Basic Physics II

LAB 5:  Using a Fine Beam Tube to Determine e/m (October 21 & 22)

 

PURPOSE

This experiment is designed to demonstrate the effect of electric and mag­netic fields on charged particles, and to measure the charge-to-mass ratio of an electron (e/m).

 

INTRODUCTION

In a Fine Beam tube, electrons are emitted from an electron “gun”.  This “gun” con­sists of a cathode C an anode A and a heater H.  The heater "boils" electrons off the cath­ode and they are accelerated toward the anode by a potential difference applied be­tween the cathode and the anode, Vaccel.  Many "miss" the an­ode (which has a hole in it) and enter the tube as a beam of electrons (see the figures below).

 

 

The tube is filled with neon under a pressure of 10-2 mm of Hg (about 1.3Pa).  The path of the electrons is visible as a fine luminous line (light circle in the figure above). This luminous line is produced when electrons collide with the neon and ion­ize it.  When the ionized electrons recombine with the neon ions, they give off light, producing the observed glow. 

A homogeneous magnetic field is produced in the tube by a current through the two circular coils just outside the tube (Helmholtz coils).  If a charged particle, such as an electron, moves perpendicular to this magnetic field, a force whose magni­tude is constant, but whose direction is always at right angles to the velocity of the particle acts on the particle and makes the particle move in a circle, i.e. the magnetic force acts as a centripetal force.  The diameter of this circular orbit may be measured by means of a millimeter scale pro­jected into the plane of the beam.  Knowing the velocity of the electrons, the mag­netic field and the diameter of the circle will allow one to calculate e/m for the electrons.

 

THEORY

An electron moving in a circle is subject to a centripetal force given by

Fc =                                                                                                                                 1.

where m = electron mass (kg), v = electron's speed (m/s) and r = radius of the cir­cle (m).

In this lab the centripetal force results from the motion of the charged par­ticle in a homogeneous magnetic field.  The magnitude of the force is

Fc = evB                                                                                                                                  2.

where e = electronic charge (C) and B = magnetic field (T).  Equating (1) and (2) and solving for e/m gives:

=                                                                                                                                    3.

To determine electron velocity, v, one equates the kinetic energy of the particle to its change in potential energy due to the accelerating potential between the cathode and anode, Vaccel (note:  lower case v = velocity and upper case V = poten­tial),

= e Vaccel                                                                                                                      3b.

where Vaccel = cathode-to-anode potential (volts).  If one solves for v and substitutes that into equation (3), a little algebraic manipulation will give the result

=                                                                                                              4.

The cathode-to-anode potential difference, Vaccel, and the radius of the electron beam can be de­termined by direct measurement.  The other quantity needed to de­termine e/m is B.  It can be calculated from the current through the coils, the number of turns, and the diameter of the coils.  For Helmholtz-coils:

B = (1.80 x 10-6) .                                                                                                             5.

Where B is in Tesla if N= number of turns, I= coil current (amps) and d= coil di­ameter (m).  This value of B can be substituted in equation (4) to determine e/m.  For the new tubes, N and d are such that

B = (7.80x10-4)I                                                                                                                      6.

where B is in Tesla if I is in Amps.

 

EXPERIMENTAL PROCEDURE:

You will be applying three different voltages to the apparatus.  One (about 6V) will heat the Cathode.  The second (100-300V) will be between the Cathode and Anode to accelerate the electrons.  You need to measure this accelerating potential.  The third will be ap­plied to the coils that produce the magnetic field.  The Current (0.5 - 2 A) supplied by the third voltage is the parameter determining the magnetic field and must be measured.

1.      Apply approximately 6 VAC across the heater terminals through a variable 2-ohm resistor.  {This should be done for you, so do not mess with it.  If the voltage is too high, it can melt the heater.}

2.      Make sure the voltage at the B+ terminal of the power supply is 0 and then connect the anode to the B+ terminal.  Now you can increase it to 150 V.  Monitor it with a DMM.  {DO NOT TOUCH THE HIGH VOLTAGE CONNECTIONS WHEN THE POWER IS ON!  YOU CAN GET A SHOCK FROM THESE VOLTAGES!}

3.      Carefully adjust the cathode heater current until a luminous beam of elec­trons appears in the tube.  (The room should be darkened.)

4.      With the battery and coils connected as shown in the diagram, switch on the current to the Helmholtz coils and adjust the magnetic field of the coils until the electron beam moves in a closed circle.  Also monitor this current with a DMM, but do not exceed 2A.   The ring diameter is controlled by the magni­tude of the magnetic field and the DC potential between anode and cathode.

5.      Use the mirrored scale to measure the diameter of the circular elec­tron beam.  Note that the magnetic field should be adjusted so that the beam is centered on this scale (i.e. so that the scale passes through the center of the circular beam).

6.      Record the accelerating voltage between the cathode and anode and the cur­rent in the coils.  Also measure the diameter of the coils.  Enter these data into your data book (in a table) and use them to calculate e/m (using the equations above).

7.      Now change the accelerating voltage and re-adjust the magnetic field so the beam is again a circle centered on the mirrored scale and repeat your mea­surement.  Make measurements for three different accelerat­ing voltages.  I would suggest 200, 240 and 280 V.

8.      Compute the ratio for each series of readings.  Compare your ex­perimen­tal values with the accepted value:  (A good way to compare them is the percent difference.)

         = 1.76 x 1011 

         Are your measured values reliable?  Justify your answer.

 

Possible Problems and Questions

There are several potential problems in this lab.  The first is accounting for the Earth's magnetic field.  It is approximately 4x10-5 T or roughly 4% of the field generated by the coils.  This could produce an error in your estimate of B of about 4%, which would produce an error in e/m of 8%.  Can you eliminate this problem?  The second is that the focus adjustment does affect the radius (r) of the electron's path.  This should not happen, but it does and you should take a look at it.  It seems to be less of a problem at higher accelerating voltages.  The final problem is to accurately measure r.  Your uncertainty here could easily be ± 2 mm.  How much would this affect your results?  (Try changing your r by 2mm and see what happens.)