Wednesday's lab

Wednesday, we'll do a lab designed to get you more familiarized with wiring and analyzing (qualitatively) simple circuits. We'll figure out how resistors work, and how to combine resistors and capacitors.

In a couple weeks time, after we've gone over some of the basic hardware and know-how you need to build circuits, we will begin a semester-long project on electronics. At the moment, my plan is to have you learn how to build simple amplifiers and oscillators, and finally make an FM radio transmitter/receiver by the end of the semester.

Must crawl before walking ... so the first labs will go a bit slowly until we've covered all the basics.

Impending quiz

Wednesday, there will be a short quiz. It will cover finding the electric field from continuous charge distributions. You will not have to do any nasty integrals (or even solve an integral), you will just have to 'set up' the expression for the electric field from a given charge distribution.

Reading 2.1-2.2 in Griffiths and glancing at the homework will be enough to get you by easily. It should take only 15min or so.

Wolfram Integrator

For all your integration needs. If this thing can't figure it out, you are probably doing something wrong ;-)

Reading for Wednesday

For Wednesday, make sure you have read Griffiths Chapter 2 through the end of section 2.4.

Today, we'll cover 2.1 and 2.2.

Lab today

Today, we'll start learning a bit about circuits. The way we'll start out is by trying to get a feeling for what current and voltage are, and how different components behave when you attempt to supply current or voltage to them.

The lab procedure will be mostly qualitative, and it is mainly designed to get you used to wiring things up and doing hands-on work with circuits.

You can find the files here. There are two parts: first, a brief introduction to the hardware and software you'll be using; second, a small procedure for the lab itself.

Homework 2 is out

Here you go. Probably best not to delay in getting started ... we'll go over a few of these tomorrow to get you started.

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.

HW1 solutions

Here you go. Sources for most of the problems are indicated as well. Let me know if you find any typos/errors.

Homework 1 problem 9

Reminder: you do not have to do problem #9 on HW1. Full solutions to HW1 will be out tomorrow.

Homework 2 will come out tonight or tomorrow, I'll post it here. It will be less tedious, and at least raise the possibility of cleverness saving you some work.

For Monday, please read sections 2.1-2.2 in Griffiths. Study the problems in those sections carefully (this should be easier now that you have your little present from this morning). Warning, the solutions guide can be quite terse.

Looking at my old PH106 content might also be clever. For now, you might want to look at the first HW set, it is very much like what we started on today. (My solutions are sometimes much more lengthy than they need to be, I was trying to be as explicit as possible.)

Friday recitation

I think we've had enough math for now. We'll cover line integrals once we actually need them in a serious way ... not for a little while at least. Instead, we'll start on electric fields and forces tomorrow, the beginning of Ch. 2 in Griffiths.

I will go over HW 1 problem 9, though, so you know how to go about it.

HW1 partial solutions

Here are the solutions to the first four problems. Let me know if you find any typos ...

HW1 #4c

You need the magnitude of r and dr/dt squared. For this, you can use the dot product - the magnitude of a vector squared is the vector dotted into itself.

|\vec{r}|^2 = \vec{r}\cdot\vec{r}=\left(\vec{a}\,\cos{\omega t} + \vec{b}\,\sin{\omega t}\right)\cdot \left(\vec{a}\,\cos{\omega t} + \vec{b}\,\sin{\omega t}\right) \\
|\vec{r}|^2 = |\vec{a}|^2\,\cos^2{\omega t} + 2\vec{a}\cdot\vec{b} \,\sin{\omega t}\cos{\omega t} + |\vec{b}|^2\,\sin^2{\omega t}

You have terms with "a dot b" in them. Just leave them be. Find dr/dt, repeat ... and those "cross terms' will drop out anyway. The rest should be easy.

MathWorld

It is the awesome. If you can't remember some bit of math, or need to pick up something new quickly, it should arguably be your first stop (the other argument being in favor of wikipedia, which in my opinion can be too terse).

Reading for the next days

By Friday, it would be good if you had read the first chapter of Griffiths. We have basically covered sections 1.1, 1.2, 1.4, and 1.5 at some level, so you should be able to skim those. Friday we'll worry about section 1.3, which is the last thing we need to get started with proper E&M ... so read section 1.3 with a little more care. We will not cover section 1.5 just yet, but will introduce the Delta function once we need it ... but please at least skim that section in the mean time.

