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PHYSICAL PROPERTIES OF THE ELECTRON

The magnetic field of a solenoid can be calculated approximately using Ampere's Circuital Law, but more exactly stated from the Biot-Savart Law. From the following representation of a solenoid:

Figure 1: Magnetic Field of a Solenoid. Physical apparatus including current supply for the solenoid and voltage supply for the tube, both filament and plates.

The magnetic field at point P along the axis, but inside the solenoid can be stated as:
(1)

where the value is B at P due to the turns of wire in the increment of length dx, which is a distance x from P and n is the number of turns per unit length. The total value of B at P may be computed by adding up the effect of all the turns of wire in the total solenoid. We thus integrate equation (1) from the left end of the coil, where x = -(L-D) to the right end, where x = D. The result is complex, but in the limit of a "long" solenoid (length long compared to the diameter) we get:
 
B = µo I n (2)

In the solenoid you are working with, there are 540 turns of wire in the length L. n is thus 540/L. You can measure L in metres easily. By adjusting the current, you will be able to then control (and determine easily) the value of B. You will also need to determine the average radius of the solenoid to do this.

With your present knowledge about solenoids and magnetic fields, we can go about determining the properties of the electron. Good Luck!

You will use a commercial vacuum to estimate the ratio of charge to mass of the electron. This tube is much like the "tuning eye" of FM tuners. You basically control the velocity of emitted electrons so that the properties can be determined.

Look at the tube. There is a circular metal cap at the top of the tube. Beneath this is the cathode. When a filament voltage is applied to it, it thermally emits electrons. These thermally emitted electrons are then accelerated horizontally to the cathode. See Figure 2.

Figure 2: Undeflected patterns of electrons accelerated to the cathode. Note the greenish line showing accelerated electron path.

The anode is coated with a fluorescent material which glows when electrons strike it. Observe this pattern. Now, if the tube is placed in a solenoid with a current in it, the electrons will be subjected to a magnetic field which you can determine at a certain point, perpendicular to the direction of motion. We must assume that the electrons have already reached their maximum velocity when we can see them (or rather their effect) so that the system is basically a beam of electrons moving horizontally in a magnetic field. The result is that the electrons will move in a circular path. See Figure 3.

Figure 3: Deflected pattern of electrons. The deflection is seen at the bottom line of the electron beam. The curve is "slight" but it is obvious that the magnetic field definitely bends the beam of electrons. Your job is to estimate the curvature of that "bend"; i.e., you must estimate the radius of a circle that includes this arc.

Having determined B, we can write the force on the electrons as:
 
F = q v B (3)

Balancing this with the centripetal force we can write:
 
mv2/r = q v B (4)

Solve for v:
 
v = q B r / m (5)

The electrons are accelerated through a potential difference in the tube. The energy it acquires is merely qV where V is the potential difference between the cathode and anode. q is in Coulombs and V is in Volts which makes qV in Joules. We can equate this to the kinetic energy acquired by the electrons:
 
1/2 mv2 = q V (6)

q/m can be written as: (Supply the details yourself)
 
q/m = 2V/B2r2 (7)

We should be able to determine this from the quantities we can readily measure in the lab.

OBJECTIVES:

  1. To predict the strength of the magnetic field in the solenoid at a selected point.

    2.  
  2. To determine the ratio of charge to mass of an electron.

    3.  
  3. From the known charge on the electron, determine the mass of the electron from the above ratio.

PROCEDURE:

  1. From known values of currents and voltages, you can be assured that circles of radii anywhere from a dime to a quarter or so will work just fine.

    2.  
  2. Using a commercial 6AF6G tube, wire the circuit as shown. Have your instructor check it before continuing. Your instructor will help set it up. The filament connections go to 6 V and the plate connections (red and black leads) go to the high voltage.

    3.  
  3. Set the high voltage between 90 and 250 volts. Turn on the power (after checked by your instructor) and inspect the pattern. Once the power is on, LEAVE IT ON to prolong tube life.

    4.  
  4. Insert the tube in the solenoid and determine the magnetic field at the point of the electron beam. Note the pattern.

    5.  
  5. Use any object available (dowel rod, pencil, coins, etc.) to determine the radius of curvature; i.e., by comparison with other arcs, find the radius of curvature of the electron beam. What you are basically doing is just "eyeballing" the radius of the beam by the technique of comparison. The human eye is an extraordinarily sensitive instrument. It can, by comparison, tell literally differences in hundreds of shades, tints, brightness of light. Here, you compare the radius of the beam of electrons with some arcs of known radius. When you agree that the radius matches your coin or other circular device, record the B and V values. You will be adjusting them until you find a suitable match. In practice, most people hold the voltage at the lowest value that gives a dim, but seeable green (phosphorous) beam, and adjust the current. The current directly determines the magnetic field, B.

    6.  
  6. Do this for several differing B and V values. The ratio of q/m should be calculated from the averaging process.

    7.  
  7. Compare this with known values.

    8.  
  8. Record limitations and their explanations, data analysis including % error, and report results. You can readily determine the true value of the q/m ratio from values in your text. This should be 1.76 X 1011. Discuss why you can only determine the ratio, and not the exact values of each.

    9.  
  9. Summarize.

    10.  
  10. Include Conclusions and Recommendations.
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