User:Stephen K. Martinez/Notebook/Junior Lab/2008/11/12

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Equipment

 * Homade phase shifter (+100kΩ variable resistor)
 * Homade transformer
 * 2-Leybold Didactic GMBH Helmholtz coils: 55506  n=320 d=.15m
 * W5MT3 Variac autotransformer
 * 514 56 ESR-Adapter
 * Leybold 578 95 variable capacitor
 * Tektronix TDS 1002 oscilloscope
 * SOAR DC Power supply ps - 3630
 * hp 6236B Triple output power supply
 * ESR 514 55 Grungerat Basic Unit
 * DPPH electron source (in search coil)
 * electrolytic capacitor
 * RF probe
 * Fluke 45 Dual Display Multimeter

Procedure
This lab has an extremely elaborate set up, the procedure for making the circuit is shown in the lab manual: lab 7 pg 49-58. Essentially the two coils are wired in parrallel and placed facing each other 1 radius apart (for the uniformity of the field) which measurement we took from the approximate middle for the diameter. These are placed into a circuit with a variac/transformer in series with a polarized capacitor, this line was in parallel with the phase shifter(hooked up to channel 1 on the oscilloscope - to provide the constant cosine wave for the ac from the magnetic field) and the power supply, which the entire element was in parallel with the micrometer. note about the capacitor(arrow points in the direction of positive current - toward the lower potential)this is an important safety issue because if the electrolytic capacitor is alligned with an incorrect polarity it will blow up. The second half of the circuit was a ESR search coil with the electron source on it connected to the adaptor and further to the power supply (to provide a radio photon to flip the electron spin direction), oscilloscope (on channel two to provide for the peak data of the radio emmision) and the frequency anylyzer. We had a great debate about the polarity of the electorlytic capacitor (which turned out to be more problematic to the circuit then originally thought). It was decided that the arrow pointed toward the direction of positive current flow, and that it should be hooked up in the direction from higher to lower potential. We finally decided on this by testing the two possible configurations in parallel and analyzed the temperture output using our various body parts (face, hands).
 * The ammeter read 2.0 on the 2000mA scale which we took to infer 4A which was just at the end of our allowed values.
 * The frequency was measeured at approximately 59.98 ± .20.
 * The Variac was set to 115V.
 * the DC power supply in the helmholtz circuit was about 8.5V.
 * The ESR power supply was set to for both ±12V

Koch notes
Steve Koch 23:36, 12 November 2008 (EST):
 * I think the circuit was not quite correct before you left (as we discussed)--the magnet current should be pretty high and we were seeing zero because it looked like the DC power supply wasn't wired correctly.
 * Also, for posterity, I think we need more details about the shenanigans with the electrolytic capacitor: The secret was to wire up two capacitors in both ways and then see which one got warmer quicker. We needed to use upper-lip thermometry to get a definitive 4-0 vote.
 * It does look like you're poised to get everything going next week, and I think you'll find it fun!

Day 2
We did not perfectly establish the circuit on day 1, so day 2 was concearned with taking it apart and trying again. We redrew the circuit so that it basically looked like 4 parrallel circuits. We had some problems with the current direction in our circuit and almost blew up the electrolytic capacitor. Then we got everything to our satisfaction with the circuit but then - the capacitor immediately blew up! It smelled like cheerios and was really hot. It was most likely caused by the high voltage output from the variac so we turned that way down. We also noticed that our multimeter was draining our current so we tried a handheld. which gave us some current. Our next problem was with our frequency - we didn't get a signal at first, then we figetted with stuff and found after creating a common ground between our power supplies and the input to the ESR adaptor that we got a nice square wave. when we plugged everything back together we had lost our sharp peaks, we messed around a lot, and finally we found on Lee Linh's Notebookold notebook that our current value was too high and when we adjusted it we found our spikes again. We measured the dc current for several selected values of the frequency after adjusting the phase shifter to make the peaks line up with our sinusoid symmetrically. The dc current we measured was with really high error as our multimeter fluctuated wildly. Therefore we got a third multimeter: And this one seemed to work well. (thanks to Dr. Koch for all his help)
 * Amprobe 37XR-A
 * Keitheley 179 TRMS Digital Multimeter

Data
Unfortunately because of our problems with the setup we weren't able together a lot of data, this is what we did gather for the medium search coil - intended for use within the frequency range 30-75 MHz. The repetition of each point was to ensure we were collecting accurate data.

Analysis
We analysed our data using the linest function of excel, and also by finding the g-factor for each and then using the mean, we encountered some questions about the dimensions of the values we were using, and we followed Lee Linh's example for our equations and graphs. Essentially:

μmu_s = -g_s(our intrinsic g-factor)*μ_B(the Bohr magneton = 5.788*10^-5 eV/T !!!)* S(spin of electron) / hbar

E=μ_s * B

E_0 ± g_s*μ_B*B which refers to the two energy stats the electron can have in the magnetic field - spin up or spin down. where E_0 was the energy before the magnetic field.

The resonance will refer to the distance in energy between these two states, and the photon that causes them to transition between the two will be of the energy.

hν=g_s*μ_B*B

For the Calculation of the magnetic field between the helmholtz coils we used some knowledge from the e/m lab B=μ R^2 N I/ (R^2 + x^2)^3/2  where μ = 4 pi x 10^-7 weber/amp-meter x=R/2 N=130 R=.15 meters
 * [[Media:ESR2.xls | This is the Excel sheet for calculating the means]]
 * [[Media:ESR1.xls | This is the Excel sheet for Linest]]
 * Steve Koch 00:02, 18 December 2008 (EST): I think I corrected your first excel sheet here: [[Media:ESR2 Stephen, Mike sjk.xls|Corrected sheet]] Actually, though, now I see that you had the radius off by a factor of 2...so, still not sure what's going on.
 * Also, this PDF from Lakeshore is really helpful for figuring out units in magnetism: [[Media:Units for Magnetic Properties.pdf]]
 * Steve Koch 17:46, 18 December 2008 (EST):Actually, see my comments On Chad's page


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