For Monday, we'll start on Chapter 2 of Griffiths. Please have a look through sections 2.1 and 2.2, we should get through that much on Monday.

We will also start doing labs on Monday, details to follow soon.

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.

Math stuff so far

So ... after 'rebooting' a bit on the math background today, how are things looking? Of the things we covered today, are there topics that still seem very mysterious?

A good gauge is probably to look at the first four homework problems. If you basically know how to do them, but they seem tedious, things are OK. If you aren't sure how to even start one or more of them, we might need to review a bit more. I'll work out some of the first homework problems in detail on Wednesday's class (but not quite all the way, since they are due at the end of the day).

Unless you have specific requests/thoughts, I planned to move on to 'vector derivatives' on Wednesday, but not yet get in to line integrals and so on. Div, Grad, Curl and so forth, continuing a bit more carefully until we have that down.

Drop a comment to let me know what you think.

(Also: please stop me in the lectures if things start to seem mysterious to you. Often, you are not alone if you feel this way, and often, it is because I skipped something I shouldn't have. You're doing everyone a favor if you ask me to clarify something, rather than letting it go.)

Lab safety

Remind me next time that you each need to print & sign one of these.

It carries no real legal obligation whatsoever, it is more of a 'gentleman's agreement' than anything.

Help desk schedule

Once again this semester, all 100-level physics teaching assistants are pooling their office hours to better assist you. Here is the current schedule. Office hours are in 203 Gallalee.

Wed class / Stray hints on HW1

Well ... since we elected to re-boot today instead of going over new material, we're not quite as far as I wanted to be. That is OK, though, since I explicitly budgeted extra days just in case we wanted to spend more time on math background.

What this means is that on Wednesday, we'll start out by covering vector derivatives (div, grad, curl) and partial derivatives, and probably get to line integrals and the remainder of the vector calculus we'll need on Friday. By the end of Wednesday's homework, you should know how to do all but the very last of Friday's homework problems.

Homework 1 has 9 problems: 1-4 are due Wednesday, and 5-9 are due Friday (in both cases, by the end of the day). Here are some stray hints on the first 4 problems:

(1) The 'separation vector' is just the result of subtracting the two vectors. A unit vector can be constructed by dividing any vector by its magnitude.

(2) Body diagonal = opposite corners of a cube; there are four possibilities. Pick any two, the angles are the same. You could define two of these as (1,1,1) and (1,-1,1) for instance. If it helps, draw two cubes stacked on top of one another ...

(3) Just grind through it ... easy but tedious. A good chance to practice the cross-product-as-determinant rule! You can double-check some of your answers by verifying that axb is perpendicular to both a and b (meaning a-dot-b is zero).

(4) The first and last are not so bad, just remember how to take the derivative of a vector function, and that a and b are constant vectors. For the second, keep in mind that a and b are not necessarily perpendicular, so your normal rule for taking cross products does not work. Either you need to write the a and b vectors in a cartesian basis (in terms x & y unit vectors, say a=a_x xhat + a_y yhat), or you need to define a unit vector perpendicular to both a and b as well as the angle between a and b.

Probably the former option, writing a and b in terms of cartesian components, is easiest. This is still general, since you have the freedom to pick the x-y plane as the same plane formed by a and b for any two vectors a and b. You should not need to do this for the first and last parts, however.

Wednesday, we'll go over problems 5-9 a bit so you know how to get started.

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.

First homework, syllabus

Syllabus ... it includes the all-important grading information.

Homework 1 ... mostly math. Your first problems are due Wed 26 Aug, the rest are due Fri 28 Aug.

First week of class

As you probably know by now, I will be out of the country for our first two scheduled meetings: Thursday, 20 Aug 2009 and Friday, 21 Aug 2009.

If you got this far, then Dr. Harrell has covered the course introduction for me, and pointed you here. Peruse the posts here for interesting information, including your first homework set ...

I will be out of the country from 19 Aug 2009 until sometime on 23 Aug 2009. I will have sporadic email access. Feel free to email me with questions during this time, but keep in mind I may not be very responsive until 23 Aug.

What does this really mean for you?

• There is no recitation on Friday, 21 Aug 2009.
• I will be back for the second regular class period on 25 Aug 2009
• You still have homework problems due on 25 Aug 2009 (see posts above)
  
• Please read the course syllabus carefully (see posts above)
  
• Please read Chapter 1 of the textbook before 25 Aug 2009