Phys 223, Labatorial 3, Winter 2016
University of Calgary
Department of Physics and Astronomy
PHYS 223, Winter 2016
Labatorial 3: Equipotential Lines
Goals:
To understand the concept of equipotential lines and how they are related to the electric field. To understand
the geometry of equipotential lines in relation to the shapes of the electrodes.
Overview:
In this labatorial, you will find equipotential lines experimentally for certain configurations of conductors
(electrodes), check your results with a simulation, and relate the equipotential lines to the electric field.
Preparation:
Randall D. Knight, Physics for Scientists and Engineers, Third Edition, Pearson/Addison-Wesley: sections
28.1-5, 29.3.
Equipment: Fluke multimeter, Anatek power supply, field probe, potential mapping apparatus, parallel
plate conductor board, dipole conductor board, connecting cables, potential mapping graph paper, tape,
ruler, pencils; applets plate mapping and charges generator, which where developed using the resources
available on the Davidson University website http://webphysics.davidson.edu.
Field lines and equipotential lines for point charges
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Question 1: Draw the field lines for the two charges shown in the figures above. Explain briefly how you
know what the direction of the field is at a certain point, using the definition of the electric field in terms of
a test charge.
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Phys 223, Labatorial 3, Winter 2016
Question 2: Draw the equipotential lines in a different colour. Explain briefly how you know how to draw
the equipotential lines for these point charges, based on the mathematical expression for the potential of a
point charge.
Question 3: Do the equipotential lines have a direction? Explain why, or why not.
Question 4: What is the angle between the field lines and the equipotential lines for these point charges?
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Question 5: Draw the field lines for the two charge configurations shown in the figures above. Explain
briefly how you know what the direction of the field is at a certain point. (Hint: Refer to the superposition
principle in your explanation.)
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Phys 223, Labatorial 3, Winter 2016
Question 6: Draw the equipotential lines in a different colour. Explain briefly how you know how to draw
the equipotential lines for these charge configurations, based on the geometric relation between electric field
lines and equipotential lines.
Field lines and equipotential lines for charged conductors
Question 8: Draw the electric field lines between the conductors shown as well as a few on the outside. Draw the equipotential lines using a different colour. Explain briefly why you drew
them the way you do.
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Question 7: What is the angle between the surface of a conductor (in electrostatic equilibrium) and the
electric field lines? Explain your answer by stating what would happen to the charges in the metal if the
angle had a different value.
Question 9: If a positive test charge is released from rest on one of the equipotential lines, in which direction
will it start moving? Describe this direction with respect to the other equipotential lines.
CHECKPOINT 1: Before moving on to the next part, have your TA check
the results you obtained so far.
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Phys 223, Labatorial 3, Winter 2016
The equipment for the experiment: The potential mapping apparatus, the conductor boards, the power supply, and the voltmeter.
During the experiment, the conductor
boards will be mounted on the field
mapping apparatus that you see in the
figure to the left (actually, you see
the underside, because that’s where the
conductor board will be mounted). The
field mapping apparatus serves several
purposes: It holds the conductor board
in place while providing a surface on
which you can draw the equipotential
lines you will measure. It provides the
voltage to the two electrodes on the
board, and it provides seven reference
points (the seven connectors that are
placed in a row along one side of the
field mapping apparatus) for measuring
the potentiala .
a If you have studied circuits before, you will
notice that there are resistors between those
connectors that divide the supplied voltage
into equal intervals. The seven connectors allow you to access these voltages.
Question 10: Figure 1 shows how the field mapping apparatus will be connected to the power supply.
Think of the power supply as something similar to a battery: It provides a voltage, but one that can be
set to different values. (Moreover, the current can be restricted to a maximum value.) We will call the two
connectors the positive and negative terminals from now on. Once those terminals are connected to the
power supply, and the power supply is switched on, what will be the voltage between them?
Question 11: For the experiment, the two connectors of the conductor board will be connected to the
terminals of the field mapping apparatus, to supply the conductor board with the same voltage from the
power supply. When you mount the conductor board, in which direction should the electrodes on the black
side of the conductor face? Explain why.
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Phys 223, Labatorial 3, Winter 2016
Figure 1: The experimental setup
Question 12: Mount the parallel plate conductor board on the field mapping apparatus. Once the conductor
board is connected to the power supply via the terminals of the field mapping apparatus, and the power
supply has been switched on, is there an electric field between the electrodes? Explain.
Question 13: Will all the points on the surface of the conductor board be at the same potential, or at
different values? Explain your answer.
Question 14: To find the equipotential lines for the conductor board experimentally, we will use a voltmeter.
Does a voltmeter measure an absolute value of potential, or a potential difference? Explain.
