EXPERIMENT 25

CHARGE TO MASS RATIO OF THE ELECTRON

This virtual experiment shows the interaction between a charged particle with some particular velocity (an electron in this case) and a uniform magnetic field. To accelerate the charged particle to a particular velocity it undergoes an interaction with a uniform electric field. Through careful measurement of certain parameters the student can determine the ratio of the charge of the electron to that of its mass. Upon opening this virtual experiment you will see a view of an electron tube.

The coils to either side of this tube represent Helmholtz Coils. When current is passed through these coils a fairly uniform magnetic field is generated through the electron tube. At the origin of the x-y-z coordinate axis is the hole in which electrons will emit from. A slide button located in the lower left hand side of the view controls the electric potential which imparts energy to the electrons allowing them to have a particular velocity as they emit from the hole. The higher the potential the faster the velocity. This velocity of each of the electrons is directed perpendicular to the magnetic field that is to be generated by the Helmholtz coils. To increase (or decrease) the magnetic field adjust the slide button located at the lower right hand corner of the view (it is initially set at zero).

As stated in the lab manual a charged particle having some velocity that is perpendicular to an applied magnetic field will exhibit circular motion. To show this first increase the electric potential until you achieve a “beam” of electrons coming out of the hole. The higher the potential the more uniform the beam will be (see diagram on the next page).

The circles drawn concentric with the hole in the plate inside this electron tube have particular radii values. You can find these four values in the lower central region of this view. They are 0.5 cm, 1.0 cm, 1.5 cm, and 2.0 cm. By increasing the magnetic field you will cause the beam of electrons to bend into a circular path. Start with an electric potential of 100 volts and increase the magnetic field to allow this electron beam path to intersect the outer most concentric circle (see diagram on the next page).

Click on the 2.0 cm choice and take note that even though this is the radius value of the ring that the electron beam is striking it is the value for the diameter of the circle of the electron beam being bent. Thus the radius of the electron beam in this case is 1.0 cm. From this potential value and current value and knowing the radius of the Helmholtz coils (10 cm) you can determine the ratio of the charge of the electron to its mass. Like all experiments you are making a judgment call as to having the beam hit this concentric circle. Here is where uncertainty comes into play with doing this experiment.

As you increase (or decrease) the slide button for the magnetic field you will see arrows depicting the direction of the magnetic field. Decreasing the magnetic field is just causing the current through the coils to flow in the opposite direction thus reversing the direction of the magnetic field.

Now, reduce the electric potential and allow the electron beam to strike the next smaller concentric circle. Compute the charge to mass ratio of the electron again using this new set of data. Again, the radius of the electron beam is half the radius of the concentric circle. Continue to do this for the final two smaller concentric rings as well as hitting the four rings with the magnetic field in its reversed condition. For this reversed magnetic field again start with an electric potential of 100 volts.

To turn this work in you must print out the data and the results. With this virtual experiment calculations are not necessary, but you must save the data. When you are satisfied with how the electron beam is striking a particular concentric ring right-click on the corresponding radius value located at the lower central portion of this view. Click on the submit data choice and the program will save this data point. Do this for all of your data. You can also view the results from this menu. When you are finished go to file located on your menu bar at the top of the view and choose print. A cover sheet and a data sheet will print out. Fill out the cover sheet with the appropriate information and submit these to your laboratory teaching assistant.

As seen in the above diagram when the mouse is placed over the region of accelerating electrons a yellow box will appear. Left click the mouse to choose a magnified version of this region.

This is the region in which the electrons are accelerated due to a force upon the charged particles within the electric field. The larger the potential difference the greater the electric field resulting in a larger final velocity of each electron exiting through the central hole in the plate. Left clicking again in the region of the accelerated electrons will magnify the view once more.

In the above view it is depicted that the electrons are not what you see as the beam of light. It is the light energy released through the interaction of the electrons with the molecules of the gas in the tube.

Another region that can be explored is that of the beam exiting the central hole in the plate. Here, another yellow square can be chosen by Left-clicking on it. In this magnified view of the beam you can change the strength of the magnetic field and see the interaction of the beam with greater detail.

Once you have completed your assignment

In this virtual experiment there is an additional set of details. By clicking on the region depicting the electrons being accelerated through a potential difference you can magnify the view. Click a second time to magnify again. In this final magnification there is a representation of the interaction of the electrons with the gas present in the electron tube. The “beam” of electrons is seen as a beam of light. This light is actually caused by the collisional process of the electrons with the gas molecules resulting in the emission of light.

By passing the cursor over the region depicting the coordinate axes you will find another detail. Here you will be able to change the accelerating potential and see the motion of electrons. You are also able to apply the magnetic field and see how it affects the electrons. To leave this view left-click the mouse and you will return to the main view.

Also, there is an additional exercise that you can work with to get a better understanding of how magnetic fields and electric fields affect a charged particle moving with some velocity perpendicular to them both (see diagram on the next page). To open these open the Help menu at the top of the view and choose Charge particle movement. The magenta colored line represents the direction and strength of the electric field while the yellow colored line represents that of the magnetic field. There are a five sliders which will each change a particular parameter along with the ability to choose between the particles having a positive charge or negative charge located near the top center of the view.

It is also possible to open more than one view (as shown in the diagram on the next page). Doing so will enable you to do a comparison between the different parameter choices that you make. To do this, go to the File menu and select New. You can click and drag each view and place them conveniently about your screen. You can also resize each view to better fit the multiple views on your screen.

Each of these views must be individually closed when you are finished with them.