Lecture Summary for February 29, 2012

First, for some reason unknown to me I apparently called the cross product "curl" a number of times today. Must be something in my tea. We covered curl last month, and although the curl can be expressed in terms of the cross product of nabla and the vector field of interest, curl is not the same as cross product. So mea culpa!

Today we covered basic units for magnetostatics, the first postulate of magnetostatics, force on a moving charge due to a magnetic field, and the Hall effect. We began the second postulate of magnetostatics.

For Friday, please review the second postulate as well as the Lorentz force equation. 

PA Sessions for the Week beginning March 7, 2012

This week's PA sessions will involve the following questions from Saiku, 5th Edition.

Curl: 3.31, 3.33
Current flow: 5.4, 5.5
Continuity equation: 5.29, 5.30
Fields at boundaries: 5.35, 5.39
Resistance: 6.23, 6.25
Capacitance: 6.41, 6.47

Poll Summary

There was actually a good turn out for the lecture preceding the break. I was pleasantly surprised. For the next few weeks leading up to Test #2, please ensure you come to class and focus on the material.

February 17, 2012 Lecture Summary

As promised, we covered the continuity equation, current flow, the electric field in conductors with current, and resistivity and conductivity.

For those of you who took an early break, we also covered:

Magnetostatics: Lorentz force law; Hall effect; Ampere's law; Curl of a vector field; The magnetic vector potential; The Biôt-Savart Law; Applications of the Biôt-Savart Law: current ring, solenoid; Energy stored in magnetostatic field.
Magnetic Fields in Matter: Magnetic dipoles; Diamagnetic, paramagnetic and ferromagnetic materials; Magnetic circuits.
Faraday's Law: Faraday’s law and induced EMF; Lenz's law; Eddy currents; Inductors

You might want to catch up on all that material during reading week.

Pre-Reading Week Lecture

Tomorrow's lecture will wrap-up electrostatics. We'll discuss the continuity equation, current flow, and resistivity. See you there. I know that you won't miss it for the world!

By Popular Demand....

.....well one person asked actually.

You can try the home edition of today's test.

Pre-Test Jitters?

I have to say, this is the first time in 11 years of teaching at Carleton that I have not been inundated with emails about an upcoming test. Weird! You folks must have ice water in your veins.

I'll be in my office from noon to 3pm for those who need any last minute help.

Formula Sheet for the Test

Folks,

You can bring one "cheat sheet", 8.5" X 11; both sides can be used. No solved problems, nor any solution methods or algorithms. Otherwise you can put what you like.

In addition, you can bring any reference you like that contains tables of derivatives and tables of integrals. You can use the simple sheet that I put on the Downloads page if you like.

Message for Serge

Serge, I took a look at those notes I photographed. What was the problem? I didn't clue in yet to what you were saying before class. Leave a comment below.

New Stuff

New lab posted.

New poll up.

I spent the day creating the test. It's long but fair, IMHO.

Poll Results

Well, ok then. If you are lost in the course and not in touch with me, I can't help you. Send me an email. I do not want any marks in the F-C range this term.

February 10, 2012 Lecture Summary

Today's lecture was the final one before the upcoming test next week. I covered electric dipoles and the associated dipole moment. This concept was then used to develop the polarization of a dielectric material. The dielectric constant was shown to be related to the material polarization.

We also went through a few problems in preparation for the upcoming test.

PASS Mock Test

Rachel suggested these questions from Schaum's 2nd edition for your PASS mock test.

 2.9, 2.20, 3.4, 3.15, 5.4, 5.17, 7.5

Image Theory Solutions

I added some sample solutions for the image theory question posed below.

Test #1 Cheat Sheet

About the upcoming test, please do not include any solved problems or "problem solving methods" on your cheat sheet.

You are also free to bring any table of integrals or derivatives that you wish. This is in addition to your cheat sheet.

Lecture Summary for February 8, 2012

Today we finished looking at image theory (but we will do some sample problems on Friday). Then we looked at forces on conductors due to charges on the conductor. Finally we discussed the concept of virtual work.

PA Questions

Here are some questions that you can consider in advance of the PA sessions this week:

• Calculation of capacitance. 6.46 and 6.47 from Sadiku 5th edition.
• Question about potential and energy storage. 4.53 from Sadiku 5th edition
• Question about E and V from a charge distribution. 4.31 and 4.34 from Sadiku 5th edition.

A Third Sample Problem for Test #1

Here is another problem to try:

A Second Sample Question for Test #1

Here's a second question to try. This one you should be able to do right now. Expect something similar on the test.

Solution:

I solved this problem using Mathematica. I solved for the voltage at any point above the surface of the conductor, and below the end of the rod, using this expression:

Note that this is more difficult than answering the question as asked, which limited the position to being directly under the rod.

Here is a contour plot of the voltage for an area under the rod, where I've assumed that the rod extends from 10m to 12m above the surface. These contour lines are equipotential lines.

To get the formula for the electrical field, I found the gradient components in the x and y axes:

The electrical field is the negative of the gradient, which is plotted below:

One more thing we can find is the surface charge density for the conductor surface. This can be found using Gauss's Law (see your notes), from which we get E=rho_s/epsilon_0. I've plotted the surface charge below (note that it is negative).

A First Sample Question for Test #1

Ok, by popular demand, I will start posting some sample problems that are highly relevant to the midterm. Here is the first one. You should be able to do parts (a) and (b). By the midterm you need to be able to do (c) and (d) also. Khadim will go through this question during next week's PA sessions.

New Poll Up

Let me know how you think you are doing.

Poll Results

So this is pretty good. Some of you are spending some good time on this course. Please invest as much time as you can this weekend, next weekend, and through the week in order to ace the midterm. The material in the course gets more difficult soon (magnetostatics) so get the best you can on the midterm which covers only electrostatics.

February 3, 2012 Lecture Recap

Today we looked at three main topics:

1. Electric field relation to conductor curvature.
2. Capacitance and how to derive the capacitance of some conductor configuration.
3. Image Theory. For this, I got as far as showing why solving certain problems is too difficult without some sneaky method. The sneaky method is called Image Theory.

Please read up on Image Theory for next class.

Quick Clarification

When I went through the electrostatic energy storage derivation I had a neuron crossed. In the screen capture below, we solve (2) for the first term on the right hand side of the equation, and substitute that into (1). That's where the negative sign comes from in the equation that follows (2).

February 1, 2012 Lecture Summary

Oh man that was a snoozefest.

I almost put myself to sleep!

I never promised that deriving normal and tangential electric field components across media would be exciting. Maybe for some.

Anyway, here's what we covered today:

Wrapped up electrostatic energy storage. We looked at it from the field quantities point of view, so no need to know the charge density. We derived a few expressions for the total energy storage. We then related these to a new concept, which was the electrostatic energy density. To cap that off, we found the energy stored in a parallel plate capacitor arrangement.

Phase two of the lecture was an example of the difference in the electric field and the electric flux as we passed from one medium to another within concentric dielectric spheres.

The final phase of the lecture was about the normal and tangential components of the electric field as we passed from one medium to another. I am sure everyone was quite bored by this, but please review your notes about it because it is important material.