I’ve often liked certain specific technological activities for improving understanding. For example, I really like motion sensors with real-time distance-vs-time displays for various motion activities. A particularly cool one is the distance-vs-time graph for an object moving at constant speed in circles.
It’s a very graphic, so to speak, connection between the unit circle and sinusoidal waves and transformations thereof. Most systems will do v-t and a-t graphs also.
About a week ago, I was looking online for a simple demo for electric fields and/or the motion of charges in electric fields. We don’t have much equipment for this topic at the school, so I have struggled to make electric fields even somewhat concrete for the students. Lots of chalk-and-talk. But online, I found a great little simulation applet (http://www.colorado.edu/physics/2000/waves_particles/wavpart2.html) that shows the motion of an electron in the electric field of a proton. So, the next day in class, I connected my laptop wirelessly to the internet and to a data projector. I illustrated a 1-D calculation I was doing on the board and then later showed some of the 2-D possibilities and we talked about the shapes and energy transformations involved. I loved it but I had no idea it was going to be such a big hit with the students.
There are more such simulations (not all fields) indexed at http://www.colorado.edu/physics/2000/applets/ and many other websites.
But I experienced an enrichment of understanding through simulation for myself today.
I had asked my students to submit proposals for the fields unit test they were writing today. I like this exercise in that it often yields perfectly valid test and exam questions (not just bonus questions) and it gives every student the opportunity to think as deeply about the material as they are ready to. The winner this time was: “Sketch the electric field diagram for two positive point charges and one negative point charge fixed to the vertices of an equilateral triangle. All three have the same magnitude of charge.” A tough problem for grade 12s, to be sure. During the test, I spent a good 15, maybe 20, minutes making a pretty detailed sketch. And although I was reasonably confident that I had a good answer, I went online to try and find a textbook answer. I didn’t find one, but I did find an applet (http://ww2.slcc.edu/schools/hum_sci/physics/tutor/2220/e_fields/java/) that would let me simulate it. Here is the applet answer and mine.
Pretty much I got it but I didn’t have the “ears” or “heart-shape” exaggerated enough.
Aside: After the test, I overheard one student asking another, “Did your answer to the bonus look like a jellyfish?” Woah. I have no idea what a sketch of a jellyfish would look like.
Then I went home and started telling Dion the story above. He had no visuals to go on but when I said I had all the key features, and listed them including, “heart-shape,” he replied, “well, of course, that’s what I’d expect – a circle subtracted from an ellipse.” Uh, what the hell was he talking about? Turns out he was thinking of the equipotential contours, which are at all points perpendicular to the electric field we were supposed to be sketching. Ah, vector calculus. Something about the derivative of a changing vector being perpendicular to it. I truly do not remember sketching equipotential contours. I probably did, but I’m sure I forgot it all 10 minutes after the exam. Anyone remember when we did that – Dimi’s E+M? ODE’s with Smith? I never took PDE’s.
So, after showing Dion the applet and how it does both field lines and equipotential contours, I started playing around with various configurations. Some pretty patterns came out. And some mundane ones. But this one really caught my attention.
The red dots are positive point charges. The grey lines are the electric field lines. The fuchsia lines are equipotential contours and at all points perpendicular to the field, of course – that much I have solidly known for some time.
But I know that fuchsia pattern from something else. If those red dots were charges moving out of the page, then the fuchsia lines would be the net magnetic field they create (per Oersted’s Principle and superposition). I use this diagram in Gr 11 Physics to explain the shape and strength of the magnetic field created by a solenoid/electromagnet.
Hang on there. The (1) electric equipotential contours perpendicular to the (2) electric field lines created by (3) static charges have the same shape as the (4) magnetic field lines created by (5) motion of charges.
(1), (2), and (5) or (1), (4), and (5) are all mutually perpendicular.
MAXWELL!
If I could just remember all that div, grad, curl stuff, I could write this down much more concisely. Actually, the Cartoon Guide to Physics (Gonick and Huffman, Harper-Collins) has Maxwell’s equations. I’ll scan ‘em for y’all later. BTW I cannot recommend the Cartoon Guide to Physics highly enough.
Anyway, who knows when I might have reencountered these ideas so intimately without the simulation software, some unconstrained time to explore, and some “expert” input from Dion. I might be able to transfer some of this experience into my lesson/unit planning.
Problem is, I am me and they are not. If I give 17 year olds unconstrained time to play with simulations, how effectively will they use that time? Will they be inclined to
And now if I can ask a favour? Can anyone figure out how to get a working local copy of these applets? I’ve downloaded all the related source files (and the objects they call) I can find and maintained the file structure, but they just won’t run. Do they have to phone home? I’d like my own copy as the internet connection at school is flaky and who know how long these websites will be maintained. Thanks.
