Saturday, February 10, 2018

Gaussian Surfaces for the win

I worked all last weekend learning how to integrate the Electric Field near an infinite line of charge, finite line of charge, charged ring and charged disc. It was brutal. The only thing worse was working my AP Physics C students through it. Students are "supposed" to learn it, it's right there in the College Board Objectives for the course:

4. Fields and potentials of other charge distributions
a) Students should be able to use the principle of superposition to calculate by integration:
1)      The electric field of a straight, uniformly charged wire.
2)      The electric field and potential on the axis of a thin ring of charge, or at the center of a circular arc of charge.
3)      The electric potential on the axis of a uniformly charged disk.

Yet the concept is infrequently seen on the AP exam so some teachers hope for the best and don't teach it. I decided I would do a one day lecture along the lines of "Just follow me through the math kids!" I figured it was the best of both worlds, they technically saw it and some might remember it and I wasn't wasting much time. They did dutifully follow the notes but based on the pained expression they didn't "get it." I didn't like that every video tutorial I found said "And now you just check your integral table ...." because my students wouldn't have one on their exam. I told students the emphasis was on the relationships, what did and did not affect the strength of the field. I told students not to memorize the equations. If the problem did appear on the exam it would probably be for a partial charged ring, also known as an arc, which was done slightly differently and seemed much easier. Combine the not fun math and my inexperience with it and I was not a happy teacher for a few days.

So what do unhappy teachers do? Go back to good teaching strategies. My kids (and I) were getting confused so I made a reference table with a (1) a description of the situation with variables, (2) a picture that matched and (3) the final equation they got from the integration. Its available here as a pdf.

When I passed out the chart I asked them, "And what are we not doing with these equations?" and students answered "Memorize them!" So they tucked them away and may never have looked at them again.

A few days later as I was reviewing Gaussian surfaces I watched Dan Fullerton's APlusPhysics video about them. He pointed out that using Gaussian surfaces around an infinite line of charge you derive the same equation as in my chart above. My mind was blown. [cue explosion noises] When I lead students through Gaussian surfaces we worked through the derivation for the Electric Field around an infinitely long charged rod using a Gaussian cylinder. I had them take out their charts and pointed out the equation was the same as what we had found a few days ago. Then I asked them to look at the disk of charge equation and asked what it would look like as it became an infinite plane as R goes to infinity. There were audible gasps. "Wait, this is so much easier than that integration." Physics works kids. Gaussian surfaces for the win.

Friday, February 02, 2018

Induction .... Nailed it!

Induction is one of those things that make students go "Whhaaaatttt???"
You have probably seen and demonstrated a moving wooden meterstick like this:
Usually when I do that demo in regular Physics my students call me a witch. I don't exactly correct them. I wanted an equally "wow!" demo but didn't want to repeat myself in AP Physics C. While searching for something completely different I stumbled upon this small image of an induction experiment.

At first I wasn't sure if I could do it but after some experimenting I found a set up that worked. I set a nail on a styrofoam cup (made some grooves in it so that it would stop the nail from rolling) instead of a metal rod. I couldn't find any metal rods that weren't gross and rusty. I used a rubber rod and wool but any friction kit combination should work.

First I charged the pith ball through induction with the rod. Then I moved the nail point close but not touching the pith ball. I would recharge the rod and bring it close but not touching the nail. The pith ball on the other end would repel. My students were amazed. They watched me do it but they still had to think about which item was charged vs neutral. It led to lots of additional questions, some we were able to answer experimentally, some would probably require some more charge:

1. What happens if you touch the nail with the rod? The nail would then have the same charge as the rod and pith ball. I presume the nail would continue to repel the pith ball even when the rod were removed. We tried this but could not confirm with the small amount of charge we had. 

2. If the pith ball is charged won't it be attracted to the neutral nail without the rod inducing a separation of charge? Yes! You'll notice in the video below that I move the nail in after the pith ball is charged. Otherwise I found that the pith ball would pull towards the nail immediately.

3. Would it work with an insulator? I presume so but didn't get a chance to try it. 

Below is the video of the demonstration for absent students:

Depending on the strength of your charge source you could set up a wide variety of things like this as discrepant events for your students to puzzle over.