# Physics307L F09:People/Muehlmeyer/Eoverm

## Introduction

SJK 02:59, 23 October 2008 (EDT)
02:59, 23 October 2008 (EDT)
I think you guys did a really good job in the lab and put an impressive amount of effort into trying out a new data acquisition and analysis method...I'm really happy about that! However, due to the extra time it took you, I think it's evident that you didn't have enough time to really make sure the method was working and you were doing it accurately, which is a big problem. I think with more time, your numbers would have been more in line with the "old method" (which of course is still way off due to the inherent systematic error.

By analyzing the motion of a beam of electrons in a magnetic and electric field, Thomson found that there is a ratio independent of all other experiemental factors: the charge-to-mass ratio. This of course proved his hypothesis that there is a constituent in this beam that is common to all matter: the electron. In this lab, we will re-live Thomson's experiment (or atleast a version of it), by acaccelerating electrons into a strong magnetic field created by Helmholtz coils surrounding the vacuum bulb. The electrons, experiencing a magnetic field force, will rotate in a circle on a plane perpendicular to the field. By oberving the radius of this circle, and by knowing the magnitude of the fields, we will be able to determine the e/m ratio. We will do this numerous times for both constant V and changing V situations. Our hope is to approximate the accepted value of

$\frac{e}{m}=1.7563 \cdot 10^{11} \frac{C}{kg}$

Brief notes on our set up, extensive notes on our data (with photographs), and a theoretical introduction can be found below in my lab notebook:

We will approximate today's accepted value of the e/m ration by taking two sets of data. A set where both V and I are changing, and a set where only V changes. The averages for all the trials of these two experiments can be found below:

## Data Summary

### Changing V and I

SJK 02:57, 23 October 2008 (EDT)
02:57, 23 October 2008 (EDT)
I think one of your values had an error, throwing it off by a factor of 100, and this made your mean way high. It's easy to correct, but definitely I want you to look at your data more carefully so you can notice this kind of thing! differing by one order of magnitude from your other (constant V) should be a red flag to make you scrutinize the data more carefully.

Also, these data would be much easier to read (and more proper significant figures) if you wrote it as, e.g., 2.5 ± 0.1 E12 C/kg (that is, less digits!)

$\frac{e}{m}=4.51731 \pm .128121 \cdot 10^{12}\frac{C}{kg}$

% Error from actual= 2,472%

### Constant V

$\frac{e}{m}=4.72128 \pm .48565645561 \cdot 10^{11}\frac{C}{kg}$

% Error from actual = 168%

### Average from both Experiments

$\frac{e}{m}=2.49472 \pm .104605 \cdot 10^{12}\frac{C}{kg}$

% Error from actual = 1,320%

## Conclusion

My approximation is terribly far off from the exact value, which is most likely due to some outlying pieces of data from trying to measure the radius of the beam circles with a bad photo program.