# Physics307L F08:People/Gooden/Notebook/070917

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## **e/m Ratio Experiment**

^{SJK 00:22, 18 October 2007 (CDT)}- This experiment is using the Helmholtz coils and a helium filled tube with an electron gun to measure the e/m ratio. That is the electron charge-to-mass ratio. A heating element inside the tube is heated to the point where electrons in the metal are 'boiled' off and with the help of a voltage applied between two plates the electrons are accelerated. The helmholtz coils are supplied with a current to generate a magnetic field that according to the Lorentz force law will cause the electrons path to be bent into a circular trajectory inside of the tube. As the electrons move through the tube they collide with helium atoms that become excited by the collision and then radiate, allowing us the see the path that the electrons are taking. Measuring the radius of the electrons circular path allows for the calculation of the Charge-to-Mass ratio.

## **Procedure**

**Materials**

This experiment requires 2 DC power supplies, 2 digital volt meters, 1 helmholtz coil, 1 vacuum tube/electron gun assymbly, and 1 high voltage supply.

**Set Up**

step 1 - Connect one of the DC power supplies in series with a DVM, that will measure current, to the Helmholtz coil jacks on the bottom left side of the apparatus. step 2 - Connect the other DC power supply to the electron gun heater jack on the front right of the apparatus. step 3 - Connect the high voltage power supply to the electron gun electrode jacks that are next to the heater jacks. step 4 - Finally connect the second DVM to the voltmeter jacks on the apparatus to measure accelerating voltage.

**Complete Set Up**

Step 1 - Once all of the equipment is connected, turn on the power supply to the heater jacks and allow the electron gun to heat up for several minuets.Keep the voltage under 6.3 volts. Step 2 - Once the electron gun has heated for several minuets go ahead and turn on the high voltage supply to around 250 volts(for best results) and begin to increase the current through the coils using the current knob on the apparatus. Also, turn on both DVM's to being measuring voltage and current through the coils.

## **DATA**

^{SJK 00:25, 18 October 2007 (CDT)}**DATA SET 1 at constant voltage - V=270 V**

Measurment 1Measurment 6I=1.04 I=.99 r1=5.4cm,r2=4.1cm r1=5.5cm,r2=4.1cm * r=4.5cm *r=4.55cmMeasurment 2Measurment 7I=1.01 I=1.22 r1=5.5cm,r2=4.1cm r1=4.9cm,r2=3.9cm *r=4.5cm *r=4.35cmMeasurment 3Measurment 8I=.95 I=1.13 r1=5.6cm,r2=4cm r1=5.2cm,r2=4cm *r=4.6cm *r=4.2cmMeasurment 4Measurment 9I=1.18 I=1.08 r1=5cm,r2=4cm r1=5.3cm,r2=4.1cm *r=4.25cm *r=4.3cmMeasurment 5Measurment 10I=1.24 I=1.30 r1=4.8cm,r2=3.9cm r1=4.6cm,r2=3.9cm *r=4cm *r=3.65cm

**DATA SET 2 at constant current - I=1.35 A**

Measurment 1Measurment 6V=270 V=320 r1=4.4cm,r2=4cm r1=4.8cm,r2=3.9cm * r=3.7cm *r=4.15cmMeasurment 2Measurment 7V=289 V=330 r1=4.6cm,r2=4cm r1=4.9cm,r2=4.1cm *r=3.9cm *r=4.25cmMeasurment 3Measurment 8V=298 V=348 r1=4.6cm,r2=4cm r1=5cm,r2=4.2cm *r=3.95cm *r=4.35cmMeasurment 4Measurment 9V=307 V=360 r1=4.6cm,r2=4cm r1=5cm,r2=4.2cm *r=4cm *r=4.45cmMeasurment 5Measurment 10V=313 V=388 r1=4.7cm,r2=4cm r1=5.1cm,r2=4.3cm *r=4.1cm *r=4.55cm

**DATA SET 3 for random values of current and voltage**

Measurment 1Measurment 6V=180,I=1.21 V=220,I=1.30 r1=3.9cm,r2=3.5cm r1=4.1cm,r2=3.6cm * r=3.7cm *r=3.85cmMeasurment 2Measurment 7V=189,I=1.02 V=230,I=1.33 r1=4.7cm,r2=3.6cm r1=4.2cm,r2=3.7cm *r=4.15cm *r=3.85cmMeasurment 3Measurment 8V=198,I=1.09 V=248,I=1.14 r1=4.6cm,r2=3.7cm r1=5cm,r2=4cm *r=4.15cm *r=4.5cmMeasurment 4Measurment 9V=207,I=1.18 V=260,I=1.01 r1=4.4cm,r2=3.8cm r1=5.5cm,r2=4.1cm *r=4.1cm *r=4.8cmMeasurment 5Measurment 10V=212,I=1.25 V=288,I=4.33 r1=4.2cm,r2=3.7cm r1=4.6cm,r2=4cm *r=3.95cm *r=4.3cm

## **ANALYSIS**

- With the three data sets, we used the formula on the e/m apparatus to calculate e/m for each

measurment and then found the mean for the set and the standard deviation.

^{SJK 00:26, 18 October 2007 (CDT)}

- Value of e/m for data set 1

e/m = 6.28343E+11 +/- .725E+11 (Koch says (6.3 +/- 0.7)*10^11)

- Value of e/m for data set 2

e/m = 3.39E+11 +/- .0272E+11 (3.39 +/- .03)*10^11

- Value of e/m for data set 3

e/m = 3.07111E+11 +/- .00840E+11 (3.07 +/- .01)*10^11

Data Analysis of set 1 and random set

^{SJK 00:28, 18 October 2007 (CDT)}- These values are all very far off from the accepted value of the charge-to-mass ratio of

e/m = 1.76e+11 coulomb/kg. Our result from our first data set is grossly inaccurate and the other two results while not as bad are still not very good. We believe that we are experiencing systematic errors in the experiment, that are most likely not human caused since the another group who performed this experiment obtained results very near ours.

- Errors that could be apart of the experiment include:faulty DVM's, or faulty e/m tube. Other

pausible sources of error could be that the equation used to calculate the ratio is incorrect and also that the constant B (magnetic flux density) for the helmholtz coils is inaccurate.