, so if yours does not look like mine, don't worry too much.

HW7 out, due on halloween, appropriately.

I don't think you'll like it at first, but we will do at least two of the hardest problems in class. Keep in mind that halloween is the Monday following Fall break.

HW 4&5 solutions

Long overdue, but HW 4&5 now have solutions. Have a look, this stuff will come back again, if nothing else on the final exam. Some of it before then.

HW6 is a beast in fact.

If you put it off until the last minute (i.e., right now) and tried to do it in one night, it isn't going to go well. You may want to ask for an extension, as it is likely to be given. This is important stuff, I'd rather you understand it a bit late than not at all. 

Clarification of HW6.1

One of you asked:

Dr. LeClair, I was curious about number one. The problem seems pretty straight forward, I would hesitate based on its straight forward reading even calling it a problem but I wanted to know more what you wanted to know from this problem and what you expected to see in our answers. Do you want us to do this purely on research and give you an answer that goes into detail on what we find, since you said, "Can you suggest ways in which two short coils or current rings might be arranged to achieve good uniformity over a limited region?" Or would you like to see a derivation that leads us to the final conclusion? My point being that I only found out what the answer is through researching and I want to know whether you would like to see me spit out a derivation to show that I know what I found is true, or would you like me to just explain where B is most uniform and why that is the case?

I guess to be really specific, a uniform field could be defined by stipulating that the spatial derivatives of the field along the axial direction vanish in the middle. Say z is the direction along the coils' axes, then dB/dz=0 and d²B/dz² = 0 halfway between the two for a very uniform field.

There is one special spacing of the coils that makes that true. So, call the distance between them (say) 2b, find the field at an arbitrary point z between them. Find the first two derivatives, and set both equal to zero at z=b. This will give you a value for b in terms of the coil radius R. Look at http://en.wikipedia.org/wiki/Helmholtz_coil for the actual construction and spacing.

So I guess ideally what I'd like to see is this - a condition that defines uniform field (derivatives zero) and a calculation that specifically finds the spacing for which it is fulfilled. I would probably give mostly full credit for researching the answer and providing a solution, but without a solid reason (i.e., derivation), it wouldn't be the full story or full credit.

Mid-semester project: fan rpm sensor

Wednesday, we'll start a mid-semester project: building an rpm sensor for a fan. Here is a rough description of the project and your expected deliverables. We'll talk about it more in class tomorrow, but it will be very free-form: I'll give you a problem to solve, a few suggestions, and see what you come up with (along with guidance along the way of course).

If you think about the last few labs we've done, and pay attention in tomorrow's lecture, a decent solution should present itself. You've already built all of the circuitry required as previous projects, the trick will be combining it all together. Similarly, you've already written the code you need (counting pulses), in principle. I have already done the project in one way, so it is workable using what we've studied.

I expect we will spend 3-4 lab sessions on this, but we'll go as long as it takes. Once this is done, we'll start longer projects of your own choosing, something that will take most of the rest of the semester to build up and fine-tune. (Maybe something like this?) Details on that to follow in a week or so ...

Condensor microphone

Today in class we talked about how one can build a microphone. Here are instructions on how to actually build a condensor microphone out of 'household' items. Basically like we said - one fixed electrode, one flexible, the sound (pressure variations) change the capacitance and generate an electrical analogue of a pressure wave (sound). 

Midterm grades

I'm about to post midterm grades. A couple of things:

• I am erring on the side of optimism with regards to your probable grade.
• The grades include HW1-4, Exams 1-2, and a lab grade of 100% for everyone since we haven't had any real reports due yet. (That changes Wednesday, however, you will have reports to do soon now that you know how to build stuff.)
• I am dropping your lowest homework. See first point.
• Some of you are missing homework sets, which is sort of a big deal with only 2 exams in. If your grade seems lower than expected, that may be why.
• If your grade seems wildly out of order, let me know - I can change things up through Wednesday.
• One of you missed the second exam. This is an even larger deal, and you should probably talk to me. It is not catastrophic, but not great either.

On Wednesday, I will show each of you your grade breakdowns, including what HW sets I might be missing from you, to make sure everything seems to be in order.

HW6 / Pulse height discriminator

On the homework, you're supposed to design me a pulse height discriminator, a circuit that detects when its input has gone above a certain threshold level. The simplest way one can do it is probably this, a single diode and capacitor. This circuit isn't great, though, since for one the threshold voltage is basically limited to the diode's forward voltage drop. That particular problem can be cured, but generally speaking, it is just not very flexible.

A much more elegant solution, like we talked about in class today, is to use a comparator. They're cheap, simple, and plentiful. This way you can make zero-crossing detectors (when does a signal change sign?) or peak detectors. The LM311 datasheet has some nice examples - look at the zero-crossing detector, and positive/negative peak detectors [pulse-height discriminator]. These circuits do basically what we want. [The LM110 in those circuits is just a 'follower' like we talked about today. All it does is makes its output the same as its input, so for the purposes of understanding the circuits, ignore it.]

So, why is this a homework problem? The rpm readout circuit you'll begin building next week will rely critically on this sort of circuit, so by the time you have to build it, you'll already have a working design ready. Details on that project to follow this weekend, we'll begin on Monday.

MIT circuits notes & more

Some nice slides & notes from MIT's intro electronics course. Might be good reference material for our upcoming mid-semester project.

Tomorrow / HW6

I think we should put off HW6 until this coming Wednesday (19 Oct), I don't feel like we've covered magnetism well enough yet. So, no HW due tomorrow.

As a result, tomorrow we'll do a little new material (Ampere's law, current loops & solenoids) and go over a few of the HW problems.

Why I was dressed up yesterday.

http://uanews.ua.edu/2011/10/teaching-award-winners-honored-at-ua-3/

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.

HW6 is out

I know you're excited.

Reference material / upcoming material

One quick thing, before you stop reading: we need to have another exam soon. We will postpone it until next week, even though I had nominally scheduled it for this coming Friday. Plenty of time, and I'd rather we get through a bit more material first.

Some time ago I wrote a short math guide for intro PH courses. You might find it useful, though it isn't as complete as I would like. Actually, you might find it more useful when you get to 300-level PH courses that use vector calculus fluently.

Also, I came across a great electronics text online from Texas Instruments geared specifically toward op-amps. We've covered enough material now that the 'Review' should make sense now, so if you want to do a little reading on what we're doing now, this is a good start. My own favorite reference is The Art of Electronics by Horowitz and Hill, which is in the Rogers library. Our coverage of transistors, signals, and op-amps has been based largely on their treatment. Great book if you can find a decently priced copy, highly recommended if you plan to continue fiddling with circuits.

For the next few classes, we'll continue our discussion of magnetism. Our focus is going to be calculating the magnetic field due to various distributions of currents and the effects of magnetic fields on moving charges and currents, without much regard to *why* moving charges create a magnetic field for the moment. We'll also cover permanent magnets a bit. Later, after we've gotten through induction and time-varying E and B fields, we'll return to the subject of why magnetic fields arise in the first place, which will require a crash-course in special relativity. For that, you might find my PH102 notes useful. Light on math by construction, but they cover special relativity, deriving B from E, and at least touch on most of the topics in PH126.

Tomorrow's lecture/lab

Having mastered the blinkenlight, tomorrow you'll build an amplifier/filter out of op-amps. Check it out.

We'll spend a little bit of the lecture-type period with me introducing new material, but the bulk of it on working out and discussing homework problems.