HPP Activity 64v1
COULOMB’S LAW
Objectives

to understand Coulomb’s Law qualitatively and quantitatively

to understand the principle of superposition
You have studied charges by observing the forces exerted by one set of charges on another. And
you have seen that even when there are equal numbers of charges on an object, those charges can
move or rearrange themselves in response to other nearby charges because of the electrostatic
force. You know that two + charges (or two - charges) repel each other while a + and a - charge
attract each other. And you have observed that the electrostatic force varies as the distance
between two charges varies. Can you now discover a mathematical model that will allow you to
determine the strength of the electrostatic force? And how might that force allow us to study
nerve impulses, heart rhythms, or brain waves?
Exploration
How might you quantify - develop a mathematical model of - the electrostatic force? What
evidence have you used to identify that the force exists?
GE 1.
1. Consider two identical conducting spheres. One sphere is touched with a
rubber rod that has been rubbed with wool. The sphere that has been touched
with the rod is now charged. Let’s say that it has a negative charge q.
Draw a picture of how the excess negative charge q is distributed on the
sphere. (Remember that a sphere with charge q has both positive and negative
charges, but more negative than positive charges.) The symbol q represents the
additional negative charges -- the excess negative charge. It is common only to
draw the additional charges, with the understanding that the object contains
positive and negative charges, but more negative charges. Explain how the
charges would be distributed on the sphere.
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 2002-2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
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2. If the second sphere is now touched to charged sphere, what would happen
to the charges, based on your previous experiments? How much charge would
be on each sphere if you waited long enough? Explain your reasoning.
3. Consider a pair of conductors hanging from non-conducting strings, as in
the diagram below. Each of the conductors has a charge q.
Initially the conductors are placed a certain distance apart. Make predictions
for the following situations:
4. How does the angle with respect to the vertical for charge q1 compare with
the angle with respect to the vertical for charge q2? Remember that the
charged spheres are identical! Explain your reasoning.
5. If the amount of charge on conductor q1 is decreased to q/2 (the other
conductor, q2, still has charge q), would the angle with respect to the vertical
for each conductor increase, decrease or remain the same? How does the
angle with respect to the vertical for charge q1 compare with the angle with
respect to the vertical for charge q2? Explain your reasoning.
6. If the amount of charge on both conductors is decreased to q/2, would the
angle with respect to the vertical for each conductor increase, decrease or
remain the same? B how much, do you predict, will the angles in this case
differ from the angles in part 1? Explain your reasoning.
f. Have your instructor carry out each of the above experiments in parts 3-6
above and record your observations.
3.
4.
5.
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6.
Invention
Newton’s 3rd Law tells us the force exerted by one charged object on a second charge object,
must have the same magnitude but opposite direction as the force exerted by the second charged
object on the first. It is difficult to perform the experiment above although, with patience, Charles
Coulomb managed to do just that although he did not hang his conductors from strings, but
instead produced a torsion pendulum which allowed him to control distances to higher precision.
What he found was the force between any two charges depends on the product of their charges.
i.e.
F q1  q2
Exploration
 forces and free body diagrams. They will be essential for
At this point you may want to review
understanding these steps. You are to consider the case above in which you have two identical
charged conducting spheres hanging from non-conducting threads.
GE 2.
1. Draw a free-body diagram for one of the two conductors in the figure
below. For each force, indicate a) the type of force (normal, gravitational, etc.)
b) the object exerting the force and c) if the force is a contact force or noncontact force.
Both of the conductors have the same amount of charge.
Invention
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Now let's try to put it all together in the form of a mathematical model. You will assume a static
situation (no motion in either the x- or the y-direction).
L

q1
x
GE 3.
1. Using your free-body diagram above, find the tension force in terms of the
gravitational force. This is the same thing as asking you to write down
Newton's 2nd Law for the vertical direction. Ask your instructor for a hint or
two.
FT=
2. Write down Newton's 2nd Law for the horizontal direction. Hint: it will
relate the electrostatic force to the horizontal component of the tension force.
FE=
3. Now combine the equations in 2 and 3 to find an equation for the
electrostatic force in terms of the gravitational force. Ask your instructor for
help if you need it!
4. Now find a mathematical expression for tan as a function of x and L.
Hint: The diagram and the definition of tangent should help.
tan =
5. Now find an equation for Fe in terms of L, x, m, and g. Notice, these are all
measurable quantities which means you can now find Fe without knowing
anything about the electrostatic force itself. Show your calculations in the
space below.
FE=
Invention
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Now collect some data and use your new equation to compare the electrostatic force to the
distance between two charges.
GE 4.
1. Obtain a video of the two charged conductors experiment. Record the mass
of the suspended ball, m, and the length L.
mass:
m=
length: L =
2. Obtain a series of x and r data points from the video. You must choose "2"
points to follow when starting VideoPoint and you must be consistent when
clicking on the centers of the balls. For the first frame click to the far left for
the left conductor (it's off screen but you still need the data point -- you will
correct for that later).
x
r
Fe
3. For each value of x and r, calculate the experimental value of the electric
force, Fe. NB: This easily done in a spreadsheet.
4. Graph your FE versus r data. Find the best-fit line and paste the graph with
the equation in the space below. Hint: you might try a power law fit!
Have your instructor discuss the significance of what you've discovered so far.
Invention
Coulomb’s Law states that the force of charged object One on charged object
Two, F12, equal to the force of charged object Two on charged object One, F21,
(this is Newton’s Third Law), the magnitude of the force is given by
F12  F21  k
Q1Q2
r2 ,
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and the direction of the force is along a line between the two objects. In the equation, Q1 is the
charge of object 1, and Q2 is the charge of object 2, and r is the distance between the objects.
Charge is measured in Coulombs represented by the symbol C. The k in the equation is a
constant and has the value 8.99  109 Nm2 /C2. It applies to the force between two small charged
objects, so small that all the charge can be considered to be at one point (even when it's really
not!). These are often called point charges.
Exploration
What happens where there are more than two charges? How would you combine the forces of
two (or more) charges that are acting on another charge?
GE 5.
1. Assume a negatively charged conducting pith ball is hanging near a
negatively charged rod, as in the picture below.
a. If a second negatively charged rod were brought in from the right of the first
rod, would the angle of the pith ball change? Explain your reasoning.
b. If a second negatively charged rod were brought in from the left of the pith
ball, would the angle of the pith ball change? Explain your reasoning.
c. Carry out the experiment in parts a and b and record your observations.
d. In each of the cases above, does the force on the pith ball depend on both
rods?
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When more than two point charges are present, the force between any pair of
charges is given by Coulomb’s Law. Therefore, the resultant force on any one
of the charges is the vector sum of the forces due to the other individual
charges. This is called the principle of superposition.
e. Is this consistent with your observations in c? Explain why or why not.
Have your instructor demonstrate how to work problems using Coulomb’s law and the
superposition principle.
SUMMARY
You should understand Coulomb’s Law qualitatively and quantitatively and be able to work
problems using Coulomb’s Law and you should understand the principle of superposition.
Activity Guide
 2002-2008 The Humanized Physics Project