CHECKPOINT 2: Before moving on to the next part, have your TA check
the results you obtained so far.
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Phys 223, Labatorial 3, Winter 2016
Connect the two wires from the power supply to the terminals of the field mapping apparatus, as shown in
Figure 1. Turn on the power supply, set the voltage to 10 V, and the current to its maximum value.
Question 15: Plug two wires into the voltmeter and place the other ends gently on the black surface of the
conductor board between the electrodes (one student should carefully hold the mapping apparatus while it
is standing on one side). What is the potential difference?
Question 16: What happens when you move one of the wires to a different place on the black surface?
Question 17: What would be the reading on the voltmeter if both points were on the same equipotential
line?
Question 18: If you want to measure the voltage between the negative terminal of the field mapping board
and the right-most reference point, where do you need to plug in the wires from your voltmeter?
Question 19: Measure the voltage between the negative terminal and each of the reference points. Record
those values in Figure 1.
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Phys 223, Labatorial 3, Winter 2016
Finding equipotential lines for the parallel plate conductor board
Ask your TA for a piece of paper with the outline of the conductors as you see them on your parallel plate
board. Tape this piece of paper to the top of your field mapping apparatus.
Since we want to mark the positions where we measure the potential, we will not simply use the wire from
the voltmeter anymore. Instead, we will use the potential mapping probe, shown in the figure on the left. It
allows you to measure the potential at a certain point and to mark this point on the paper. One arm goes
under the field mapping apparatus and makes contact with the conductor board. The other arm goes above
the mapping board and has a hole for a pencil right above the point where you measure the voltage. You
will use those marks to create a map of the electric potential.
Question 20: We want to find equipotential lines for the reference points on one side of the board, as
defined by the equipotential reference connectors. One wire from the voltmeter will be plugged into the field
mapping probe, and the probe will be used on the area between and around the conductors. Where do you
have to plug in the other wire?
CHECKPOINT 3: Before moving on to the next part, have your TA check
the results you obtained so far.
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Phys 223, Labatorial 3, Winter 2016
Now connect the two wires from the voltmeter to the first reference point and to the field probe. Move the
probe around on the board until you find a place where the potential difference is zero. Mark the paper at
that point. Then, find more points with potential difference zero, and mark them. When you have enough
points, connect the dots, and you will have found your first equipotential line. Label this line with its
reference voltage (refer to Figure 1).
Remove the wire that connects the probe to the first equipotential reference connector, and plug it into the
second. Find the equipotential line for this point with the same method as above. Repeat this procedure
for all the equipotential reference connectors.
Question 21: How does the shape of the equipotential lines that you found experimentally compare to
what you previously predicted?
Studying equipotential lines quantitatively
Put a new sheet of paper on the board, and draw an
axis perpendicular to the two plates, as shown in the
figure to the left. We set the origin to the negative
plate.
Plug one of the wires from the voltmeter into the negative terminal of the apparatus, while the other wire is
still in the probe. Use the field probe to measure the
potential at 7 points along the axis. Then, measure
the distance of each of these points from the origin of
the x-axis. Enter the values for the potential and for
the distance in Table 1.
Table 1: Measurements for the parallel plate conductor board
x (in meters)
electric potential (in Volts)
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Phys 223, Labatorial 3, Winter 2016
Question 22: Use LoggerPro to graph the potential as a function of position x. Sketch the
graph in the coordinate system provided, label
the axes, and indicate the positions of the negative plate and the positive plate.
Question 23: Use LoggerPro to fit an equation to your graph. Write down the equation for the fit.
Question 24: The slope of the function V (x) is its derivative, dV /dx. In one dimension the electric field
is given by E = −dV /dx. What are the magnitude and direction of the electric field that you obtain from
your fit?
Question 25: Does the magnitude of the electric field that you obtained from the fit depend on x? Explain
using what you know about parallel plate capacitors.
CHECKPOINT 4: Before moving on to the next part, have your TA check
the results you obtained so far.
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Phys 223, Labatorial 3, Winter 2016
Equipotential lines for a dipole conductor board
Question 26: Now select the dipole conductor board (it looks like two metal circles separated by a distance).
Sketch what you expect the equipotential lines to look like in the space below.
Question 27: Find the equipotential lines for the dipole conductor board experimentally. Then, compare
your result to your prediction in the previous question. If there are differences, try to explain them.
Question 28: Where are the equipotential lines closest together, and where are they farthest apart? Give
your answer with respect to the geometry of the electrodes.
Question 29: What can you say about the field in a region where the equipotential lines are close together,
as opposed to a region where they are far apart?
Last Checkpoint! Clean up your area, and put the equipment back the way
you found it. Call your TA over to check your work and your area before
you can get credit for the labatorial.
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