# Gas station without pumps

## 2012 November 27

### Magnetic fields with no lab

Last week we did measurements of the magnetic field around a single wire, and I had planned to “do a lab winding a helix of wire and measuring the field around it.  We’ll use the computational problem (18P79) to compute the expected field in different places, and try measuring the wound solenoid in corresponding locations.  This means that in setting up the program we’ll have to make the number of turns, the radius of the solenoid, its length, and the current through the solenoid all easily changed, to match the simulation to the coil that we wind.”

As it turned out, my son had the simulation finished and we spent most of an hour exploring what the program told us.  The initial picture showing magnetic field arrows near the coil looked fine, but I suggested trying a different visualization: having a particle trace out a magnetic field line.  We expected to see something like the classic pictures of iron filings around a bar magnet, and were surprised to see the magnetic field coiling out from the end of the solenoid.

We did a bunch of debugging.  We looked at at the contributions to the field from the different segments of the coil, by color coding arrows from a fixed observation position. The simulation had n segments for each turn of the helix, so we summed the segments mod n, to get the different contributions from the different parts of the helix.  We also tried varying the number of turns of the helix, and we played with the step size for the particle tracing out the field line.

We finally got some very nice drawings of the field lines coming out one end of the solenoid, spiraling out, then spiraling back in to the other end, and running through the center of the solenoid.  It took us a while to realize that the behavior was indeed what we should have been expecting, because the helix has current running parallel to the axis of the helix as well as around the helix.  A simulation (as the book suggests) using only circular rings would not have included this longitudinal current, and we would have missed some interesting views of the magnetic field.

I’m wondering whether we could have gotten a similar result by superimposing two fields: one computed from a stack of circular rings and the other from a wire down the axis, both with the same current.  I might try writing a program that compares the two approaches.

Because we spent an hour doing simulations and looking at the results, we did not get around to doing homework comparisons (a good thing, since I haven’t done the homework yet) nor did we get around to winding a coil and measuring the magnetic field, which I still want us to do.

## 2012 November 20

### Physics lab with magnetometer

Filed under: home school,magnetometer — gasstationwithoutpumps @ 16:10
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Today we did not go over homework problems in our weekly physics time, but did a lab instead.  I rewrote the code I had for using the Freescale MAG 3110 magnetometer chip on the Sparkfun breakout board, so that I could zero-out the measurement for easier differential measurement.  What we did then was to make a big loop of wire (26 gauge magnet wire—the same wire we used for our Young’s modulus experiment) from the floor to the ceiling beams, holding it to the floor with a couple of books, so that we had a straight vertical wire in the middle of the room, several feet from other wires.  We put the magnetometer near the wire, recording the distance and the orientation of the sensor, then zeroed the reading and measured the magnetic field 3 times. We then put a current through the wire (about 200 mA), measuring the current and the magnetometer reading (again, 3 sets of x,y,z values).  We did this for several distances and magnetometer orientations.

We also did one pair of measurements without the wire, zeroing the sensor in one orientation, then turning it around 180° and making another measurement.  This should give us an independent check of the units that the sensor readings are in, since we expect this measurement to be twice the strength of the Earth’s magnetic field (according to the World Magnetic model, as displayed in Wikipedia, we should have about 49µT at a 60° inclination, so the horizontal component should be about 24.5µT, and our measurements should show about a 49µT difference).  Of course, the rotation may not have been an exact 180° horizontal rotation, so we can’t really use this measurement to calibrate the sensor.

The manufacturer’s data sheet claims that the resolution is 0.1µT, but we recorded the sum of 10 successive readings, so our units are 0.01µT.  The repeatability of the measurements was not too bad—probably around ±0.5µT (I’ll have my son compute standard deviations for each set of 3 readings).  We only measured out to 5cm from the wire, since at that distance the field we were measuring seemed to be buried in noise.

My son’s task is to take the recorded field measurements and plot field strength as a function of distance for the measurements we made (probably correcting for differences in current, if those are large enough to matter).  He should also compute the expected magnetic field around a long wire for that field. There are several measurements at one distance, as we tried to verify that we were reading the orientation of the chip correctly—that distance might be a particularly good one for comparing the measured and computed field strengths.

Next week, we’ll try to do a little homework comparison, but we’ll also do a lab winding a helix of wire and measuring the field around it.  We’ll use the computational problem (18P79) to compute the expected field in different places, and try measuring the wound solenoid in corresponding locations.  This means that in setting up the program we’ll have to make the number of turns, the radius of the solenoid, its length, and the current through the solenoid all easily changed, to match the simulation to the coil that we wind.

## 2012 November 16

### Chapter 18 homework

Filed under: home school,magnetometer — gasstationwithoutpumps @ 20:53
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My son and I have both finished reading Chapter 18 of Matter and Interactions, so it is time to assign homework for us.  I’ll also need to spend some time this weekend setting up the magnetometer again, so that we can do experiments on Tuesday.  The experiments at the end of Chapter 18 seem awfully childish—most more suited to a fifth-grade classroom than to a calculus-based physics class. Using the deflection of a compass to get comparative strengths of a magnetic field and the Earth’s magnetic field is cute, but the huge size of a compass big enough to read the angle (at least 1cm) makes for very rough estimates of the field, unless it is nearly constant.  I hope that we can do something a little more fine grained and quantitative by using the magnetometer.

Problems: 18P38, 18P41, 18P56, 18P57, 18P59, 18P61, 18P64, 18P67, 18P75, 18P77

Computational problem: 18P79