Description:

This experiment determines the ratio of the electron's charge to its mass, via the interactions of electrons with a magnetic field. By combining this ratio with the results of a Millikan-type experiment, we can obtain a measurement of the electron's mass.

 


 
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Possible Incorporated Topics:

  • Magnetic fields
  • Centripetal force
  • Kinetic energy

 


Theory:

Recall from your study of introductory mechanics that when a particle moves along a circular path it is constanly

accelerating, and there must be a centripetal force producing this acceleration. This force is given by the following equation:

F= mv2/r
 

Where m is the particle's mass, v is its speed, and r is the radius of its circular path. By applying a magnetic field of strength B perpendicular to the velocity of the moving electrons, we will produce a centripetal force of strength

 

F = evB
 

Where e is the charge of a single electron. By combining the two equations above, we get the following expression for the

charge over mass ratio of the electron.

 

e/m = v/Br
 

In this experiment, the electrons will be injected into the magnetic field by first accelerating them through a potential difference V.

Assuming the electron is at rest when it enters the accelerating region, the electric potential energy when the electron enters the

region must equal the kinetic energy when the electron leaves the region. In other words,

 

eV = 1/2 mv2
 

Putting this equation into the one previous to it yields the following expression which gives the e/m ratio in terms of the accelerating voltage and the applied magnetic field and the radius of circulating electron's path:

 

 e/m = 2V/B2r2
 

The magnetic field and the accelerating potential can be manipulated independently, while the radius of the beam's path depends on both V and B. By thoughful experimentation, you can determine the e/m ratio.

 


 Apparatus:

  • XH R 60-10 DC power supply
  • 620 9 B DC power supply
  • E/M apparatus

 


 Procedure:

  • Connect and plug in the apparatus. Make sure that the outputs of the power supplies are set to zero before turning them on.
  •  

Figure 1: Apparatus

 

 

  • With no current going through the magnet coils (i.e., Helmholtz coils), apply the acelerating potential so that the electron beam moves up in a vertical direction. Adjust the grid voltage to focus the beam.
  • Applying the magnetic field will bend the electron beam
  • The more current that goes through the magnet coils, the more tightly the beam will bend 

 

 

 
Figure 2: 0 applied Volts 
 
Figure 3: 17 applied Volts 
 
Figure 4: 24 applied Volts 
 

 

You can use the magnetic field to bend the beam to a specific radius (one of the concentric circles in the vacuum tube). You'll know the beam is hitting one of the radius' because you'll see a green glow from the phosphorescent coating on the lines

 

  • Reverse the current through the magnetic field to "flip" the electron beam over. Doing a measurement at a particular radius, then "flipping" the beam to hit the same radius on the other side is a way to get more accurate data. We recommend using the average of the magnetic field measurments required to hit the same circle as a best-measure of the field required for that radius.
  • Be sure to note uncertainties in potentials and currents, and to deal with the uncertainty in beam position

 

 


SAFETY WARNINGS! 

  • Please be sure to note any warnings of maximum current/voltage load on the main apparatus. It is possible to burn out the coils and damage the apparatus