Physics307L F08:People/Gooden/Notebook/070917

e/m Ratio Experiment



 * 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.

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.
 * Complete Set Up

DATA

 * DATA SET 1 at constant voltage - V=270 V

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

Measurment 1                    Measurment 6 V=270                            V=320 r1=4.4cm,r2=4cm                  r1=4.8cm,r2=3.9cm * r=3.7cm                        *r=4.15cm Measurment 2                    Measurment 7 V=289                            V=330 r1=4.6cm,r2=4cm                  r1=4.9cm,r2=4.1cm *r=3.9cm                         *r=4.25cm Measurment 3                    Measurment 8 V=298                            V=348 r1=4.6cm,r2=4cm                  r1=5cm,r2=4.2cm *r=3.95cm                         *r=4.35cm Measurment 4                    Measurment 9 V=307                            V=360 r1=4.6cm,r2=4cm                  r1=5cm,r2=4.2cm *r=4cm                            *r=4.45cm Measurment 5                    Measurment 10 V=313                            V=388 r1=4.7cm,r2=4cm                r1=5.1cm,r2=4.3cm *r=4.1cm                           *r=4.55cm
 * DATA SET 2 at constant current - I=1.35 A

Measurment 1                    Measurment 6 V=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=3.85cm Measurment 2                    Measurment 7 V=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=3.85cm Measurment 3                    Measurment 8 V=198,I=1.09                     V=248,I=1.14 r1=4.6cm,r2=3.7cm                r1=5cm,r2=4cm *r=4.15cm                         *r=4.5cm Measurment 4                    Measurment 9 V=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=4.8cm Measurment 5                    Measurment 10 V=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
 * DATA SET 3 for random values of current and voltage

ANALYSIS
measurment and then found the mean for the set and the standard deviation.
 * With the three data sets, we used the formula on the e/m apparatus to calculate e/m for each

$$e/m=\frac{2V}{(B*I)^2R^2}$$

e/m = 6.28343E+11 +/- .725E+11 (Koch says (6.3 +/- 0.7)*10^11) e/m = 3.39E+11 +/- .0272E+11 (3.39 +/- .03)*10^11       e/m = 3.07111E+11 +/- .00840E+11 (3.07 +/- .01)*10^11 [[media:Book1.xlsx|Data Analysis of set 1 and random set]]
 * Value of e/m for data set 1
 * Value of e/m for data set 2
 * Value of e/m for data set 3

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. 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.
 * These values are all very far off from the accepted value of the charge-to-mass ratio of
 * Errors that could be apart of the experiment include:faulty DVM's, or faulty e/m tube. Other