User:Cristhian Carrillo/Notebook/Physics 307L/2010/11/10

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e/m Ratio

  • Please note that Ginny was my lab partner for this lab.


The purpose of this lab is to measure the charge-to-mass ratio of the electron by studying the effects of electric and magnetic fields on a charged particle.


Total Apparatus
(bottom) Hewlett-Packard DC Power Supply (Model 6384A, 4-5.5V, 0-8A) and (top) BK PRECISION Digital Multimeter (Model 2831B, SER. NO. 000-03-0618 , 5 WATTS, 8 VA,50~60 Hz)
e/m Experimental Apparatus (Model TG-13)
(left of e/m E. A.) SOAR corporation DC Power Supply (Model 7403, 0-36V, 3A), (top right) BK PRECISION Digital Multimeter (Model 2831B, SER. NO. 099-10-0357 , 5 WATTS, 8 VA,50~60 Hz), (bottom right) Gelman Instrument Company Deluxe Regulated Power Supply (500 V, 100 mA)
measuring scale
image of electron beam
  • Hewlett Packard DC Power Supply (Model 6384A, 4-5.5V, 0-8A)
  • e/m experimental apparatus (Model TG-13)
  • SOAR corporation DC Power Supply (Model 7403, 0-36V, 3A)
  • Gelman Instrument Company Deluxe Regulated Power Supply (500V, 100mA)
  • 2 BK Precision Digital Multimeter (Model 2831B)


  • Make sure to ground all power supplies properly before use
  • Check cords, cables and machinery for any possible electrocution points on fuses of cords
  • Protective grounding conductor must be connected to ground
  • Be careful with the mercury tube


We followed the descriptions in Professor Gold's manual and Alex Andrego's Notebook for the setup.
Below are the steps we followed to setup the experiment
  • We first used BNC cables to conncect a regulated 6-9V DC supply rated at 2A to the Helmholtz Coil jacks.
  • Connected the ammeter in series between the supply and the coil jacks.
  • We connected the 6.3V power supply rated at 1.5 A to the heater jacks of the electron gun.
  • Connected a high voltage source at 150-300V DC rated at 40mA to the electrode jacks of the electron gun
  • Please note that the voltage determines the average velocity of the electron in the beam.
  • We then connected the DC voltmeter at the jacks labeled "voltmeter" on the base panel.
  • Be sure to turn the current adjust control to zero and set the switch on the panel to the e/m position.
  • Make sure that nothing is connected to the jacks labeled "Deflection Plates" at this time.
  • Allowed the electron gun filament to heat up for a few minutes after we turned on the heater supply.
  • We then applied a 200V DC potential from the high voltage supply to the electrodes.
  • Then we turned off the light to begin the experiment.
  • Make sure that a black cloth to cover the tube and to backdrop the beam while observing the beam of electrons.
  • We then adjusted the current control until the beam formed a circle by turning on the coil current and increasing the current adjustment control.
  • We then used the scale behind the bulb to measure the radius of the loop of the beam.

Calculations and Analysis

Below is our raw data {{#widget:Google Spreadsheet |key=0AqzpS6URre5adEVENnRPMkZHTXpKeWVDM2o4V242WUE |width=800 |height=500 }}

  • The following equations were used to calculate the e/m ratio.
We found the Helmholtz configuration from Professor Gold's Manual to be:
, , and
The permeability of free space is given as
From these values we can calculate:
We know that the energy of the electron is equal to the kinetic energy:
The magnetic force for a charge is...
The centripetal force is...
Finally we set the centripetal force equal to the magnetic force and obtained:
According to Professor Gold's manual, the current accepted value of is:

Below is the average and SEM that we found using the above equation we obtained when we set the centripetal force equal to the magnetic force.

  • Average
  • SEM
  • Percent Error
The other way to find is to plot
  1. vs. , where is constant.

  1. vs. , where is constant.

From this graph we have that:
We also have that the equation of slope is:
Therefore we can calculate the ratio of by:
So we have:

Discussion on Error

Reasons for our systematic error

  • We had to measure the radius of the electron beam by eye using a fixed ruler in the back of the apparatus. This was hard because we had to roughly estimate for each of the measurements.
  • Looking at the second graph above, we can clearly see that there was a larger error for the ratio than the first graph.
  • Percent Error for the second graph
  • This percent error came out better than I thought it would be, so I assume that the error for the first graph would have been even smaller.


  • I would like to thank Ginny for the great help with this lab and all the other labs we have worked on.
  • I would like to thank Katie for helping us with the setup.
  • Alex Andrego and Anastasia Ierides for the great pictures and setup instructions.