Lab 11
Find e/m

A beam of electrons in an evacuated glass tube emerge from an electron gun and pass through a hole in the center of a circular anode. A small amount of argon in the tube will ionize and make the electron beam visible. The tube is centered in a pair of Helmholtz Coils. When current is passed through the coils a magnetic field is generated, perpendicular to the path of the electron beam. The magnetic field causes the electron beam to deflect into a circular trajectory and strike the anode.

The goal, today, is to investigate the deflection of an electron beam in a magnetic field and to use the deflection to find the charge-to-mass ratio (e/m) of the electron. See Figure 1.

Figure 1. Magnetic Deflection

Review Theory

Suppose an electron enters a region of space at a right angle to a uniform magnetic field, B. The electron will move with constant speed in a circular path of radius, R. From Newton’s second law:

where, e, is  the charge of the electron, v, is its velocity and, m, is its mass. The velocity of the electron is determined by its kinetic energy. If the electron accelerates through a potential difference, V, before it enters the field, its kinetic energy will be given by:

Combining these equations gives an expression for the charge-to-mass ratio of the electron.

The electron beam will strike one of four circular grooves cut into the surface of the anode as the current in the Helmholtz Coils is increased. See Figure 2.

Figure 2. Electron Beam Trajectory

Each groove is filled with P1 phosphor (manganese-doped zinc orthosilicate) that will fluoresce under electron bombardment. The radius of the electron beam trajectory, R, is related to the groove radius, r, and the electron gun spacing, d, by the equation: