# Physics307L:People/Ozaksut/E over m

### From OpenWetWare

day one lab notebook: http://openwetware.org/wiki/Physics307L:People/Ozaksut/Notebook/071121

day two lab notebook: http://openwetware.org/wiki/Physics307L:People/Ozaksut/Notebook/071128

## Contents |

## e/m

## Goal

- measure the charge to mass ratio of an electron
- understand EM

## Theory

Electric currents induce magnetic fields. The magnetic field along the axis of symmetry generated by Helmholtz coils is given by an equation relating number of coils, current in the coils, and radius of the coils. Helmholtz coils are special because the magnetic field between them is nearly constant for a larger area than for other magnetic field inducing coils. We know the number of coils and radius of coils, and we will control the current in the coils using a power supply.

The magnetic field generated by a current in the counterclockwise direction will be parallel to the ground, in the direction of the experimenter. The force on a charged particle in the magnetic field will be qvXB, so any particle with initial velocity in the counterclockwise direction will continue to travel in a circle, in the counterclockwise direction, due to the force on the particle directed towards the center of the circle.

The centripetal force on the electron is ma=mv^2/r, and the centripetal force is equal to the force the electron feels from the field, we equate ma=mv^2/r=qvXB=qvB because v, B are perpendicular always. q/m=v/rB. now, r=mv/qB.

The kinetic energy of the electrons when they leave the electron gun is given by mv^2/2=qV. so the velocity is v=(2qV/m)^1/2. q/m=v^2/2V. v/rB=v^2/2V. v=2V/rB.

We will accelerate electrons off of an electron gun with different voltages between Helmholtz coils and measure the radius of the circular path they make because collisions with electrons in the helium release photons all along the path. With this information, we can calculate the ratio e/m.

Northwestern's lab manual is a thorough guide to this lab.

## Equipment

- Helmholtz coils
- three power supplies
- electron gun and helium bulb
- three multimeters

## Setup

First, we connect banana plugs from a DC power supply (Soar Corporation DC Power Supply 7403) to the electron gun heater jacks on the e/m apparatus for 2 minutes at .7 A current, 6.3 V voltage. (Uchida e/m Experimental Apparatus Model TG-13)

Then, we turn on the 200V DC power supply (Gelman Instrument Company Deluxe Regulated Power Supply) and connect it with banana plugs to the electrode jacks on the apparatus at 200V, 25mA. The electrodes are what supply the accelerating voltage to the anode which pulls excited electrons from the cathode. We want to know the accelerating voltage precisely, so we connect a voltmeter (BK Precision Digital Multimeter 2831 B), to the Voltmeter sockets on the e/m Apparatus with banana plugs.

Finally, we turn on the coil current (Soar DC power Supply PS3630) connected in series through a multimeter (Wavetek True RMS 85 XT) to ensure accuracy in our calculations at 1.96 A and 8 V.

A mirrored ruler is mounted on the back of the Helmholtz coils so that measurements of the electron beam radius can be taken.

## The Procedure

To measure the radius of curvature of the beam of electrons we made sure the beam was eye level, and then we measured the radius of each side of the path separately by making sure the edge of the beam that we wanted to measure was lined up with the same edge of the image of the beam on the mirrored ruler to try to reduce parallax error looking through a round glass helium bulb. This was necessary because the radius of the electron beam would theoretically shrink as the electrons in the beam lose energy to exciting other electrons in its path. Additionally, since the beam had some thickness, we decided to take measurements from the outer edge of the beam, because those electrons would be the most energetic, they would have lost the least amount of energy to other electrons, and thus would correspond most accurately to the accelerating voltage in the electron gun. We took threee sets of data for the radius of curvature, once holding accelerating voltage constant and varying coil current, once holding coil current constant and varying accelerating voltage, and once with random combinations of accelerating voltage and coil current. We recorded our data in Microsoft Excel, and used Excel to do the data analysis.

## Data

## Results

We calculated the ratio e/m to be 3.09E-11 ± 1.48E-11 coulombs/kg. The current accepted value is 1.76E-11, so our relative error is 44%. I am unsure of what could have affected the result, but I did notice that the left radius was actually greater than the right radius for many of our calculations. Because I knew where the path was (so, I knew my electrons were definitely losing energy), I thought that maybe the magnetic field inside the Helmholtz coils might not be constant, because the radius at the end of the path should have been smaller than at the beginning.