Jen Kaelin is a longtime AP Physics reader. Once when we were grading the same question, we competed to see how many hand turkeys we could find drawn on part (c)*.
* Not really, College Board Lawyers. The competition was something I made up just now for humorous value. The hand turkey was authentic, though.
The other night she told me about her frustration and then elation at her AP Physics C E&M class as they struggled to understand Gauss’s Law. They simply couldn’t effectively visualize some Gaussian surfaces.
I’ve had good luck before bringing in physical items to help with more difficult visualizations in E&M. My personal favorite* was the top of a sour cream container for visualizing magnetic flux. Know which way the magnetic field points, then place the sour cream top where the wire loop is. This allows you to see, in three dimensions, whether the field lines penetrate the sour cream top, whether they point alongside the sour cream top and thus produce zero flux… or somewhere in between.
* And my students’ favorite, as they walked into the exam and all told the proctor confidently and firmly, “Mr. Jacobs TOLD us all to bring these sour cream tops into the exam. Yes, really. And the top to a butter container is acceptable too, he said, but not margarine because he hates margarine.”
I also used the sour cream top when the Gaussian surface required was the “pillbox”, as with a very large plane with two-dimensional charge distribution. But a spherically symmetric charge distribution requires abstraction. I can show my class a sphere - a racquetball, e.g. - but they can’t open up the racquetball to see the charge distribution inside.
Unless you use an onion, like Jen did.
Jen brought in onions, peeling back layers to visualize how the volume and surface area get much smaller as the radius decreases. She found plush onions online, and many of her students started carrying these around school. First as a joke, I’m sure, but the mnemonic stayed with them. Jen finally felt comfortable with her class’s ability to use Gauss’s law under spherical symmetry.
You got a good physical manifestation of an abstract idea? Post a comment…
If you have an area of tall grass or something similar around your school, it's worth going outside with a hula hoop to teach the concept of electric or magnetic flux. Lower the hula hoop over the grass so it contains as much grass as possible, then remove it. Tell the students that when you put the hula hoop back, you want it to contain less grass and have them figure out the three different ways to do this (stretching the hoop to reduce its area, rotating the hoop to change its angle, or mowing the grass to change the field). From there, students should be able to come up with a predicted equation for flux.
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