Lab 2 Electrostatics with Aluminum Balls

All matter consists of atoms, which have electrons that can either be stripped away to become charged or shifted within an atom or molecule to make it polarized. Under both circumstances, the interaction can be understood using the principle first described by physicist Charles-Augustin de Coulomb. Electrons, which are part of the atom, are too small to be seen by optical light, however, electrons can be observed through the forces that they exert. For example, in an ink jet printer, the ink droplet gets electrically charged so that it can be steered to the desired spot on the paper using an electric field. A charged balloon can stick to your hand, when the electrostatic force is larger than the gravitational force. Here, you will transfer excess electrons onto aluminum spheres and observe their Coulombic repulsion. The separation distance is related to how many electrons were transferred. Each electron carries a charge of \(-1.6 \cdot 10^{-19}\)C, so from a charge measurement it is possible to find the number of electrons.

By the end of this activity, you should be able to do:

  1. Hands-on opportunity to construct an electrostatics setup
  2. Keep observations organized in a lab notebook
  3. Interpret data to optimize parameters

2.1 Goals

  1. Design your setup such that the ball separation \(r\) is maximized by selecting the proper Aluminum ball mass \(m\) and length of the string \(L\).
  2. Determine the charge \(Q\) and total number of electrons that you can remove using different ways of charging a PVC rod. Determine the best method to transfer a maximum amount of charge.

2.2 Prediction

Two charged Aluminum balls are attached to each end of a string. The middle of the string is pinned up, so that the Al balls dangle in the air, but slightly repel each other.

  1. Draw a picture that includes the 2 Al balls, string, and pin point; then make a force diagram for one Al ball, showing the 3 forces: string force, Earth’s force, and Coulomb’s force from the other Al ball. In equilibrium, the sum of forces is 0 N, so draw the vectors with that in mind. Label the length \(L\) of the string, the ball separation \(2r\) from the center of one Al ball to the other center, and the mass \(m\).

  2. Add the angle between the vertical and the string, \(\theta\), and relate it to the radius \(r\) using the length \(L\). Predict what will happen to \(r\) for a fixed charge \(Q\), which is transferred to each AL ball, if the string length \(L\) is increased. Make a graph of \(r\) versus \(L\). (Hint: you can make a model based on the force diagram and find an analytical solution.)

  3. Similarly, what happens to the separation distance \(r\), if you increase the mass \(m\) of the Aluminum ball, make a graph of \(r\) versus \(m\). (Hint: you can make a model based on the force diagram and find an analytical solution.)

  4. Using the force diagram, find a relation using Coulomb’s Law that provides you with the charge \(Q\), given the mass \(m\), length \(L\), and separation radius \(r\).

2.3 Equipment

  1. Al foil, scissors, tape
  2. Fine insulating string (about 2 m)
  3. PVC rod and fur, sweater, wool, or socks
  4. Metric ruler
  5. Common lab scale

2.4 Procedure

  1. Use a long (about 50 - 200 cm), fine, insulating string and tightly crumple a ball of Aluminum (conductor) to the end. The diameter of the Al ball should be less than 1 cm. Prepare a second string with another Aluminum ball at the end. Use your predictions to choose a good length \(L\) and a good mass \(m\) for the Al ball. Record the mass of the Al ball and all other relevant quantities.
  2. Affix the two strings in a single point, such that the two Al balls touch each other.
  3. Rub the PVC rod in the fur and transfer the charge to the Al balls in different ways, explore repulsion and attractive forces and note your observations.
  4. Measure the separation of charged Al balls \(r\) and determine the charge \(Q\) and number of electrons transferred.
  5. Repeat procedure and optimize your setup for string length, ball mass, and friction material that you are using to generate a large charge.
  6. Propagate the uncertainty and determine \(\Delta Q\).

Share your chosen length \(L\) and mass \(m\), the radius \(r\), and the computed charge \(Q\).

2.5 Measurement

Make a table similar to this one to record your parameters. Here \(m\) is the mass of the Aluminum ball, N = the number of electrons, and material is what you are using to charge the PVC rod. You can compute the uncertainty \(\Delta Q\) using the emperical propagation method, which uses the worst case scenario.

2.6 Graph

Make a bar plot of the charge Q versus the different methods that you used. Include the error bars from the propagated uncertainty.

If data available from your experiment or the class discussion, plot \(r\) versus \(L\) for an approximately fixed charge, and plot \(r\) versus mass \(m\). How do the experimental curves compare with your predictions?

2.7 Discussion

Report the length \(L\) and mass \(m\) that you used. What is the maximum separation \(r\) that you found? What is the uncertainty \(\Delta r\)? How many electrons were you able to remove? What method (materials) produces the most charge? Do you observe attractive and repulsive forces? When and how?

2.8 Summary

Discuss the goals including what is the best length, material, and mass to create a large separation distance of the Aluminum balls. What is the charge that you could generate and what is the uncertainty? How many electrons would that correspond to? What is the uncertainty of your measurement? How does your measurement compare to the class results.