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Ratio of Charge to Mass for the Electron

Introduction: The object of this lab was to determine the measure of the ratio of an electron to its mass. This is done by accelerating a stream of electrons through a measured potential difference. The stream of electrons moves through a uniform magnetic field. It is perpendicular to the velocity of the electrons. The path of the electrons is circular because of this fact. The ratio of e/m can be found by the relationships between the measured accelerating potential difference, the diameter of the circular path described by the electron, and the magnetic flux density.

Theory: British scientist Sir J.J. Thompson (1856-1940) first discovered that the electron was a discrete particle of electricity. From his discoveries came the accepted value for e/m which is 1.75890*10^11 coulombs/kg. With this information we could then accurately determine the mass of the electron.

The force F acting upon a charge that is moving with a velocity v perpendicular to the magnetic field B is

This force is centripetal. These forces cause the electron to move in a circular path. The centrifugal force of reaction of the electron is equal in magnitude to the force on the electron by the magnetic field. Therefore the following equation is valid for this experiment. R is the radius of the path of the electrons.

Through a potential difference, the kinetic energy acquired by the falling electron is:

From these last two equations, we can make a third equation involving all of the variables.

With this apparatus for this experiment, we can determine values for V, B, and r. With these values we can determine the ratio for e/m. The current in these two Hemholtz coils produces a magnetic field which bends the beam. Since the coils are vertical, the beam is horizontal. This is because the beam and the magnetic field are perpendicular. In the experiment, since the distance between the coils is equal of the radius of both of the coils, a nearly uniform magnetic field is produced at the midway point. The currents in the coils must yield fields of the coils that are in the same direction as their common axis.

At a central point, the magnitude of the flux density B is:

N is the number of turns per coil. In this experiment N=129. I is the current in the coils. This is always changing. R is the coil radius. For the experiment R=10.75 is the permeablilty of free space. =4 *10^-7 weber/amp*m . Later we will come to find that when the specified units are used, e/m is expressed in coulombs/kilogram.

Data: Connect the apparatus as shown in the following diagram. The electron stream should have a diameter of about 2mm.

Set the rheostat for high resistance close to the circuit field coils and then vary the current to (3-5) amp until the electron beam bends into a complete semicircle. Arrange the plate potential so that the accelerating potential difference can very and change the field current until the beam falls on the marked circles. The plate potential, the field current, and the radius of the described circle were recorded as follows.

Because these values for e/m were so different than the predicted value of e/m (1.75890*10^11 coulombs/kg) the experiment was run a second time, but with a higher voltage and current. The data was recorded as follows:

Conclusion: From this data, and use of the working equation for e/m, it can be concluded that our experiment was consistent, but off from the given value of e/m by a fairly constant amount. This can be caused by several sources of error. One might be that we did not take the magnetic field of the earth into account. Another could be a magnetic field created by a nearby object. Still a third source of error might have been that we could not determine which ring on the plate that the electron beam curve actually hit. This experiment does show that given a Magnetic field, a V, an I, and an R, we can calculate e/m and compare this value to our given value for e/m.

Special Thanks to Dr. Tarvin and the Samford University Department of Physics for direction and extreme patience with this project

Bibliography: