The e/m of the Electron Apparatus
This self-contained apparatus is designed for the measurement of the ration of the charge of an electron to its mass by observing and measuring the radius of the circular path under the influence of a uniform magnetic field. The magnetic field is provided by a pair of Helmholtz coils surrounding a vacuum tube. The vacuum tube has a downward pointing electron gun in an evacuated bulb that has a little helium added so that the path of the electron in tube is visible. The helium gas added to the tube fluoresces when struck be the moving electrons and produce a bright, clear view of their circular path, Thus, the circular tracing of the electron path is undisturbed by the previously emitted electrons, contributing to a more accurate measurement.
Principle of Operation
In general, this device contains all the basic pieces of a large accelerator, like the Tevatron at Fermilab, although this is much simpler in nature. This apparatus has a source, an accelerator, and a method for data readout.
The first part of the machine is the source of the electrons. Electrons are emitted be an indirectly heated cathode located near the source of the electrons. The cathode is connected to the negative lead of a high voltage power supply. The cathode is partially shielded by a surrounding high voltage grid which has a small aperture to let some of the electrons pass through. The anode it mounted below the grid and connected to the positive lead of the same high voltage supply. Electrons escaping through the grid are rapidly accelerated toward the anode, but some of them pass through a hole in the anode grid and for the electron bean. This is the accelerator part of the device.
The energy given to the electron falling through the potential, V, is eV, where V is the cathode to anode potential and e is the charge of the electron. This is the kinetic energy of the electron, so we have:
Solving for the velocity, we find:
Now we take into account the fact that the electron is traveling in a transverse magnetic field provided by the Helmholz coils. This means it will be deflected into a circular path by the Lorentz Force, F = evB, where v is the velocity and B the magnetic field. Since we will apply a magnetic field strong enough to bend the electron into a circular path, we can set this force equal to the centripetal force, F = mv2/r required to maintain circular motion.
Using equations (2) and (4), we can arrive at an expression for e/m:
The only other thing we need to know is the strength of the magnetic field, which can be calculated from the current in coils, as shown:
Here mo is the permeability of free space, N is the number of turns in each pair of coils, I is the coil current, and a is the coil radius.
We now have everything we need to determine the ratio of the electronís charge to its mass. By trying several different magnetic fields and changing the accelerating voltage, it is possible to make a fairly accurate measurement of the ratio. Often basic principles like this are behind some of the current scientific research being done in the field of physics.