# Charge to Mass Ratio

## Charge to Mass Ratio Lab Summary

**Goals**

This lab was fairly straight forward. Our goal was to measure the charge to mass ratio of the electron. We prescribed the strength of a magnetic field perpendicular to an electron beam and the accelerating voltage on the beam. These two forces twist the beam into a circle. We then measure the radius of circle and through the use of certain equations, these measurements result in a ratio of the charge to mass.

**Theory**

In this experiment, the beam is twisted into a circle by the magnetic field, but the inertia of the electrons causes them to resist the twisting. By increasing the accelerating voltage of the electrons, we increase their momentum, causing the beam to straighten. Conversely, when the strength of the magnetic field is increased, the beam attempts to curl. By measuring the radius of the circle that the beam makes under known accelerating voltage and magnetic field, the charge to mass ratio can be determined.

[math] \frac{e}{m} = \frac{V^{2}}{B^{2} \times R^{2}}[/math]

Magnetic field can be expressed in terms of the current of the Helmholtz coils and the number of rings in the coils. Fortunately, Dr. Gold in his lab manual solves this equation for us in for our particular setup ahead of time.

[math]B=7.8 \times 10^{-4} \times I[/math]

**Results**

My data yielded an overall result of 1.556x10^11±2.146x10^10. However, there are a few notable traits of my data. The data taken under constant voltage yielded a very high accuracy, but in excess of 25% error of the excepted value. My calculations yielded an error of 26±4% On the other hand, the data taken with constant current had a much lower error, on the order of 12%, but it deviated much more significantly from the mean. The final error from the excepted value 12±12%. I noted experimentally that the voltage varied much more significantly than the current as a possible explanation for my data. Secondly, it should be noted that there could be significant systematic error with the measuring of the radius, as it must be "eye" against a backdrop with a measuring rod.