User:Colin Bentley/e/m Ratio

Purpose

The purpose of this lab was to determine the charge to mass ratio of the electon experimentally using an electron deflection apparatus. My colleague for this experiment was Peng Cao.

Setup

The main apparatus consisted of a magnetic coil in conjunction with a cathodic electron gun and a charged plate, combined into one device. This was supplied with power from two DC voltage sources, one of which was a low-voltage source hooked up to the magnetic deflection coil in order to supply it with a steady current, and the other of which was a high-voltage source connected to the accelerating plate. An auxiliary output from one of the DC sources provided power for the electron gun. A DC ammeter was placed in series with the coil circuit, and another was placed in series with the heater element for the electron gun. A DC voltmeter was connected in parallel with the voltage source supplying the deflector plate. We set up our equipment and without difficulty and the experiment itself went smoothly.

The gun emitted electrons from a hot cathode which were then accelerated by the charged plate and passed through an aperture to create an electron beam. The beam was deflected by the perpendicular magnetic field, and was made to form a complete loop by adjusting the magnetic field. The desired e/m ration can then be calculated from known variables.

Data

We recorded the coil current, plate voltage, and radius of the beam loop through the magnetic field in increments of 5 volts ranging from 250 to 300 volts, taking 5 measurements for each voltage increment by varying the current in the loop and observing the resulting deflection. Our data was consistent with expected values and within a reasonable margin of error given the overall accuracy of the device. A preliminary calculation using a set of values corresponding to 255V applied voltage, 1.982A coil current and radius of deflection of 2.85 cm substituted into the relationship giving the e/m ratio in terms of B, voltage V, and radius r, [math]\displaystyle{ e/m = \frac {2V} {r^2B^2} }[/math], and the relationship for determining B for our particular magnetic coil setup given the current, [math]\displaystyle{ B = 7.8\times10^{-4} \times I }[/math], yielded an e/m ratio of 2.627x10^11 C/kg, with an error of 49% from the given value of 1.759x10^11 C/kg.

Conclusion

This experiment proceeded smoothly and yielded a well-behaved data set. The apparent error in accuracy of the data was non-negligable, yet overall was not tremendous. That is, it did not deviate by an order of magnitude or more from the given value, an indication that we were not doing something horribly wrong. The error rate will be discussed and the data analyzed in more detail in the full report.