# Physics307L F07:People/Trujillo/Final Report

The e/m Ratio Experiment

Lorenzo Trujillo University of New Mexico Albuquerque, NM ltrujillo@ztec-inc.com

## Contents

### Abstract

Charged particles moving at speed v in a magnetic field B experience a force given by F = qv * B. Assuming the electrons move in a circle, use this force in Newton’s second law to derive the ratio e/m in terms of v, B, and r, where r is the radius of the circle and e is the magnitude of the electron charge. This is great, but, we can’t directly measure v or B. We can, however, measure voltages and currents which will be enough. The electron beam is created when electrons are accelerated across a potential difference,V . Conservation of energy gives: 1 / 2mv2 = eV . We can measure this potential difference and use it to find the speed.

### Introduction

Electrons are boiled off a a cathode and are accelerated through an electron gun into a magnetic field at right angles to the velocity vector of the ejected electrons. The magnetic field is produced by two Helmholtz coils outside a nearly evacuated glass bulb that contains the electron gun and a tiny amount of helium gas. The magnetic field causes the electrons ejected from the electron gun to change their direction of travel, causing the electrons to travel in a circle until they hit the electron gun again. The electron travel path is observable if the apparatus is observed in a darkened room because as the electrons travel, some may excite the helium molecules in the bulb, resulting in a faint glow along the electrons' travel path. The radius of the circular travel path is strongly determined by the charge-to-mass ratio of an electron, the accelerating voltage of the electron gun (since this determines the initial velocity of the electrons once they enter the magnetic field), and the current fed into the Helmholtz coils (since this determines the strength of the magnetic field).

### Materials and Methods

For the e/m experiment, we used the Helmholtz Coils apparatus along with some power supplies and meters to monitor the accelerating voltage we were injecting.We started by setting up the test apparatus using 2 power supply's and 1 multimeter. The supply's were used to  supply the test apparatus with both the Helmholtz coil current and the accelerating potential. The multimeter actually measures the Helmholtz current (no larger than 2A). After seeing the electron beam we started just playing around with the settings just to get a feel for the setup and the test apparatus. After we felt comfortable with the equipment, we started taking measurements on the electron beam. The measurement procedure is outlined in Professor Golds lab handbook. One thing that was not documented was the use of the "focus" knob on the apparatus.  We first first fixed the coil current to 1A, varied the accelerating potential (V) from 200V,  incremented the potential by 20V up to 260V measuring the radius of curvature at each increment. We determined the measurement error by observing the uniform width of the beam from measurement to measurement. The same type of procedure was done with data set #2 except this time we fixed the accelerating potential at 200V and varied the coil current starting from 1A to 1.6A in .2A increments. In both data sets, before we measured the radius of the beam, we adjusted the "focus" knob to "clean-up" the beam.

### Results and Discussion

In a magnetic field of strength B, the Lorenzts force acting on than electron with velocity v is F = evxB. If the magnetic field is uniform, as it is in the Helmholtz arrangement, the electron follows a spiral (helix) path along the magnetic lines of force, which becomes a circle of radius r if v is perpendicular to B. As we increased the coil current we noticed that the ring was getting smaller (r was decreasing). By increasing the current, the magnetic field became stronger and since the radius of of the electron path is proportional to the strength of the B field (from the equations above)and the e/m ratio decreases as well. The reason why we are able to see a visible light trail is because some of the electrons collide with helium atoms. The atoms are excited and then radiate visible light. Furthermore, when we fixed the coil current and varied the accelerating voltage, the radius r increased significantly as did the e/m ratio which was translated a decrease in B field strength allowing the electron to be loosely bound. Something that we didn't now was that a unique feature of the e/m tube is that the socket rotates, allowing the electron beam to be oriented at any angle (from 0-90 degrees) with respect to the magnetic field produced by the Helmholtz coils.

### Good data and analysis

e / m = 2V / r * B2 B was calculated for varying I SEE RAW DATA ATTACHED

Accelerating Voltage (V) Coil Current (A) Radius Left (cm)errorcalculated E/M ratio
2001.004.90.21.76e11
2001.204.80.21.02e11
2001.404.60.36.68e10
2001.604.50.34.57e10
2001.004.80.21.76e11
2201.004.90.11.89e11
2401.005.10.21.98e11
2601.005.20.32.11e11

My REVISED excel sheet could be found here: Image:Lab 2 e m calculation.xls

### Good figures(dont ask me why my graphs are all jacked)

I saved them in every godam format you could think of and they didn't appear!! Thanks for that other pic by the way!

### Conclusions

For some reason I was not able to get an accepted value for e/m. At first I was on the right track but after second guessing myself and doing some additional testing, the number that Tomas and I we getting were not reproducible. Some of the problems that we saw with the test apparatus was first the focus knob (what does that do and how bad does i affect our measurements), the underlining affect of parallax, and the fact the the actual bulb turns, obviously changing the radius of curvature. I guess I was not fully satisfied on how the experiment turned out but all and all, I was able to conceptually able to understand what is supposed to happen

### Acknowledgments

-Tomas Mondrago

-Dr Steve Koch

- That smelly TA guy