Coulomb’s Balance

The main part of the labscript (part 2) consists of the commercial manual but you should read through and consider the points below when referring to the manual.

AIMS

This experiment is designed to demonstrate the inverse square law between charges. Please consult the PASCO Scientific Model ES-9070 Coulomb Balance Manual for details- This note merely introduces you to that script, and outlines what you might attempt in the laboratory.

You may well find that it is actually rather difficult to make an accurate measurement of the exponent n in the power law:

where F a force, k is some constant, R is a distance and q1 and q2 are the charges. For a Coulombic or gravitational force, you'd expect n to be equal to two. Since it is difficult to get n=2, it is important that you try to get some idea of the accuracy of your result. In fact, determining the experimental error of your result in some ways is more important than your result itself.

APPARATUS & TECHNIQUE

The idea of this experiment is simple:

In the apparatus both spheres are charged up. The spheres repel each other, and swing apart. By twisting the torsion wire, you can make the two spheres swing back together. If there are no complications, then the force is directly proportional to the angle you must twist the wire. By repeating the experiment for different values of each of the variables in the above equation, you can test their interrelationships.

This is a commercial item of equipment, and the manual has been written quite carefully. You should go through the manual, and consider the additional points below.

  • p.2 The 'boxed' note about indirect measurement of the exponent is wrong. Write down a clear and correct description of the 'indirect' experiment, and its result.
  • p.4 You will be using an enclosure to shield against draughts. You may need to be careful about charges induced on the walls of the enclosure. Can you do anything about the first tip, on page four, which recommends you try to keep humidity down? Can you think of a way to test this possible error? The tip about grounding the experimenter is particularly recommended!
  • pp.5-6 You should inherit the equipment so that it has been set up as indicated in Fig. 5, and as described in the final smaller-type paragraph on p.6. If it is misaligned in some way, proceed through the appropriate steps on pp.5-6. If you are unsure about making an adjustment, consult a demonstrator.
  • p.7 Calculate the capacitance of the spheres, and so estimate the magnitude of the charges you are putting on them.
  • p.12 The tables for your results are good suggestions. Do not feel obliged only to record this suggested data - you may wish to record more information.

Consider the lines of force emanating from the charged spheres; where are they terminating? Is this likely to affect the measured force?

REPORT

In your Report you should assume that the reader is familiar with the ideas behind this experiment, and knows roughly how the equipment is set up. Therefore, you do not need to reproduce large sections of the printed instructions.

On the other hand, you will need to describe the details, particularly those you have developed personally. For example, if you have used the correction factor B of p.8, you should explain what it is, and discuss whether it makes your data analysis more reliable.

As indicated earlier, I would like you to estimate how accurately you can measure the exponent n by this technique. You should consider all known effects which will make your answer incorrect. Then you must try to quantify them, experimentally or theoretically, or, if at all possibly, by both techniques.

Also, you should describe how you succeeded in overcoming the difficulties of this experiment, such as leakage of charge, or stray charging effects.