Chapters

Page 6
This text is meant to accompany class discussions. It is not everything there is to know about uniform circular motion. It is meant as a  prep for class. More detailed notes and examples are given in the class notes, presentations, and demonstrations (click here.)
Let's Make an "Electron Gun"

First start with a source of charged particles. A thin wire connected to a battery will work if we can get the wire to glow.

THe hot wire will emit the particles we need. Now that we have a source of charged particles, they will need to be moved. They can't be hit like a bat and baseball because their positions are too random. Another way to move the charges is with an electric field.

Setting up an electric field is easy. All that is needed is a charged particle. Or better yet two charged particles so the field can be controlled. Batteries are devices with separated charged particles. Connect two flat plates to the two sides of a battery to control the electric field.

Putting these two items together creates an electron gun!

One battery heats up a wire while the other battery creates an electric field that is needed to propel the charges.

 How good it this electron gun?

 Recall Kinetic energy is (1/2)mv2. Work = (Force: in the direction of displacement)(displacement) The sum of the energies at one location of motion equals the sum of the energies at a second location in the motion. (Including work done to add or remove energy from the system.)

To figure this out, look at the kinetic energy of the electrons as they leave the gun.

You know F=qE. If the electron starts from rest, then the kinetic energy when it reaches the opposite plate is found from conservation of energy relationships.

But it does not stop there. The concept of voltage and the unit of a "Volt" are defined as

Where Volts are the units of "Voltage." The math symbol for Voltage is "V" the unit symbol is the same, capital " V. " Charge is measured in Coulomb's. The letter "q" represents a single charge. The letter "Q" represents a collection of charges. A capital "C" is used to represent the units of charge.

This is the same voltage that appears on the outside of a battery. In this case the batteries look like the rectangular 9 Volt batteries. Let's look at the units of "Ed." ("Ed" is the electric field times the distance between two plates.)

 Further Analysis of the electron gun

The electron gun uses a 9 volt battery to energize the plates that accelerate the electron. The plates are separated by 15 cm. This is 0.15 m. The mass of an electron can be looked up, qelectron = 1.60 x 10–19 C. It is also on the electrostatic constant sheet. (Click here to see it.) The charge of an electron is used so often that it is given its own variable, .

Wow that looks VERY fast. This design could have some merits. Calculate the kinetic energy of this electron assuming it starts from rest.

Example

Find the energy associated with a electron that starts at rest at the left plate and is released. To put this in perspective, if the electron’s energy was given to a 1000 kg small car, then how fast would the car have to travel?

Below is an movie from YouTube showing how the problem is actually solved. The video is located here, http://www.youtube.com/watch?v=YYTxeXi0Ibw . Click it to see the solution.

by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)