Interactive Lecture Demonstration 3 – Van de Graaf Generator

In this activity, we will use a Van de Graaf generator to explore properties of conducting objects in the presence of electric fields. Refer to section 15.8 of Serway and Faughn for a diagram and description of how a Van de Graaf works.

We will see examples of each of the following important laws about conductors (note that we are only considering conductors in equilibrium here, and that we are assuming the conductors are perfectly conducting):

1)      Any excess charge on a conductor in equilibrium is always located on the outside surface of the conductor.

2)      The excess charge on a conductor produces no net electric field inside the conductor.

3)      Electric field lines must be perpendicular to the surface of a conductor.

4)      A conductor completely shields its inside from any outside electric fields. Therefore, inside a conductor, there is always no net electric field.

5)      The density of excess charge on a conductor, and therefore the electric field outside a conductor, is always highest at the parts of the conductor that are the most curved (i.e. that are sharpest).

In your answers to the following questions, refer to the above laws by their number where needed.

1. The Van de Graaf operates by transferring charge via a belt from its grounded base to a metal brush located in the center of the dome. Once some charge has been transferred to the brush, the transferred charge will repel any additional charge that the belt brings upward. How, then, can the Van de Graaf continue to add charge to the brush in the dome ?

2. An aluminum pie plate will be levitated above the Van de Graaf. Do a net force problem to determine the charge of the Van de Graaf, assuming that the charge of the pie plate is 1 mC. The mass of the pie plate and the radius of the Van de Graaf will be measured.

3. Using the charge you calculated for the Van de Graaf, calculate the magnitude of the electric field at the surface of the dome. Compare your answer with the electric field magnitude needed to ionize air.

4. An uncharged pith ball brought near the Van de Graaf will be attracted to it. Draw diagrams showing the distributions of excess charge on the Van de Graaf and the pith ball, to explain the attraction.

5. Now the pith ball will be enclosed in a hollow conducting sphere and again brought near the Van de Graaf. Predict what you will observe in this situation. Draw diagrams showing the distributions of excess charge on the Van de Graaf and the hollow sphere, to explain your observations.

6. Now add electric field lines to your diagrams in #5.
7. You will notice sparks between the Van de Graaf and nearby objects. When a thumbtack is taped to the side of the Van de Graaf, the sparks will tend to happen near the thumbtack. Explain what causes the sparks, and why they tend to happen near the thumbtack.