Chapter 17 of Matter and Interactions, “Electric Potential”, went very quickly. I had allocated 3 weeks to it back when I was making up a schedule, but we polished it off in a week. When we went over the problems yesterday, there were a few discrepancies between the results my son got and the results I got.
On 17p45 and 17p47, which involved electron guns with high voltage, he had computed the electron velocity without a relativistic correction, while I had done the calculation with the correction. Since speeds were around a quarter the speed of light, the relativistic correction makes a difference, but not a huge one.
On three other problems, the discrepancies were all errors on my part (mainly sign of electric field), though in one case (17p80) it took us a while to find where I had goofed, though it was immediately obvious that his sign was right and mine wrong, just by looking at the extreme case, where the potential was being measured right at the charge whose sign was reversed. I had forgotten that the field pointed down in the region of interest, and so left out one negative sign.
Chapter 17 went quickly in part because there were no experiments I could think of to do. About the only relevant experiment I can think of would be to build a Van de Graaff generator (or other electrostatic generator). That might be fun to do, but would take more time than I want for one experiment. So we’re closing Chapter 17 after only one week, and racing on to Chapter 18, on magnetic fields.
I’ve not finished reading Chapter 18 yet, but I can see several experiments we can do. We can do the 5th-grade science experiments that the book suggests—I even have some of the wires and compasses salvaged from the 5th grade classroom when my wife’s school did a massive cleanup this summer (half the building had to be vacated for construction after the July 4 fire). But there is no reason to stop there. I have multimeters and a MAG3110 magnetometer, and we’ve previously written code to re-center the magnetometer readings, so we can actually measure currents and magnetic fields. We might not even need to do the centering of the magnetometer, since we can do measurement of the magnetic field at a location as a series of different measurements with different currents, and look just at the differences in the readings. The full-scale range of the magnetometer is supposed to be ±1000 µTesla (the Earth’s magnetic field is about 25 to 65 µTesla at the surface) with sensitivity of about 0.1µTesla, so the magnetometer should be far more sensitive than using little compasses. It also measures the field along 3 axes, so we can look at the vector for the field, not just measure in one plane.
I’ve not finished reading Chapter 18 yet, so I’m not quite ready to assign problems, but I think that the computational problem for 18P79 (simulating the magnetic field of a solenoid) is worth doing, particularly if we compare the results from using a number of parallel rings to the results from using a helix, though I’d be satisfied with just the helical simulation. We don’t get to inductance until Chapter 23, but we may want to wind a coil that matches our simulation and measure the magnetic field from it. We’ll have to add some series resistance to make sure that we don’t fry our wall-wart power supplies (nor turn our solenoid into a fuse), but we should be able to wind a coil on a cardboard tube and measure the field in various locations with the magnetometer. We should probably start with measuring the field around a straight wire first, though.
If we use a long piece of wire (say L=1m) and measure close to it, (say r=1cm), we should see a field of about , so to see 2 µT, we’d need I = 0.5 * 2E-6 T * 0.01 m / (1e-7 T m/A) = 0.1 A, which is quite a reasonable value to produce from a battery or wall wart. With a 12v supply and a 22Ω resistor, I could provide 0.54A, except that the 22Ω resistor I have is only a 2w resistor and would get too hot trying to dissipate 6.5w. Actually, I’m not really sure what the rating of the resistor is—it is 18mm long and 8mm in diameter, most likely a carbon resistor, and the only resistors that size I found online were 2W resistors. With a 5V supply, we’d get about 0.23A or 1.14w, and stay well below the 2w limit, while still getting a magnetic field that we could measure 1cm away (about 45 µT). By using the dimensions of the MAG 3110 breakout board to set distances, we could measure fairly reliably at distances of 0.5 mm, 2mm, 6mm, and 8mm from the wire. (I’m not quite sure about the 0.5mm and 2mm—the breakout board+chip is 2.5mm, and the board alone is 1.5mm, but I don’t know where in the 1mm thick package the magnetometer sensor really is—we could use the 1/r dependence of the magnetic field strength to try to figure that out.)
So next week: string up a longish wire, add a 22Ω series resistor, a 5V power supply, an ammeter, and a switch, then measure the current and the magnetic field at various distances. If we get that working, wind a solenoid, measure the field around it, and compare the measured field to a simulation.