User:Darrell Bonn/Notebook/307L Lab book/lab 2 e over m summary

e/m

Lab Partner: Boleszek

Purpose and Process

The purpose of this lab was to measure the electon charge to mass ratio: e/m. The procedure is fairly straight forward. Utilizing the e/m device, an electron beam is manufatcured and accelerated into an evacuated tube. A magnetic field is placed perpendicular to the beam path and the path curvature is then measured. By accurately measuring the magnetic field strength and the initial velocity of the electrons and the curvature of the beam the charge to mass ratio is simple to compute.

Data and Calculations

Complete notes on our data acquisition can be found in our Lab Manual

There are several variables in this lab. The obvious ones are the accelerating voltage, the magnet current and the measured path radius that are used in the calculations. Another is the heating element voltage, which does not go into those calculations, but which I believe had a significant impact on our data as discussed below.

Two basic sets of data were taken, one keeping the accelerating voltage constant and another keeping the magnet current constant. These data were evaluated separately to look for systematic errors associated with either variable. Each set of data was taken on two separate days with the second days data being far more complete.

The data was ported to a matlab file for processing. It's format was very simple. Data is entered into appropriate arrays, magnetic field is calculated based on the e/m setup. The radius data is then averaged and e/m produced for each data point. From these a mean and standard deviation are calculated and the followind output is produced:

Day 1, Constant magnet current: E/m = 4.606E+011 with std dev of 6.645E+010

Day 1, Constant accelerating voltage: E/m = 4.169E+011 with std dev of 4.872E+010

Day 2, Constant magnet current: E/m = 3.706E+011 with std dev of 1.947E+010

Day 2, Constant accelerating voltage: E/m = 3.729E+011 with std dev of 2.369E+010

The standard deviation of this data would seem to indicate a fair amount of accuracy for any given set of data. However, clearly we've missed the accepted value by

These are all fairly far away from the accepted value of -1.76E11 C/kg. in spite of the fact that the standard deviation of this data would indicate some decent accuracy. Note that the data from day one has a significantly larger than that taken on day two. Also that for each day the two methods produce similar numbers within each others error range. This would seem to indicate a systematic error.

Looking back over the data acquisition notes it seems the likely culprit is the filament voltage.

Summary and Comments

It seems likely that a large part of our error came from having the filament too high. This would impart too much energy to the electons and skew our data.

It is also possible that improved current readings contributed to differences between the two days data