General Discussion

The ``discovery" of the electron by J. J. Thomson in 1897 refers to the experiment in which it was shown that ``cathode rays" behave as beams of particles, all of which have the same ratio of charge to mass, e/m. Since that time, a number of methods have been devised for using electric and magnetic fields to make a precise measurement of e/m for the electron. When combined with the value of the electron's charge, which is measured in the Millikan Oil Drop Experiment, the determination of e/m leads to an accurate value of the mass of the electron. In the present experiment, electrons are emitted at a very low velocity from a heated filament, then accelerated through an electrical potential V to a final velocity v and finally bent in a circular path of radius r in a magnetic field B. The entire process takes place in a sealed glass tube in which the path of the electrons can be directly observed. During its manufacture, the tube was evacuated and a small amount of mercury was introduced before the tube was sealed off. As a result, there is mercury vapor in the tube. When electrons in the beam have sufficiently high kinetic energy (10.4 eV or more), a small fraction of them will collide with and ionize mercury atoms in the vapor. Recombination of the mercury ions, accompanied by the emission of characteristic blue light, then occurs very near the point where the ionization took place. As a result, the path of the electron beam is visible to the naked eye.

The tube is set up so that the beam of electrons travels perpendicular to a uniform magnetic field B which is proportional to the current I through a pair of large diameter coils (so-called ``Helmholtz Coils") in which the coil separation is selected to produce optimum field uniformity near the center.

For an electron moving in an orbit perpendicular to B, the centripetal force evB is balanced by the centrifugal force , where r is the radius of the orbit, v is the velocity and e and m are the charge and mass of the electron. Thus

The velocity of the electron can be computed from the potential energy that it loses in passing from the filament to the cylinder:

From the above equations, you must derive (before coming to class) an equation for the straight line graph of I vs. the curvature 1/r and an expression for e/m as a function of the measured and computed variable.