# User:Emran M. Qassem/e/m Ratio

## Overview

In this lab we measured the ratio of e/m for electrons using an electric field on a charged particle.SJK 01:12, 13 October 2010 (EDT)
01:12, 13 October 2010 (EDT)
actually you mean a magnetic field on a charged particle having been accelerated by an electric field
Knowing the electric field, measuring voltage, current, and the radius of curvature of the generated electron loop, we can calculate the e/m ratio.

The accepted value is $1.76 * 10 ^{-11} \frac{coul}{kg}$ as gathered from the lab manual. (Steve Koch 01:14, 13 October 2010 (EDT):Typo in your accepted value, should be +11)

## Procedure

After setting everything up correctly according to the lab manual, we set voltages and currents, took measurements and logged them in the spreadsheet.

Our first set of measurements, we didn't understand what was needed so we took two sets of current measurements for 5 different voltage measurements. Once we discovered that we needed to take 10 measurements, 5 currents at a constant voltage, then 5 voltages at a constant current, we did that and created some spreadsheets with that data.

Once we had the data, we used the LINEST spreadsheet function to give us a fitted line based on a slope and intersection, and from that we generated data points and built a graph based on them.

## Results

SJK 01:24, 13 October 2010 (EDT)
01:24, 13 October 2010 (EDT)
In your primary notebook, I see that you calculated a few different values for the e/m ratio, but here you only report one, which happens to be closest to the acceptable. You don't say why, and of course you would need to say that. In this case, I don't think the one you report is your "best," despite it being the closest--this experiment is known to have substantial unavoidable systematic error, so you actually shouldn't be close with careful measurements.

Using the results from the best fit line graphs, and using the equations given to us in the lab manual, we calculated e/m and found it to be $1.83 * 10^11 \pm 8.5 * 10^9 \frac{C}{kg}$ based on the error from our best fit line.

I was quite satisfied with these results. SJK 01:19, 13 October 2010 (EDT)
01:19, 13 October 2010 (EDT)
Satisfied with some good measurements and analysis, I'd say yet. However, satisfied that you're measuring the value without lots of systematic error? That discussion is lacking, but should be in your future labs. In this case here, your 68% confidence interval is something like 1.74 to 1.92 * 10^11 ... which is consistent with the accepted value--but so far I don't know how you did that since it should be impossible with this apparatus!.

## Error

The calculated result is off by 1 sigma from the accepted value, which is at about 68 percent accuracy. Error can be caused by our data collection as we could not get the exact measurement of the electron particle radius of curvature as the bulb had distortion and was very difficult to measure because of the low intensity of the particle beam which reduced visibility.

Systemic error can be caused by the equipment.

## Conclusion

Although our results were fairly reasonable, our data collection was all over the place at first, as we were not clear on what we needed to do. We learne how to use the spreadsheet and how to make graphs with best fit lines, which also very useful for this and future experiments.