HPP Activity 66v1
Electric Energy and Electric Potential
Graph
Figure 1 A human EKG taken with the Pasco ScienceWorkshop interface.
Invention
Have you ever had, or known someone who had, an EKG? An EEG? Or have you ever wondered
what a heart monitor is actually measuring? What are doctors measuring when looking at brain
waves? To understand these things we must move beyond the idea of electric forces and instead
look at measuring electric fields around the body. As you have seen, electric fields can tell us
about the charges that produced the fields but so far, we can only determine electric fields by
placing a test charge in the field and watching what it does. This is not very practical in the
human body!
If you were to charge a glass rod and a positive test charge and move the test charge toward the
rod what would happen? You can also use the test charge to explore some unknown collection of
charges by observing the net force on the test charge due to all the other charges in the collection.
GE 1. Work on a Charge
1. Write the physics definition of work in the space below in both words and
in equation form. If you don't remember, look it up in your textbook.
2. When you move the positive test charge toward the positive rod, do you do
work? Explain.
3. Does the electric field do work on the test charge? Explain.
Activity Guide
 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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4. Give the rubber rod a negative charge.
5. Move the positive test charge toward the negative rubber rod. Is the work
you do positive or negative? Explain.
6. Relate the sign of the work done in moving a positive test charge with the
direction of the electric field through which it is moving.
7. In the drawing below, let W be the work done in moving the positive test
charge from A to B. What is the change of potential energy of the test charge
as it moves between A and B? (Think about the gravitational analog; what is
the direction of the force and the direction of motion?) Where would be a
logical place to define PE = 0?
Test charge
starts here
8. If the + charge were released at point B, what would happen to it and why?
Would it gain anything and if so, how much of it would it have at point A
compared to point B?
9. Now we will define an electric potential difference as the potential energy
difference between two points divided by the magnitude of the test charge.
VB-VA = (UB-UA )/q= -W(A to B)/q (remember we did this for gravitational
PE too.)
(Note the similarity with the definition of the electric field for which the force
is divided by the magnitude of the test charge.)
Is the electric potential positive or negative near a “+” charge? Near a “-”
charge? Remember that PE (or U) is zero far away from any charges (review
question 7). For each charge, "+" and "-", sketch a curve of potential vs the
distance from the charge on the axes below.
Activity Guide
 2010 The Humanized Physics Project
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V
d
Your instructor will discuss the equation for the potential near a point charge.
Examples of using the electric potential concept to predict the motion of a
charged particle will be worked.
Exploration
Of course you must still be wondering what all this has to do with EEGs and EKGs! You are
nearly to the point of making the connection.
GE 2 Equipotential Surfaces
Sometimes it is possible to move along a surface without doing any work.
Thus, it is possible to remain at the same potential energy anywhere along
such a surface. If an electric charge can travel along a surface without doing
any work, the surface is called an equipotential surface. In the next activity
you will try to guess the shape of the equipotential surfaces for several
configurations of charge.
1. Suppose that you have a test charge and you start moving your test charge
at some distance from the charge below (such as 4 cm). What path could you
move along without the electric field doing any work on your test charge?
What is the shape of the equipotential surface for this case? (Remember that
in general you can move in three dimensions.) Explain why you think so.
Sketch your predicted path on the drawing below.
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2. Find some equipotential surfaces for the charge configuration shown
below, which consists of two charged metal plates placed parallel to each
other. What is the shape of the equipotential surfaces? Remember you are
trying to decide how a test charge could move so that the electric field does no
work on it. Sketch the path on the drawing below and explain why you think it
should be that way.
+
+
+
+
+
+
+
+
—
—
—
—
—
—
—
—
3. Find some equipotential surfaces for the electric dipole charge
configuration shown below. Sketch your predictions on the sketch below
and explain why you drew them the way you did.
Activity Guide
 2010 The Humanized Physics Project
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4. In general, what is the angle between the equipotential lines you have
drawn (representing that part of the equipotential surface that lies in the plane
of the paper) and the direction of the electric field lines? Again, explain why
you think so. Your answer should include an argument based on the physics
definition of work.
Application
Now you will turn around the problem and you will determine the electric field around a
distribution of charges by measuring the electric potentials and by using what you know about
the relationship between electric potentials and electric fields.
GE 3 Electric Field Mapping Using Equipotential Surfaces
Objective: To map electric fields from equipotential surfaces
In this activity you will plot equipotential surfaces and then draw in the
electric field lines.
The experimental set-up consists of a carbonized paper with conductors
painted on them. A voltage is applied across the two conductors so an electric
field exists between them. With a pointed probe, you can measure the electric
potential at various points on the paper. From these measurements, you can
plot the equipotential surfaces and then draw in the electric field. There are
sheets of special graph paper available for your drawings.
1. Attach the voltage supply to the paper with the two point charges and set
the voltage to 10 volts. Find a series of points on the paper that have a
potential of 0 volt, 1 volt, 2 volts, etc. up to 10 volts. Draw at least 6
equipotential lines on the graph paper.
Activity Guide
 2010 The Humanized Physics Project
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2. Replace the two "point charges" with the parallel lines. Repeat your
measurements to find the equipotential lines. Sketch the equipotential lines on
the graph paper.
Analysis
1. Make a sketch of the equipotential surfaces for each conductor arrangement.
Then draw in at least 5 electric field lines. Start each electric field line on the
10-volt equipotential line. Remember that the electric field is always
perpendicular to the equipotential surface. Do the drawings on the graph paper
and have the instructor scan your drawings so that you can include them in the
activity file.
2. Go to the PHET simulation “Charges and Fields”. Create the two charge
configurations considered above. Plot equipotential lines. Compare your
sketches with the simulation sketches of the equipotential lines.
Activity Guide
 2010 The Humanized Physics Project