The purpose of this lab is to measure the charge to mass ratio (e/m) for electrons whilst studying the effects that electric and magnetic fields have on a charged particle. For N coils carrying current I with radius R, the magnetic field along the symmetry axis x is given by:
According to J.J. Thompson if the electron has finite charge e and has mass m it will obey the laws of motion for a charged particle moving through a magnetic/electric field. The e/m ratio is the charge to mass ratio of an electron which can be determined if the energy of the electrons and the magnetic field strength are known. "In this experiment [we will be] observing the behavior of electrons in a magnetic field and determine a value for the electron charge-to-mass ratio e/m. The apparatus consists of a large vacuum tube supported at the center of a pair of Helmholtz coils,... The vacuum tube contains an electron gun which produces a collimated beam of electrons that is deflected by a magnetic field. An electron gun has two main parts: a filament that produces electrons through thermionic emission, and an anode that is placed at high positive potential so as to accelerate thermal electrons from the filament to the main region of the vacuum tube,... The magnetic field produced by the Helmholtz coils deflects the electrons into circular trajectories and these paths are made visible through collisions by the electrons with a trace amount of mercury vapor present in the vacuum tube." The Electron Charge-to-Mass Ratio e/m
Equipment
Hewlett-Packard DC Power Supply (Model 6384A, 4-5.5V, 0-8A)
SOAR corporation DC Power Supply (Model 7403, 0-36V, 3A)
Gelman Instrument Company Deluxe Regulated Power Supply (500 V, 100 mA)
2 BK PRECISION Digital Multimeter (Model 2831B, (1)SER. NO. 000-03-0618 & (2)SER. NO. 099-10-0357 , 5 WATTS, 8 VA,50~60 Hz)
e/m Experimental Apparatus (Model TG-13)
Safety
Before we begin, some points of safety must be noted:
First and foremost your safety comes first and then the equipments'
Check the cords, cables, and machinery in use for any damage or possible electrocution points on fuses of machinery by making sure the power cords' protective grounding conductor must be connected to ground
Be careful to ground all power supplies properly before use
Be careful while handling and working with the mercury tube
Make sure the areas containing and around the experiment are clear of obstacles
treating [math]\displaystyle{ \frac{2}{({7.8\times10^{-4}{I})}^{2}}\times\frac{m}{e}\,\! }[/math] as a constant which gives us a linear relationship with this as our slope.
In order to determine the slope we need to plot our data:
Taking into account our slope uncertainty value of [math]\displaystyle{ \pm 0.00000072021\,\! }[/math] the range of our measured ratio [math]\displaystyle{ \frac{e}{m}\,\! }[/math] is...
treating [math]\displaystyle{ \sqrt{\frac{(7.8\times10^{-4})^{2}}{2V}\times\frac{e}{m}}\,\! }[/math] as a constant which gives us a linear relationship with this as our slope.
In order to determine the slope we need to plot our data:
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Note: Due to the fact that all values of current are negative, we took the absolute value of the current for graphing purposes because the negative sign was purely directional.
Taking into account our slope uncertainty value of [math]\displaystyle{ \pm 1.730792\,\! }[/math] the range of our measured ratio [math]\displaystyle{ \frac{e}{m}\,\! }[/math] is...
The only way to achieve measurements for the radius of our electron beam was to measure by eye using a fixed ruler in the back of our apparatus. This could cause a huge source of error because we were basically estimating for each measurement. This also caused a lot of rounding error because we were estimating we were not able to give very specific measurements.
Steve Koch 15:39, 14 November 2009 (EST): As I mentioned on your summary pages, I don't think this is the source of your systematic error. Unfortunately we didn't get to talk about this at all during the lab class, but the experiment is basically forced to have a lot of systematic error, and you can hypothesize on the reasons if you do this lab for your formal report.
Summary
If you wish to see Alex Andrego's informal summary of this lab follow this link
If you wish to see Anastasia Ierides's informal summary of this lab follow this link