Testing MathJax

Just a quick test of MathJax for posting mathematics on my blog:

Here is an inline equation: $\sin^2(x)+\cos^2(x)=1$.

Here is a displayed equation: \[\frac{\pi}{2}.\]

Final Marks

I just submitted your final marks. They will need to be processed before you can see them --- maybe a day or two.

There were no failures.

The marks ranged from D- up to A+.

A couple of people did poorly on the exam and got a lower term mark than they probably should have.

I was happy with the marks and the exams looked pretty good overall.

If you are surprised with your mark send me an email and I can show you what happened.

Exam Marking

I am almost finished with the marking and should submit the marks Sunday evening (tomorrow evening).

Note that on question 5 the parts (a), (b), and (c) were labeled with "5 points" but the value of the question was listed as 30 points. The 30 point figure was correct --- the exam adds up to 200 points and that only worked out if question 5 was worth 30 points.

That being said, I've given you all the best mark based on considering question 5 as being worth either 15, or 30.

So it worked in your favour.

From Khadim

Hi Dr. Leon,

I booked the conference room 4124ME for review between 11am to 4 pm tomorrow Wed.
Would you post the information online and email it to the students as well.

Regards,

Khadim

From Rachel

Hello,

Could you please post on your course website that there will be a PASS mock exam tomorrow Wednesday April 18 from 3pm to 6 pm in PA 112.

Thank you

Exam Practice

Just to get your grey matter moving:

Some Class Notes

Someone emailed me about class notes for the last lecture. They are not neat, but this is what I wrote in class on my iPad. They may jog your memory or be of some help.

Also, someone asked for the old notes of Dr. Gauthier concerning Faraday's Law and Lenz's Law. I am not responsible for any errors in these slides ---- my lecture notes given in class covered the same material.

Verify Your Marks

I am still waiting for the Lab #5 marks. By the way, you should send an email to Deepak and Khadim, and ask them when and where to pick up your materials.

The marks I have recorded are below. Please verify them and if you see any problems let me know. The last four digits of your student ID is shown under the ID column.

Note that I took the better of your first or second test, or the combination that gave the highest score out of 25 (the term weight given to the tests).

Inan Inan Question

I'll leave this post up until Sunday night, and then I will delete it. The final question on the exam is taken from one of the following pages:

[EDITED TO REMOVE PHOTOS]

Ok, Ok, OK!

These threatening emails are getting serious!

Here are the old lecture slides (Dr. Gauthier's) concerning Polarization, for those who missed the class.

Final Exam Redacted Version

Probably by the time you've studied every possible permutation of the questions in the redacted version of the exam you will be more than ready for the real exam.

Test #2 Remarking and Solutions

Folks,

Deepak was last seen under a bus.

Ok, he made amends and has corrected the marking.

The average mark is now 69%, still not my cup o' tea, but not bad. I will return the tests tomorrow.

Meanwhile, you might want to check out the official solutions.

Other PA Sessions this week.....

....should go to their usual location (4124ME).

Please go to room 340 in the Azrieli Pavillion today for your PA session. Note that is not the Azrieli Theatre --- don't get confused.

Upcoming Lectures

Some slide material based on Dr. Gauthier's old slides may be useful for the upcoming lectures. I will probably modify/skip these on the fly during the lecture. Depends on how hot the room is!

March 21, 2012 Lecture Summary

We looked at:

Magnetic Vector Potential

The Magnetic Dipole

Force on a Magnetic Dipole

Ring Of Current Mathematica Solution

Here is the Mathematica solution for the magnetic field generated by a ring of current, on the axis of the ring of current.

PASS Mock Test #2

Rachel sent me word that there will be a mock test tonight in 112PA starting at 5:30pm. The mock test will be repeated on Thursday starting at 1:30pm (I assume in the same location).

Sample Questions for the Midterm

Folks, as requested, here are a few questions to get you thinking:

Ohhhh.......So Now It's MY Fault?

Ok, I am not disagreeing. You're a smart bunch and I was fairly shocked at the scores.

Please leave some (anonymous) comments that will help me help you to score better on the next test.

Let me know what you think was wrong with the first test, or why the scores were so low.

I am listening.

Solutions to Test #1

I posted the solutions to the first test. Please review them, and let me know if you see any problems.

Lecture Summary for March 2, 2012

Today we discussed again Postulate #1 for magnetostatics, and what sort of problems can be tackled using it.

We moved on to Postulate #2 for magnetostatics. We did a few examples of problems or situations involving forces on current-carrying conductors.

We looked at Lorentz's force equation.

We went over the solutions to Test #1.

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.

Tomorrow Lab #2 Begins

The second of five labs for the course begins tomorrow. You can find the lab document by clicking on the lab #2 menu tab at the top of this web page.

