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2013 June 10

Chapter 23 homework

Although my son has taken both the AP Physics C: E&M exam and the SAT2 Physics exam already, we haven’t finished the Matter and Interactions book yet, so we’ll keep going over the summer to finish off the last 3 chapters (23: Faraday’s Law, 24: Electromagnetic Radiation, 25: Waves and Particles).  He read the chapters before taking the exams but has not done any exercises or labs for them yet.

Chapter 23 includes inductors, so we’ll probably do some inductor labs, looking at current in response to a step change in voltage and perhaps making an LC oscillator.  I have some 220µH inductors, so we should be able to do current changes slow enough to track with the Arduino data logger and make an audio frequency oscillator.  We may try winding our own air-core inductors with different core diameters, and measure the inductance in several ways (say by fitting a time constant to the current change, with a frequency measurement of an LC oscillator, and by nulling a bridge circuit comparing to a known inductance).  We’ll probably also do some sort of eddy current demo (dropping a magnet through a copper tube, for example).

Homework exercises for Chapter 23:  23P29, 23P30, 23P32, 23P34, 23P35, 23P38, 23P40, 23P42, 23P43, 23P45, 23P46, 23P47, 23P51, 23P52.


2013 April 23

Chapter 22 homework

We finally finished off Chapter 21 of Matter and Interactions today, about 2 months behind my original schedule, having been repeatedly distracted.  We never did get around to measuring the magnetic field of a coil as a function of distance or current, either, though we’ll probably get back to trying that after the AP exams.

It looks like there is a chance my son will get to take the AP CS and AP Physics C: E&M exams this year, even though my first 5 attempts to find a place for him to take them failed. He needs to take the late exam for AP CS, since it conflicts with the Oregon Shakespeare Festival field trip and no one in the County offers Physics C—my attempts to get one of the high schools to offer the exam (which is at the same time as Physics B) all failed.  His consultant teacher is trying to arrange to be the proctor for him on the late AP CS and the late Physics C: E&M exams (it is now too late to register for the regular exams) through another high school in the same district.  I’m hopeful that she’ll be more successful in moving the bureaucracy than I was as an outsider.

Of course, he’ll probably never get any credit for taking the exams, since many of the schools he is applying to don’t do AP credit anyway, and he’ll have to retake physics at any of the schools he’s likely to choose.  But the exams will help validate that he has done rigorous work in physics, which should help him get into the colleges that would be a good fit for him. The AP CS exam is so low level that all it validates is that one has learned some Java syntax—but it might help with admissions offices also, as most will not be familiar with the new Art of Problem-Solving Java course.

In any case, we have to speed up a bit on the physics, despite the distractions, so here are the problems for Chapter 22 “Patterns of Fields in Space”: 22P15, 22p16, 22p18, 22P22, 22P23, 22P25, 22P29, 22P31, 22P33, 22P37.

2013 April 7

Destroying a hard drive

Filed under: home school,magnetometer — gasstationwithoutpumps @ 13:08
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Sorry that I’ve not posted in a week, but my laptop has been in the shop, getting the hard drive replaced.  The destruction of the old drive happened last Sunday in a physics lab I was doing with my son.  We were planning to measure the magnetic field of a coil as a function of current, distance, radius, or number of turns (but probably not all those variables, as that would have gotten tedious).  We weren’t getting a noticeable reading from the magnetometer, so I got out a neodynium magnet to see if the magnetometer was working.  It was—in fact the magnet saturated the magnetometer easily.  When I went to turn off the program that was streaming data from the magnetometer, I carelessly put the magnet down on my laptop—right over the hard drive. That mistake turned out to be an expensive one.

The computer continued to work that day, but the next time I tried to restart it, it wouldn’t boot up.  I took it down to the local computer shop on Monday, where I found out that the extended warranty had expired 6 months ago, so I had to pay labor as well as materials for replacing the disk, which ended up costing me $376 (as long as they were replacing the drive, I had them upgrade from a 500GB drive to a 1TB drive, since I was running out of disk space).  When I finally got the computer back on Saturday, I spent most of the day restoring the system from my backup drive.  Now I need to replace the backup drive, since Time Machine complains that the old drive does not have enough space to do a full backup.  It looks like that will cost me another $100–$150 for a 1–2TB backup drive.  I don’t have many choices of drive, since I need a Firewire 800 interface (my old MacBook Pro does not have USB 3 or Thunderbolt). So my moment’s carelessness cost me the use of my laptop for a week and about $500.

After having confirmed that the magnetometer was ok, we did a rough calculation of how strong the field from the coil should be, to see whether we ought to be detecting. (I know, we should have done that first.)  We were running about 33mA through a coil of 5 turns with a diameter of about 4.4cm. Using the formula B(z) = \frac{\mu_0}{4\pi} \frac{2 \pi R^2 N I}{(z^2+R^2)^{3/2}}, with I=0.033A, R=0.022m, and N=5, I computed that the magnetic field right at the center of the coil (z=0m) should be 4.7µT,  at 1cm (about as close as I could get the magnetometer) it should be 3.6µT, and at 2cm (where the measurements were being attempted) the field should be about 1.9µT.  The magnetometer has a resolution of 0.1µT per count, but the noise level was high enough that counts of 20 (2µT) would have been barely detectable. I suspect that a lot of the noise was because we had not immobilized the magnetometer.  According to the World Magnetic model, as displayed in Wikipedia, we should have about 49µT at a 60° inclination due to Earth’s field, so changes in orientation of 1° in the magnetometer would causes changes of about 0.9µT.

We’ll repeat the experiment (without having a strong magnet near the laptop!) using more current (say 300mA), more turns (40), and a smaller radius (a diameter of 1.25cm). With those values, we should be able to get a field of  1.2mT at the center of the coil, 180µT at 1cm, 32µT at 2cm, and 11µT at 3cm. We’ll also immobilize the magnetometer in my plastic-jawed Panavise, and make measurements by subtracting the field with the current off from the field with the current on. We may even double the signal by subtracting the field with the current in one direction from the field with the current in the opposite direction.


2012 November 14

Chapter 17 done, on to magnetic fields

Filed under: home school,magnetometer — gasstationwithoutpumps @ 20:53
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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 \frac{\mu_0}{4 \pi}\frac{2 I}{r}, 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.

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