In this lab activity you will simulate what Coulomb did to derive the equation to describe the electrostatic force. This activity will be broken into two parts. The first part of this lab investigates the relationship between the distance of separation (r) on the electrostatic force , while the second part investigates the relationship between the amount of charge (q1 and q2) and the resulting electrostatic force .
In this part of the investigation you will examine how Coulomb gathered data from a torsion balance experiment to determine the relationship between the distance of separation and the electrostatic force. You will be given sample data to graph and analyze to find the relationship.
You will need a calculator, a pencil, an eraser, a straight edge or ruler, and a piece of graph paper. If you decide not to use graph paper, you will need a graphing calculator or a computer that has spreadsheet software to do graphing. Below is a diagram of Coulomb’s torsion balance apparatus set up for the experiment.
Before starting the experiment Coulomb had to identify the manipulated variable and predict what would happen when metal sphere A was released. Study the previous diagram, and answer the SelfCheck questions about it.
SC 7. Identify the type of force that causes the acceleration of sphere A.
SC 8. Determine if the force will push sphere A away from sphere B or toward sphere B. Support your answer.
SC 9. Assume that sphere B is fixed in position and that sphere A is free to rotate. Determine if the arm holding sphere A will rotate clockwise or counterclockwise (if viewed from above as shown in the illustration.)
SC 7. The acceleration is caused by electrostatic force acting on sphere A. According to Newton’s third law, an equal force is acting in the opposite direction on sphere B.
SC 8. The force on sphere A will act to push it away from sphere B since each sphere has a negative charge and like charges repel.
SC 9. Sphere A will rotate counterclockwise since it is repelled from sphere B.
If the arm on the torsion balance rotates, it will cause the torsion spring to tighten with a certain force. This is indicated on the scale. Coulomb had predetermined the graduation of the force scale in grains of force. In this simplified version, the scale is set in units of force that will be referred to as F units.
SC 10. Remember that spheres A and B are identical in size and both are made of metal.
SC 10.
The following multimedia will show you the results when Coulomb released sphere A from different distances. Click on the “Next” button to see the different force and distance values and fill in the results for SelfCheck 11.
SC 11. Study the diagrams, and create a chart of data values showing the distance of separation and the corresponding force for each trial. Remember that you can use a graphing calculator or a spreadsheet instead of a paper chart.
SC 11.
Distance (r) Between the Centres of the Two Charged Objects (cm) 
Electrostatic Force Acting on Sphere A (F units) 
1.0 
16.0 
2.0 
4.0 
4.0 
1.0 
8.0 
0.3 
SC 12. Draw a graph of as a function of r. You can use the following steps as a guide:
SC 12.
You could also use your graphing calculator.
If you used a graphing calculator or computer software to answer this question, be sure to communicate your answer in the proper format.
Data Entry:
r (cm) entered into L1
F (F units) entered into L2
Window Settings:
x: [0,10, 1]
y: [0,20,1]
Plot Setup:
To plot F (F units) versus r (cm), enter L2 for y and L1 for x.
SC 13. Earlier in this lesson, the suggestion was made that the equation describing the electrostatic force that acts on one charge due to the presence of a second charge could be an inverse square relationship.
SC 13.
Distance (r) (cm) 
(F units) 


1.0 
1.0 
16.0 
2.0 
0.25 
4.0 
4.0 
0.063 
1.0 
8.0 
0.016 
0.3 
You could also use your graphing calculator.
Although the data chart will look the same, the use of technology allows a very efficient approach. Instead of completing four individual calculations to determine values for , simply define a third list in terms of the inverse square of all the values for r in L1.
Data Entry:
r (cm) entered into L1
F (F units) entered into L2
, determined by defining L3 as follows: “L3 = (1/L1)2”
If you used a graphing calculator or computer software to answer this question, be sure to communicate your answer in the proper format.
Data Entry:
r (cm) entered into L1
F (F units) entered into L2
entered into L3: “L3 = (1/L1)2”
Window Settings:
x: [0,1, 0.1]
y: [0,20,1]
Plot Setup:
To plot F (F units) versus , enter L2 for y and L3 for x.
Now that you have seen Coulomb’s observations and learned how to change the curved electrostatic force vs. distance of separation graph into a straight line graph you should have an understanding of how the two variables relate.
SC 14. Based upon your results for SC 13, write a mathematical expression describing the relationship between and r.
SC 14.
The electrostatic force is inversely proportional to the square of the distance (r2). Mathematically, this is written as .