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.

Wednesday: more circuits

Though we are a little behind where I imagined we would be, we are ahead of where we have to be, so we'll spend the rest of the week learning how to build and analyze more complex circuits. We're almost far enough that I can let you design your own projects ...

Wednesday, we'll re-hash what we know of transistors and learn how to build a basic amplifier (on paper, for now) [slides I'll use]. We'll then focus our attention on comparators, a simple-yet-powerful device that compares two input voltages. This will serve as an introduction to feedback and basic logic circuits, which will let us build all sorts of neat things.  Such as a relaxation oscillator, which you will actually build in the lab [circuit]. We'll use it to make an LED blink periodically without any code at all. So far as circuits go, we only need to know about a few more components (inductors and op-amps primarily) before I'll just start turning you loose on projects.

Next week, we'll move on to magnetism and magnetic fields, which means back to more abstract things for a while. Lab-wise, next week we'll try to learn a bit more about coding for the Arduino. Once you have a bit of software knowledge to go with your hardware knowledge, we can do very neat things. You should start looking at some possible projects.

Wednesday's class & lab

Last time, we learned basically all we needed to know for analysis of steady-state dc circuits. Today we will put some of the rules we came up with into practice and learn a few more tricks for circuit analysis. We'll also add a few more elements to our toolkit - in particular, diodes and transistors - to go with the resistors, voltage & current sources we already know.

For the lab, you will be constructing one of two transistor-based circuits: an automatic night light, and a burglar alarm that senses when a door opens. For the former you will use a photoresistor or phototransistor as a light sensor, and for the latter you will use a Reed switch and a magnet as a motion sensor. Both circuits are derived from a very basic transistor-based current source, which we will analyze in class.

I've written some notes on transistor circuits, since you will not find them in your textbook. We will not go into great depth, just enough to learn how to make some neat and functional circuits. I you are an EE major, this will either be review or a preview ...

Notes for today's lecture

It won't be on the exam, but if you are curious to go through today's material on fluid dynamics at a bit more leisurely pace, I've written up some notes.

UPDATE: I did some cleaning up of the notes. I added quite a bit on fluid rotation (like what curve describes the shape of water going through a drain), and also added a few examples. Specifically, I showed how the Hall effect (current flow in the presence of a magnetic field) requires a tensor conductivity, and treated the case of steady flow through a cylindrical pipe. The latter is a rare example of an analytical solution to the Navier-Stokes equations (given a good number of reasonable assumptions), and quite practical.

The updated notes are in the same location linked above.

No, it is still not going to be on the final, it is just cool. ;-)

This week

Owing to popular demand, this week we'll cover relativity. This brings up two key points:

(1) Your next homework is out, and covers relativity. All problems are due this coming Friday.
(2) You'll want to read Ch. 1 of these notes, which cover relativity at the level we require. I'll try to have printed copies of that chapter for you tomorrow.

Monday's lecture should bring us all the way through time dilation and length contraction, while Wednesday's lecture will cover Lorentz transformations, spacetime diagrams, and energy & momentum.

Friday, we'll derive E from B and apply what we've learned to tie E&M together. For that, you should read section 6.1.2 in the notes linked above, which derives E from B for the special case of a point charge moving parallel to a current-carrying wire at constant velocity.

Magnetic Dipoles

This will come in handy next week when we get to the vector potential. For now, it contains the solution to one of your homework problems, albeit using a method we have not discussed yet ... still, it may help you set up the problem.

Some notes on electrical measurements

This is an unfinished document that is part of another project - the start of some notes on how to perform electrical measurements in general, and specifically on samples of real, live materials. After our next meeting, it might be of interest.

Basically, the more interesting part at the end shows you how to calculate the resistivity (or conductivity) of a conducting material from experimental data, the so-called 'four point probe' technique. Moreover, you can figure it out for conductors of various interesting shapes, like thin films, using very general symmetry-related arguments. We'll cover the necessary background in Friday's recitation.

If you're studying or planning to study anything materials- or device-related, you will see the four-point probe technique again. It is not hugely difficult, but not commonly covered in any depth, and usually just taken on faith. So, when you do see the four-point probe expressions again, you can smile and know that they are not, in fact, magic.

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.

Reading for next week

Next week, we'll start to discuss circuits, having learned enough about electrostatics to do something practical. The Griffiths book has next to nothing on circuits, so I'm supplementing this material with my own notes, which you can find here. [23Mb PDF]

For Monday (21 Sept), please read sections 3.6 & 3.7 along with the whole of Ch. 4, covering capacitors and electric current. It should be light reading - almost no math.

For Wednesday (23 Sept), please read Ch. 5, covering basic dc circuits.

(Chapters 2 and 3 might be worth skimming to make sure you've got the qualitative aspects of electrostatics down, if you have time. It is all stuff we covered already, but sometimes the math hides the qualitative understanding ...)

Additional reading that might help

You might also find Chapter 2 in my PH102 notes useful, for a more qualitative introduction to electric forces and fields.

Some useful notes from PH125 for future reference

Look here. A bit on motion along curved paths, and another little bit on central forces.

The bit on curved paths I will assume you are familiar with at this point, or can pick it up quickly. We spent quite some time on it in PH125. If you were not in PH125, you will see it in Cal III very soon, or I'd be happy to go over it with you in office hours. It will come up gradually during the semester.

The bit on central forces is very incomplete, and follows the central force notes. Most of what you actually need to know about central forces this semester we will go over in class anyway, the skeleton notes I have up might be a useful reference down the road.

At some point, perhaps this semester, both will be merged into the 'math guide' anyway I suppose.

Slides from the first lecture / schedule

I've uploaded the slides [~6Mb PDF] that Prof. Harrell will be using for the first lecture, which is mainly a course overview and a math review.

Prof. Harrell will (probably) go through all of this material, I'll pick up where he left off on Monday 24 Aug and we'll go further into derivatives of vector fields. Wednesday 26 Aug, we'll go through integration over vector fields (line integrals) and start doing some actual E&M.

Don't worry too much if the math seems frightening during the first few lectures. After our brief tour of vector calculus, the math will get less scary again. The quick overview in the beginning is meant to give you an idea of what we'll need during the semester, and as these topics come up in real situations, we will review them in more detail at a slower pace. Any math that is not part of a prerequisite course I will cover in class, and I will try hard to bridge any gaps between our textbook and what is covered in, e.g., Cal II.

A short math guide

Clearly, a work in progress, but meant to be a quick reference for things we'll need this semester.