# Physics307L:People/Gonzalez/E/M

## E/M

About 110 years ago J.J. Thompson measured the charge-to-mass ratio of an electron by observing electron behavior in an electric and magnetic field. The field was created using Helmholtz coils, in which a current was sent through the coils creating the magnetic field. More about John Thompson can be found in this Wikipedia article: J.J. Thompson

This experiment attempts to duplicate his findings, after connecting all of the equipment we turned it all on and ran a series of measurements using both constant current and then constant accelerating potential. The electrons were measured through a vacuum tube filled with helium, when the electrons collided with the helium the gas would react and create a small visible green line. The electrons were then manipulated by the magnetic field created by the Helmholtz coils until a circle could be observed. The measurements of the circle were then taken and the respective current on the Helmholtz coils and the accelerating potential on the electrons was recorded as well.

For this experiment I had Jared as my lab partner.

### Data Analysis

SJK 18:53, 15 November 2009 (EST)
18:53, 15 November 2009 (EST)
A few comments were put on your primary notebook page, worth repeating here. First, I think you used standard deviation instead of standard error of the mean for your uncertainties! Also, I think you're missing the slopes analysis. In terms of comparing to the accepted value, you need to compare the discrepancy from the accepted value (accepted minus your measurement) to the size of your uncertainty. Then, you can say whether your measurements are consistent with the accepted value or whether there is substantial systematic error. Given that your uncertainty (that you're reporting) is quite small, and your discrepancy quite large (20%), does that mean there's systematic error?

Several measurements were taken and from that plots involving the radius of the circle created by the electrons vs the inverse of the current and the radius squared vs the accelerating voltage were made. However, the relation between accelerating potential on the electrons, the current on the coils, and the measured radius were also used to find the E/M ratio:

$\frac{e}{m}=\frac{2V}{\left(rB \right)^{2}}$

From using this relation I was able to come up with $\frac{e}{m}=2.12(4)*10^{11}$ when the accelerating potential was at 200V
and $\frac{e}{m}=2.25(8)*10^{11}$ when the accelerating potential was at 188V.
As noted in the lab manual the more accurate readings are more likely to occur when using a higher potential, which was the case here. The accepted value of e/m is 1.76e11, according to the lab manual.

My measurements were off by 20.6% when using 200V and 27.9% when using 188V.

### Error

The greatest factor into my error was due to error in measuring the radii of the beam since such measurements can be subject to parallax. also a higher accelerating voltage would've been more favorable. These errors could've caused me to overestimate the size of the beam, also since the electrons are colliding with the helium atoms they are slowed down and therefore not going as fast as predicted through the equations.