We won't cover magnetostatics for a little bit yet, but the lab is straightforward so I am willing to bet you will handle it well.

PA Questions

If anyone has any particular questions, or just suggestions for what area of the course to focus on, please add your comments to this posting. We will try our best to cover those areas in the next PA.

Electrostatic Energy

Today's lecture started out with Green's Theorem. Combining the point form of Gauss's Law with the integral form of Gauss's Law, one can show that the flux of the electric field is related to the divergence of the electric field by the Divergence Theorem, which is a specific example of the more general Green's Theorem.

Next, we derived the expressions for the amount of electrostatic potential energy stored in a collection of charges. We looked at both discrete charge assemblies, and also continuous distributions of charge.

We covered one example problem (find the amount of work required to assemble a ball of charge of radius "b" and charge density "rho").

Lastly, we looked at the electrical flux density, about which we will have more to talk about next week. So please read up on flux density. You should also read about boundary conditions.

New Poll Up

Another week, another poll. Please answer truthfully. And one time only!

Failures

Ok, so the poll from last week is closed. Could those of you who wish to fail please send me an email so I can enter in your marks from now? No need to write the exam. Hopefully I will see you again next year.

PS: My goal is to have no failures this year. Please help me make my dream come true!

Yesterday's Lecture

Ah yes, the lecture of yesterday. Who remembers it?

We covered divergence, which involved a derivation for the divergence expressed in Cartesian co-ordinates. Then we combined the divergence concept with the integral form of Gauss's Law, and arrived at the differential form of Gauss's Law (also known as the point form). After that, we used the fact that the electric field vector is given by the negative gradient of the voltage potential, substituted that into the point form of Gauss's Law, and presto mundo we had Poisson's equation. Setting the volume charge density to zero then led to Laplace's equation.

We tried one practice problem, which was to use Laplace's equation to find an equation for the voltage in the region between two parallel plate conductors of known potential and known separation distance. From the voltage equation we found the electric field between the plates.

I pointed out that the electrical field is constant, and increases with increasing plate voltage difference and decreasing plate separation. This has important ramifications for capacitor design (e.g. allowable dielectric, voltage rating).

PA #1 Solutions Update

Ali slightly adjusted his solutions for PA #1. I updated the downloadable copy.

Failure Rate in ELEC 3105

As I write this, 55 people have voted in the poll about mark expectations, with 26 votes cast for an "F" mark in the course. Since there are only 34 students currently registered in the course, I can only assume that some students plan on failing multiple times?

PA #1 Solutions

Ali sent me the solutions to the first PA session questions.

Upcoming PA Questions

I asked Hassna to go over the solutions to the following questions from the THIRD edition of Sadiku: 4.32, 4.33, 4.34, 4.35, 4.39, and 4.41. She will cover them plus a few from the FIFTH edition. I am waiting for her to confirm which ones --- when confirmed, I will edit this post and add them here.

PASS Calendar

Rachel sent the PASS calendar to me, which you can download and view.

Conductors in Electrical Fields and Equipotential Surfaces

Today we mostly covered conductors in electrical fields and equipotential surfaces. We also started divergence of the electric field, which will lead us next week directly to Poisson's equation. Please read up on divergence and Poisson's equation.

Voltage Stuff

Today I finished off voltage potential. We looked at voltage potential arising from various charge distributions. I gave some clarification concerning the sign on the "work equation". We looked at how to get the electric field from the voltage function. We solved an example problem for a ring of charge and the associated voltage potential along its axis.

You should try to take the voltage we derived for the ring, find its gradient, and see if that answer is the same as the one you found during your PA session.

I was happy to see a few more people volunteering answers in class. Interactivity is welcome in my lectures, and no one should feel shy to speak out!

PS: Here is the solution to the little problem I gave last Friday, courtesy of your classmate Kenneth. The objective was to look at each motion path around a charge, and decide if moving a test charge along that segment would require you to input energy, have the field release energy, or result in no change of potential energy.

Yannick Wins!

Yannick noticed an error in the first lab, and for that he automatically earns an A+ in the course*. The error was following equation (5), and the statement was that cos(90)=1, which is clearly not true.

------
* A+ dependant on total marks earned in the course, of course.

Rico Wins!

Well there you go, Rico is the best penguin. But we already knew that!

Tomorrow's Lab

Tomorrow I have a MASc defence starting at 2pm, so I will not be coming to the start of the lab.

If there are any problems that the TAs cannot resolve, please send me an email --- I will keep an eye on my email during the defence.

I will drop by as soon as the defence concludes, probably between 4pm and 4:30pm.

Good luck.

Saturday Break

You can't work all the time. You might like my cousin appearing at the NAC tonight. You can find her band on YouTube.

Enjoy your Saturday!

Thank You

Thank you for showing up for a late Friday lecture despite the miserable weather.

