User:Dan C. Wilkinson/Notebook/Physics 307L/10/13/10

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Steve Koch 01:12, 22 December 2010 (EST): Good notebook. You do a good job of saying what you planned to do, but do not say what you actually did. Also, analysis methods are missing.

e/m Ratio


  • Uchida e/m Experamental Apparatus model tg-13
  • 3 Digital multimeters (2 wavetec 85xt, 1 fluke 111)
  • Soar DC power supply
  • Hewlett Packerd 6236b triple output power supply
  • Gelman delux regulated high voltage power supply


  • The Soar DC supply is connected in series with the fuke multimeter (set to measure amperage) to the helmholts coil jacks in the e/m machine.
  • The Hewlett Packerd supply is connected in parallel with the wavetek multimeter to the heater plugs that supply energy to the cathode.
  • The Gelman power supply is connected directly to the electrode jacks. These supply an accelerating volgage to the electrons. There are seperate plugs that measure this voltage connected to another wavetec multimeter.
John Callow's Setup


The lab manual gives us the magnetic field along the axis of summetry inside the Helmholtz coils. Here the radius is given by R, the number of turns in the coil N, the permeability of free space by [math]\displaystyle{ \mu_0 }[/math], the current by I, and the axis of symmetry by x.
[math]\displaystyle{ B = \frac{\mu_0 N I R^2}{(R^2+x^2)^{3/2}} }[/math]
Our setup can be represented by
[math]\displaystyle{ B = (7.8 \times 10^{-4}) \times I }[/math]
Now we know the magnetic field for a given current we can determine the e/m ratio for the electron.
[math]\displaystyle{ \frac{e}{m} = \frac{2 \times V}{B^{2} \times R^{2}} }[/math]


  • We set the voltage and current to recorded values.
  • We first focused the electron beam by turning off the current and noticing that the focus changed the collumnation of the electron beam. An unfocused beam looks like a cone. Focusing the beam brings it to a "spot." Now the current can be turned on and the beam doubled around on itself.
  • We also had to adjust the bulb position to get good radius measurments ie the left hand radius is the same as the right hand radius and therefore only one radial measurment will sufice.
  • We set the cathode voltage to 6.002Vdc.
  • First we plan to keep current constant and vary the voltage. We will take 5 radius measurments.
  • Second we plan to keep voltage constant and vary the amperage. We will take 5 radium measurment.


Inverse Current vs Radius
Inverse Current vs Radius

{{#widget:Google Spreadsheet |key=0AunM4cHOH1N7dHFXS0FxUXQyWTZrWXJzZ1ZRSEF6TWc |width=900 |height=400 }}

Possibilities for Error

This experiment has many potential sources systematic error. The sources range from the focus (width) of the beam to the alignment of the bulb. The bulb that houses the electron gun and therefor the electron beam is adjustable in two dimensions. First the bulb may be rotated to ensure the beam runs perpendicular to the magnetic field. Second the bulb may be moved back and forth to align the center of the bulb with the center of the scale so accurate beam radius measurements can be made. Both of these adjustments are made by eye and are therefore are open to much human error. It would be productive for the manufacturer of the equipment to mark the bulb/coils/scale so that adjustments are more than arbitrary.