# Notes for e/m lab exercise

#### Feb 12, 1999 Aug 28, 2000

The goal of this lab is for you to determine the ratio of the charge on an electron, e, to its mass, m. You will do so by measuring the size of the circular path an electron travels in a magnetic field.

You can look up the known values for the electron's charge and mass in the front cover of your textbook, and therefore calculate the actual ratio e/m. Will your experiment verify this value? Only you can tell.

The way the experiment works is explained in this week's manual. Basically, a current running through a set of copper coils creates a uniform magnetic field. There's a simple relationship between the size of the current running through the coils and the strength of the magnetic field it creates: see your manual for the equation. A high-voltage power supply accelerates electrons in a small electron gun located within a glass bulb; the larger the voltage, the faster the electrons shoot out of the gun. The glass bulb is filled with a tenuous hydrogen gas. When electrons knock into the hydrogen, it emits a bluish glow.

Now, if the magnetic field is zero, then the electrons move in a straight path -- they smash into the walls of the bulb. But, if a current flowing through the coils creates a magnetic field, then the electrons feel a magnetic force as they move through the field. This magnetic force pushes them into a circular path.

Some combinations of voltage and magnetic field strength cause the electrons to make a nice, round circle within the bulb. You should measure the radius of this circle and write it down. Other combinations cause the electrons to smash into the walls of the bulb, or not come out of the electron gun cleanly. You can simply mark those combinations with an "X" in your table of measurements, and ignore them in later calculations.

The tricky part of this experiment is figuring out how to measure the radius of the circular path accurately. Read the section of your manual that explains how to make an accurate measurement! If several different people look at the same circular path, they will probably report slightly different radii; the size of the differences between their measurements is an indication of the uncertainty of the measurements.

Your lab manual has equations relating the strength of the magnetic field, B, the voltage of the electron gun, V, and the radius of the circular path, R, to the ratio e/m. You must figure out how to rearrange the equation so that it looks like this:

```                            e
(something)  =  (---) * (something else)
m
```
If you then make a graph in which you plot "something" on the y-axis, and "something else" on the x-axis, the slope of the data points in that graph will be equal to the ratio e/m. You can determine the value by drawing a best-fit line through the points. You can determine the uncertainty in the value by drawing lines which have the maximum and minimum reasonable slopes.

On the graph, try to draw errorbars for each point. You may find that some errorbars are too small to draw -- if so, then write "error bars in this direction were too small to draw." To calculate the size of the errorbars, you'll need to figure out the uncertainty in each value of B, V, R, and the uncertainty in the combination of these variables which you are plotting.

Does your range, from minimum to maximum possible value of e/m, include the book's value?

Be sure to discuss the largest soure(s) of error in this experiment. The more quantitative you can be in your discussion, the better.