Today we finished off some examples of electric fields due to charge distributions. We used Gauss's Law to find the field for an infinite charged line and an infinite charged plane. We discussed the physical meaning of these problems. Then we moved on to voltage potential, and discussed the meaning of voltage potential in terms of the amount of work required to place charges in certain configurations.

Gaussian Surfaces and Electric Flux

Yeah, it can be confusing. However, learn the concepts and then do practice problems until it makes sense.

Here are the slides I used today. Please review the two examples I did not cover today, and we will look at them Friday.

Important Matters

Item #1: New poll on the right side of the page.

Item #2: Lab #1 will be posted shortly. Check the tabs at the top of the page.

PA Locations and Times

For the rest of the term, the PA sessions will be held as follows:

Mondays, 2:35-5:25pm, 411SA

Tuesdays and Thursdays, 2:35pm-5:25pm, 4124ME

I am updating the calendar page on this blog later today.

PA Session Info

The email I just sent to your TA:


Ali,

This is a large email, so please confirm that you received it ok.

Can you please cover the following topics during the upcoming PA sessions? If the students say they already know something, then spend minimal time on it. No sense in boring them to tears.

Review Material

-----------------------

1. Coordinate systems (cartesian, cylindrical, and spherical). The students should know how to specify a point, a differential surface element, and a differential volume in each coordinate system. The review questions 3.1, 3.2, and 3.3 are quite helpful in the attached PDF, taken from Sadiku, 3rd edition. The students also need to know how to find a unit vector in each coordinate system, given two points.

2. Divergence. Focus on Cartesian coordinates. Source material is in the attached PDF.

3. Laplacian. Focus on Cartesian coordinates. Source material is in the attached PDF.

Practise Problems

--------------------------

So far we've covered Coulomb's Law, the electric field, sketching field lines, and electric fields for continuous charge distributions. Covering a few problems about continuous charge distributions would be helpful.

I asked the students to calculate the electric field from an infinitely long line of charge at a distance R from the line, where the linear charge density is rho_s. Can you go over the solution to this problem with them, and ask them to aid in the solution --- in other words don't just feed them the solution. There are a number of ways to solve this, including using Gauss's Law (we did not cover Gauss's Law yet). A good solution to the problem is attached as a PDF.

Can you also cover:

-- the electric field on the axis of a disk of charge. See attached PDF.

-- use the previous problem solution to solve for the electric field above an infinite sheet of charge. See attached PDF.

-- the electric field on the axis of a ring of charge. There is a solution to this one here: http://youtu.be/80mM3kSTZcE

I don't know how long this will take. Don't freak out if you can't cover it all!

Electric Fields Lecture

Today we looked at electric fields from point charges, line charges, surface charges, and volume charges. We tried one problem involving a line charge, but many students saw it before in a physics lecture. I suppose that is ok, since this is only the second lecture. Let me know though if there is too much repeated material.

So far I am leaning toward a class intelligence that is not near a sack of potatoes.

The question to ask yourselves: is it better to remain silent and be thought a fool, or speak out and remove all doubt? (Little Friday night joke there for all of you studying ELEC 3105, as I know you all are, right?!)

PA Sessions Next Week

Ali will lead the PA sessions next week. The sessions will be held as follows:

Monday, 2:35-5:25pm, 411SA
Tuesday, 2:35pm-5:25pm, 4124ME

Thursday, 2:35pm-5:25pm, 4124ME

PASS Sessions

I received the following message this morning:

PASS (Peer Assisted Study Session)
Facil: Rachel Katumba
Email: pass@carleton.ca

PASS is:
 A pre-made study group.
 A chance to meet new people.
 An opportunity to get a kick-start on studying.
 A fun and friendly place to go over course material.
 A ready-made review session.
 A license to avoid cramming.

PASS is NOT:
 Not a tutorial.
 Not another lecture.
 Not mandatory.
 Not evaluative.

PASS supports this class because it is a traditionally difficult course.
PASS Workshops will be held twice a week for 1.5 hours. Both workshops cover the same material.

Below are three time slots, we will decide on the best two out of three time slots on Wed Jan 11.
 Wed 6 – 7.30 pm
 Fri 1 – 2.30 pm
 Fri 2.30 – 4 pm

Note: Workshops begin in the week of Jan 16.

Introductory Lecture

Today I introduced myself to the class and showed a few projects from my research team that involved material from ELEC 3105.

We then started on basic electrostatic theory, specifically Coulomb's Law.

For next lecture, if you could please review some vector material from a previous math course that would be helpful.

Also, you might find some videos on YouTube helpful. I like the ones by a user named "derekowens". Just go to YouTube and check out his channel, especially the videos concerning Coulomb's Law.

Please post links to any excellent course-related videos in the comment section below.

Or, any funny videos at all.

Well Hello There.