Lab 7
Measure E-Field

A deflection tube contains two parallel, conducting plates. The plates are separated by a grid that will illuminate under electron bombardment. A beam of electrons is generated by a source of electrons called an electron gun. The electron beam is deflected when an electric field is created between the plates.

The goal, today, is to find the strength of the electric field from the trajectory of the electron beam measured at the grid of the deflection tube. See Figure 1.

Figure 1. A Deflection Tube

Review Theory

An electric field will exert a force, F, on a charged particle. From Newton’s second law, a particle of mass, m, will accelerate in an electric field of strength, E, with an acceleration, a, given by:

Suppose an electron is projected horizontally along the x-axis of a coordinate system, into a uniform electric field directed along the y-axis. The motion of the electron will mimic the motion of a projectile fired horizontally in the earth’s gravitational field. By analogy:

where, v0, is the initial velocity, y0, is the offset from the y-axis (the position of the undeflected beam) and, y’, is the deflection. Substitution gives:

Eliminating the time, t, gives the trajectory:

If the electron accelerates through a potential difference, V, before it is deflected by the field, its kinetic energy will be given by:

Substituting this result into the equation for the trajectory gives:

This equation is a parabola of the form:

where y = (y' - y0) and, A, is called the parabolic constant that relates the field strength to the acceleration voltage: