Published on January 7, 2009
Classen e/m Experiment Report Jennifer S. Nalley Lab Partner: Chris G. Cumby February 6, 2007 I
Abstract The Classen e/m Experiment performed was intended to demonstrate how the charge to mass ratio of an electron can be determined by allowing a current run through an apparatus known as the Helmholtz Coil. It is known that a current running through a solenoid creates a magnetic field. The Helmholtz Coil setup is roughly based on this principle. Although the propagated error calculated from our data differed from the standard deviation by a factor of 10, the results obtained were considerably reasonable given the large magnitudes (small numbers) that were recorded. Introduction and Theory The experiment, takes advantage of the fact that the electron displays a unique behavior when introduced into a magnetic field. The primary apparatus used in this experiment, the Helmholtz Coil, provides a duo of coils that are wire-wrapped. A Helmholtz Coil, provided with a current source, in turn yield a magnetic field, which exists horizontally through the coils. Equipped with the Helmholtz setup, and provided with specific mathematical formulas: • Magnetic field B produced at the center of the Helmholtz Coil 8µ o NI B=magnetic field B= N= turns of coil 125 R R=radius of coil I= current in coils µo= permeability of free space= 4лE(-7) weber/amp- m II
*1 weber/meter^2= 1 Tesla • Formula derived to give the relationship between the charge and mass of an electron V= electric potential in Volts B= the magnetic field from experiment given formula e 2V = r= radius of anode circle around ( Bexp r ) 2 the electron beam m e/m =electron charge over electron mass in kg We were able to measure and manipulate the fundamental components which are needed to measure the charge to mass ratio of an electron, and compare it to the accepted value, that is = coloumbs 1.7588 × 1011 kg Apparatus and Procedure The primary piece of equipment used in this lab was a Helmholtz Coil with a vacuum tube at center. The ideal Helmholtz coil set-up is often known for, if not partially defined by its geometric proportions. It is the Helmholtz’s dimensions that allow for the specific equation used for magnetic field to work without a complex manipulation of any proportionality constant. The unit has two identical coaxial circular “coils”. The distances between the two coils are (ideally) proportional to the radius of either coil. Each coil is wrapped with N turns of wire. III
B In our experiment, the number of wire turns N = 133. We measured both the distance between the coils, and the radius of the coils in two ways: from the outer to outer most components, and inner to inner. It was decided to use an average of these measurements, as they were the most consistent with the ideal Helmholtz coil proportions. This choice was determined by our possibly poor assumption that the manufacturer would have the ideal proportions in mind when it was designing the apparatus. The setup we used included: • CENCO apparatus- a three element electron tube with adjustable current and plate voltage. Cathode- serving as an electron source (electron gun). i. (-) Grid- charged to a positive potential to accept and ii. focus the electrons from the cathode into a beam. (+) Anode disk - charged to a higher positive potential to iii. actively attract electrons. • Helmholtz coil(s) IV
At the midpoint between the coils of the unit (1/2 the radius) was the anode disk. Mounted upon the disk, rested a vacuum tube with a filament. In order for there to be visible “action” in a vacuum tube, electrons must have something to interact with. The vacuum tube contained enough inert gas, so that the electron beam that was to be produced would illuminate. From below the tube, the electron exit was secured in such a fashion that electron rays emitted would eject vertically, perpendicular to the magnetic field, which would be initiated via power supply to the cathode. The anode at the center of the setup was designed to be disk shaped so to surround the point of electron emission. Like a dart board, the disk was scored with four concentric circles whose individual radius would become our electron beam target. In our case, the electron beam darts would come out of the bull’s-eye, and be made to bend into a semicircle via magnetic field then hit the disk from which it originated. V
The radii of the circular targets were given as follows: 2.0 cm, 1.5cm, 1.0 cm, and 0.5 cm. Because the earth has its own magnetic field, it was taken into account both numerically and directionally. We used a compass to position the apparatus so that the magnetic field running horizontally through the two coils would be aligned with the direction of the earth’s magnetic field. The right hand rule proved helpful in the determination of the Helmholtz field direction. The northern component of the earth’s magnetic field at our geographical location was found to = 24,708.3 nano-Tesla. *(NOAA) VI
With the lights off, the current and voltage were adjusted in a variety of ways to vary the magnetic field, which in turn would control the curvature of the illuminated electron beam. In order to preserve the filament, precaution was taken to never exceed a current of 0.7 Amps. The goal was to aim the beam at each of the given radii one at a time. The levels for voltage and current were recorded at each radius respectively for the grid, filament, plate, and field. By changing the direction of the current, we were able to replicate the process for readings with our magnetic field going against that of the earth’s field. Each variation was repeated several times, and is recorded in the data. With the data gathered and equations provided, we attempted to calculate the charge to mass ratio of an electron, and compare it to the current accepted number. Data and Analysis The accepted value for an electrons charge/mass ratio is = coloumbs 1.7588 × 1011 kg Our average e/m ratio(s) for readings taken: Lined with earths magnetic field = 2.24065 × 1011 c/kg (± 0.4 × 1011 ) c/ i. kg Lined against the earths magnetic field = 2.01474 × 1011 c/kg (± ii. 0.4 × 1011 ) c/kg VII
Although our propagated error and standard deviation were off by a factor of ten, when comparing our average readings to that of the accepted value, they are not so far off as so to consider the experiment a total failure. *The bulk of hard data will be found on the following page(s). There are several factors that may have contributed to the error in our obtained calculations. Some of these include: o On our first day of collecting data, there was no compass provided. We made due with the assumption, or rather hope, that the device was already positioned somewhat correctly. On the second day, a compass was provided, but we failed to use it to its full potential. We merely noted the general north direction instead of actually bringing the compass close to the apparatus and finely positioning it. In our situation this may have actually led us to more error, because at a later time I noticed something odd. There were two identical compasses in the lab, each reading a completely different, inaccurate north. It is believed that these two compasses had been previously used near an electronics lab, which left their orientation way off. VIII
o Out of the four different disk radii, we were consistently only to line our beam on the outer three. To position the beam on the innermost circle would have required us to increase our magnetic field. Our own uncertainty about the nature of the equipment led us to believe that we needed to increase our voltage to level that was higher than the 0.7 ampere maximum that the filament preservation warranted in order to do so. o We very well could have underestimated the uncertainty of any of the variables involved: the electron beam radius, the measured dimensions of the apparatus, the plate, grid, and field readings. In all of these, we may have been overconfident in our measurement precision, although again, as mentioned before, our results were quite good given the magnitude scale of our data. o It may have been a mistake to assume the manufacturers given data to be correct. More measurements could have been at a minimum verified. IX
Conclusion If executed properly with great precision, this experimental procedure could be used to calculate the e/m ratio with a great accuracy. Acknowledgements Resource for earths magnetic field- Geomagnetic Online Calculator National Geophysical Data Center (NGDC) NOAA Satellite and Information Series NOAA website: http:www.ngdc.noaa.gov/seg/geomag/jsp Halliday/Resnick/Walker- Fundamentals of Physics, 7th edition Chapter 29, problem # 50 X
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