The first is the experiment of Joseph John Thomson, who first demonstrated that atoms are actually composed of aggregates of charged particles. Prior to his work, it was believed that atoms were the fundamental building blocks of matter. The first evidence contrary to this notion came when people began studying the properties of atoms in large electric fields.
If a gas sample is introduced into the region between two charged plates, a current flow can be observed, suggesting that the atoms have been broken down into charged constituents. The source of these charged particles is a heated cathode that, in fact, causes the atoms of the sample to ionize. These were known as cathode rays. In 1897, Thomson set out to prove that the cathode rays produced from the cathode were actually a stream of negatively charged particles called electrons. (See Figure 1.8 in the textbook for Thomson's experimental setup). From Maxwell's theory, he knew that charged particles could be deflected in a magnetic field. A schematic of the experimental setup is shown below:
We now zero in on the field region and set up a coordinate system as shown in the figure below:
In this coordinate system, electrons enter the region between the plates with an (unknown) velocity in the -direction. In order to determine this velocity, electric and magnetic fields are both applied, and each gives rise to a force on the electron. These forces are in the -direction. The electric force , where is the magnitude of the electric field, and the magnetic force is , where is the magnitude of the magnetic field, and is opposed to the force on the electric field.
If these forces balance, then there will be no deflection
of the electron in the -direction, i.e. all of the
electrons' motion will be along the -direction, which
was the initial direction when they entered the field region.
If the forces balance, then the total force on the
electrons will be zero, that is or
Next, the magnetic field is switched off, so that the total force is due entirely to the electric field. Since the force is non-zero, if the charge carriers can be deflected by the force, this provides evidence for their being fundamental particles. If they are fundamental charged particles, then they should have a well defined mass and charge. In this second part of the experiment, the specific trajectory followed by the particle will be used to determine the ratio of the charge to the mass of the particle.
When there is only an electric field, then there is a nonzero force in the -direction but no force in the -direction. Thus, this problem is exactly the same as that of a projectile in a gravitational field. As can be done in the projectile problem, the and motion of the electrons can be analyzed separately and independently.
In the -direction, the motion is very simple because there is no force in this direction. The electrons simply move with a constant velocity , which we already determined has the value . Note that this value is correct even though there is no magnetic in this part of the experiment! It is just the velocity we determined from the previous part of the experiment, and this value has not changed. Thus, as a function of time , the -position of the electrons is
The force in the -direction is a constant, hence motion in the -direction is analogous the gravitational force. The constant force gives rise to an acceleration , and the -position at time is then
In 1906, Robert Millikan was able to determine the value of the charge on the electron in his ``oil drop'' experiment. A schematic of his experiment is shown below:
The currently accepted
values of and are: