Miss T. understands physics, far better than I ever could. So while our less than traditional method of learning it at home – without a text or math problems – may not help her pass an SAT, I know that once she takes one of those courses she will be in a better place to put the math in context than I ever was.
This week we started in on the wonderful world of electricity in her book, Asimov’s Understanding Physics. First, we worked on understanding magnetism. Now we’re on to what is known as static electricity, the first form of electricity studied in the 17th and 18th centuries. Electricity and magnetism, as any quantum physicist knows, are pretty much two forms of the same phenomenon. I thought I had a pretty good grasp of this, but, as it turns out, my grasp was limited. And I worried that Miss T’s was as well, because she refused to take what she learned and diagram it into her notebook.
Miss T. just hates to draw, but she does love painting word pictures and she also loves the science blog “what if?” on xkcd. While the section she read for the day was only 4 pages long (science readings being far shorter than a comparable reading in literature or history), we still broke it into pieces for her narration. She reviewed the discovery of subatomic particles, the understanding that the electric “fluid” of Ben Franklin’s day is actually flowing electrons, and the reversal of the concept of “positive” and “negative” charge. (Miss T’s dad, who studied electrical engineering in college, confirmed that electrical engineers still maintain the idea that the direction of flow is from positive to negative, and use the concept of “hole current” to describe this flow). The next concept she narrated concerned how electric force is measured, and while she understood the idea that gravitation is a far weaker force controlling electrons than electric force, she skipped over how Asimov demonstrated this mathematically. Finally, we arrived at the concept of electric lines of force.
Here’s where my understanding fell apart. Because electricity and magnetism are basically two forms of the same phenomenon, as any quantum physicist knows, there are analogous terms for similar observations. However, the ideas started to challenge what I thought I knew about electricity.
The permittivity of substances is just such a challenge. Permittivity refers to the attraction a substance has for electric lines of force. A substance is an insulator if it allows the lines of force to pass through it, and the ratio (or relative permittivity) of the density of lines of force through the substance vs. through a vacuum is called the dielectric constant. Air has a permittivity of close to 1, the value of water is 78. Water is considered an insulator or a dielectric.
“Whoa there!” I said. “I thought an insulator stopped electricity! It couldn’t possibly attract lines of electrical force.” And, in fact, Asimov had said so in the preceding section, when discussing Stephen Gray in 1729 discovering that certain substances resist the flow of electric fluid. They are called insulators from the Latin word for “island” because they “wall off electrified objects, preventing the fluid from leaving and therefore making the objects an island of electricity, so to speak.” (Asimov, Understanding Physics, p. II-159)
Miss T. was silent, so I read aloud the concluding paragraph:
Electric forces between charged particles decrease, then, if a dielectric is placed between; they decrease more as the dielectric constant is increased. The constituent particles of a substance like common table salt, for instance, are held together by electric attractions. In water, with its unusually high dielectric constant, these forces are correspondingly decreased, and this is one reason why salt dissolves readily in water (its particles fall apart, so to speak) and why water is, in general, such a good solvent. (p. II-165)
“The only way that makes sense to me,” I said, “is if you can separate the idea of electric force from the flow of electrons.”
Miss T. was silent, her eyes closed. I thought she was shutting me out, but she only said, “Wait a minute, Mom, I’m going to help you with an analogy.”
Finally, she came up with this word picture, illustrated above in the xkcd style. “Imagine you are an electron, and you are running. Think of your kinetic energy. Now think of a brick wall.”
“The brick wall takes all of your force, your kinetic energy, and disperses it through the bricks. Air will not absorb your kinetic energy, so the force stays with you and allows you to pass through. That’s what happens to the electrons.”
So I, who spent most of her life thinking that “ekeltricity” (the word of a semi-famous wizard) was just some form of wizardry, may just get a handle on this, thanks to my daughter’s power of analogy-making. This further demonstrates to me the power of narration, even at the high school level, even with a subject I couldn’t possibly understand well enough to teach. For if my daughter can understand it well enough to make me understand it, she’s learned her stuff. In science, particularly upper level science, it doesn’t do to let a less than complete narration pass. Find a way, any way, to help the student access the idea.