# Physics307L F09:People/Le/Notebook/071105

## Purpose

To observe "spin-flipping" of electrons when they are exposed to an external B field, and then to calculate thier famous gs factor.

## Procedure

Last Year's Manual See pages 54-63

Circuit drawing of the setup for the coils
Cicuit drawing of the setup for the probe
Sample output from Oscilloscope

The setup was the most important and difficult part of the lab. The circuit shown to the right, and in the lab manual, was all we had to go by while putting everything together. The main points of setting up the circut are as follows:

• The coils had to be connected to each other in parallel
• The transformer (attatched to the VAC) had to be in parallel with the adjustable power supply
• The capacitor had to be in series with the transformer but in series with the adjustable power supply (making sure the polarity on the capacitor was in the correct direction)
• The phase shifter has to be in parallel with everything else, but connected to the oscilloscope directly.

After the coils are setup, the probe has to be setup. Following the diagram to the right, connect the probe unit's BNC cable to the ESR adapter, the freqency end to a frequency meter, the output into an oscilloscope and plug in a +12V and -12V to power the entire unit (able to be achieved using either a dual polarity power source, or wiring 2 voltage supplies together). Placing one of three different coils in the end of the probe, with the sample inside the coils, that half of the setup is now complete.

Once everything is wired, place the 2 coils in front of each other about 1 radius apart. Then place the probe's wire with the sample in between the coils as close as possible to the center. With everything on we start reading the oscilloscope. Channel one reads the magnetic field of the coils and channel 2 reads the RF freq in the probe.

Depending on the coil in the probe (see manual or data set below for details) adjust the voltage through the Helmholtz Coils and/or the freqency of the probe until the probe readings have small "spikes" in them. Calibrate the image by placing the bottom of the spikes at the zero line and then using the phase shifter, try to sync the magnetic field with the RF spikes. Once the pictures are symmetric, record the data and redo it for different coils, at different freq/voltages.

## Equipment

• type w5mt3 variac autotransformer
• fluke 111 true rms multimeter
• homemade phase shifter
• soar model ps-3630 dc power supply
• 2x's leybold didactic gmbh helmholtz coils n=320 diam=.15m
• 514 55 esr-grundgerat esr basic unit
• tektronix tds 1012 oscilloscope
• 514 56 esr addapter
• HP 721A power supply x2
• dpph electron source

## Data

### Small Coil

range 75-130mhz

Freq (mhz) Current in coils
75 1.016A , 1.159 A
90 1..288A , 1.385 A
105 1.47A , 1.620 A
120 1.669A, 1.850
80 1.096A, 1.231A

Note: fist column of current values indicates 1st set of data taking (that we deemed to be flawed since we feel we did not calibrate the setup properly)

### Medium Coil

range 30-75mhz

Freq(mhz) Current in Coil
50 1.089A, .770A
30 .411A, .446A
40 .690A, .600A
60 1.043A ,.914A
70 1.18A ,1.130 A

Note: fist column of current values indicates 1st set of data taking (that we deemed to be flawed since we feel we did not calibrate the setup properly)

### Large Coil

range 13-30mhz

Freq (mhz) Current in Coils
13 .238A
17 .247A
21 .337A
25 .356A
28 .481A

## Data Analysis

To find the intrinsic g factor, we will use the formula below.

$\mu_s=\frac{E}{B}$ and we know the energy of the electron because we know its accelerating voltage.

$B=\frac{\mu R^2 N I}{ (R^2 + x^2)^{3/2} }$ where $\mu = 4 \pi x 10^{-7} \frac{weber}{amp-meter}$ $x=\frac{R}{2}$ N = 130 R = .15meters

The electron can be either spin up or spin down with energy $E_0 +/- \frac{g_s \mu_b B}{2}$

Since the electrons have certain states they prefer to be in, we can see that the conditions for resonance is when

• hν = gsμbB

where ν is the frequency of the probe

### Small Coil

h*nu nu_B*B
.3102 e-6 .5228 e-11
.3722 e-6 .6247 e-11
.4342 e-6 .7307 e-11
.4963 e-6 .8344 e-11
.3308 e-6 .5552 e-11

### Medium Coil

h*nu nu_B*B
.2086 e-6 .3473 e-11
.1241 e-6 .2012 e-11
.1654 e-6 .2706 e-11
.2481 e-6 .4123 e-11
.2895 e-6 .5097 e-11

### Large Coil

h*nu nu_B*B
.0538 e-6 .1074 e-11
.0703 e-6 .1114 e-11
.0868 e-6 .1520 e-11
.1034 e-6 .1606 e-11
.1158 e-6 .2170 e-11

After graphing the above tables, and taking a linear trend, I get a gs value of 1.68±.021, where my uncertainty was found using the "linest" command in Excel.

### Conclusion

Comparing our value of gs to the accepted value of 2.0023

$%error= \frac{|Actual-Experimental|}{|Actual|}x100$

$%error= \frac{|2.0023-1.6858|}{|2.0023|}x100$

%error = 15.8

#### Possible Sources of Error

• The Helmholtz coils may not have been aligned exactly parallel. One may have been higher than the other. Also, the lab notebook wanted then 1 radius apart, but the best we could do is have the stands touching each other as the closest spot
• This could mess up the uniformity of the B field
• The Helmholtz Coils get hotter as the current flows in them, changing their resistances, possibly changing the B field
• Steve Koch 00:15, 4 December 2007 (CST):But you kept measuring the current, right?
• The RF coil had to be in the middle of the B field (where the field is most uniform) but could only be in about 40% of the way (since we could not separate the coils to make more room).
• The RF coil is metal, which attracts B fields, which could have skewed the field itself
• Steve Koch 00:15, 4 December 2007 (CST)I wouldn't say "attracts B fields". Plus, it is not ferromagnetic, so do you think it affects anything appreciably?
• The Earth's and surrounding electronics' B fields could interfere with the Helmholtz's (although it is assumed that the coils' field is strong enough to negate any outside fields).
• Calibrating the oscilloscope and making sure the graphs lined up required alot of "eyeballing" which may lead to human errors

#### Possible Fixes

Since I feel that most of the error comes from the perturbation of the magnetic field, larger coils will produce a larger, more stable magnetic field, and allow the coils themselves to be placed further apart to allow the RF coil to be more in the middle.