Name:
Lab Partners:
Date:
Pre-LAB 2 Preparation
Electric Potential, Equipotentials, and Electric Fields
(Due at the beginning of Lab)
Directions: Read over the Electric Potential, Equipotential and Electric Field Lab, and then
answer the following questions about the procedures.
Question 1 (a) What is the expression for work done on a particle of charge q displaced by a
distance d at an angle θ with an uniform electric field of strength E?
(b) What is the change in electric potential in this process?
Question 2 In each of the figures 1(a), 1(b), and 1(c) a particle with a positive charge of
magnitude q is moved a distance d in an electric field E. The magnitude of the charge, the
distance d, and the strength of the electric field E are the same for all three figures. In figure 1a
the path along which the particle is moved is parallel to the field, in figure 1(b) it is perpendicular
to the field, and in figure 1(c) it makes a 45◦ angle. In which figure is the work done by the
field greatest? In which figure is it least? Explain your answers.
(a)
B
(b)
(c)
A
A
B
B
A
Question 3 If q = 5 × 10−9 C, E = 500N/C, and d = 0.02 m, calculate the amount of work
done by the field on the particle in each of the figures.
Question 4 What is the change in the electrical potential energy in each of the figures? Be
sure to properly indicate the sign (+ or −) of the change in potential energy.
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Question 5 If E = 500 N/C and d = 0.02 m, calculate the electric potential difference between
points A and B in each of the figures 1a, 1b, and 1c.
Question 6 What is the definition of equipotential surface?
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Name:
Lab Partners:
Date:
LAB 2
Electric Potential, Equipotentials, & Electric Fields
Objectives
• To review the definitions of work and potential energy, and to apply these definitions in
the context of electrical forces.
• To understand the definition of electric potential, or voltage.
• To learn how to map equipotentials.
Overview
If you lift a particle from one point to a higher point against the pull of a gravitational
field, the gravitational potential energy of the particle increases. This increase in the particles
potential energy is equal to the amount of work you have done.
∆PEgrav = W
Similarly, if you push a charged particle from one point to another against the force of an
electric field the electrical potential energy is increased, and you have to do an amount of work
equal to the electrical potential energy difference:
∆PEelec = W
Conversely, when a particle falls from one point to another in a gravitational field, the gravitational field does work on the particle, the gravitational potential energy decreases, and the
gravitational potential energy difference is negative. When an electrically charged particle
moves from one point to another due to an electric field, the field does work on the particle,
and the electrical potential energy difference is negative.
These labs have been adapted from the Real Time Physics Active Learning Laboratories [1].
The goals, guiding principles and procedures of these labs closely parallel the implementations
found in the work of those authors [1, 2].
Investigation 1:
Work, Electric Potential Energy, and Potential Difference
In Physics I, we defined work in terms of the force required to move an object, the displacement
through which the object is moved, and the angle between the force and the displacement:
W = F · d = F d cos θ
The magnitude of the force exerted on a positively charged particle by an electric field is
F = qE.
For a positively charged particle, the force is in the direction of the electric field.
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Activity 1.1: Work Done on a Charge Traveling in a Uniform Electric
Field
Questions 1-1, through 1-7 should be answered before coming to class. Note that some of these
questions are in the pre-lab assignment.
Question 1.1 In each of the figures 1(a), 1(b), and 1(c) a particle with a positive charge of
magnitude q is moved a distance d in an electric field E. The magnitude of the charge, the
distance d, and the strength of the electric field E are the same for all three figures. In figure
1(a) the particle is moved parallel to the field, in figure 1(b) it is moved perpendicular to the
field, and in figure 1(c) it is moved at a 45◦ angle. In which figure is the work done by the field
greatest? In which figure is it least? Explain your answers.
(a)
B
(b)
(c)
A
A
B
B
A
Question 1.2 If q = 5 × 10−9 C, E = 500 N/C, and d = 0.02 m, calculate the amount of work
done by the field on the particle in each of the figures.
Question 1.3 What is the change in the electrical potential energy in each of the figures? Be
sure to properly indicate the sign (+ or −) of the change in potential energy (Note: if the work
done by the field is positive, then the field has used up energy to do this work, so the change in
potential energy is negative.)
The electric potential difference is defined as the electrical potential energy difference per
unit charge:
∆V = ∆PE/q
The unit of electric potential difference is the Volt. One volt corresponds to 1 Joule/Coulomb.
Question 1.4 If E = 500 N/C and d = 0.02 m, calculate the electric potential difference
between points A and B in each of the figures 1(a), 1(b), and 1(c).
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Question 1.5 Do you need to know the amount of charge, q, in order to answer question 1-4?
Why or why not?
Question 1.6 In each of the figures, which point is at the higher electric potential, A or B?
Explain.
Question 1.7 If the charge q were negative instead of positive, would your answers to question
1.6 stay the same?
Measuring Potential Differences between two points in an electric field
In this activity you will measure the electric potential difference between between pairs of points
in the electric field set up by pairs of conducting electrodes.
To make these measurements you will need the following equipment:
• Computer-based laboratory system.
• Experiment configuration files.
• 2 differential voltage sensors.
• Water tray.
• Electrodes mounted on a plastic grid.
• Signal generator set to 60 cycles per second frequency.
• Two stiff wires to use as probes.
One of the sets of electrodes is a pair of bars mounted on a plastic grid as shown in Fig. 2.
+
−
Figure 2: Two parallel Conducting Plates
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This arrangement simulates two parallel conducting plates. This is an important arrangement because it gives a uniform electric field in the region between the plates away from the
ends.
Step 1: Place this set of electrodes in the tray, and pour in enough water to come up about
1/4th of an inch over the plastic grid.
Step 2: A clear plastic sheet has been cut out to go over these electrodes. Place it so that it
lies flat on top of the plastic grid.
Step 3: Open the file L3A1 2 (Potential Differences). This file will display two meters that
will be used to measure potential difference.
Step 4: You have two differential voltage sensors, one connected to input 1, the other connected
to input 2. Connect the voltage probes, if they are not already connected. Clip the leads
of each of the voltage sensors together to assure that the potential differences between
the leads are zero. Click the zero button, and zero all sensors.
Step 5: Connect the signal generator to the two electrodes. The red post on the signal generator is considered positive; connect it to the electrode marked +, and connect the black
terminal to the electrode marked −.
Step 6: Note that the leads connected to the voltage sensors are marked + and −, with the
red lead corresponding to +, the black to −. Connect voltage probe 2 with the red clip
on the positive electrode, and the black clip on the negative electrode. Turn on the signal
generator and adjust the frequency to 60 cycles per second. Then turn up the amplitude
so that meter 2 reads 6 volts. Note, the meter takes a few seconds to adjust itself to the
correct reading. Adjust the amplitude slowly enough that the meter reading can keep up.
Step 7: You will use the two stiff wires as probes to determine the potential difference between
pairs of points. Clip the bare copper ends of these wires to the two leads of voltage sensor
1.
Comment: In a device that measures potential difference, + refers to the higher potential, and − to the lower potential. If the voltage sensor gives a positive value with the −
probe at A and the + probe at B, then we consider the potential difference from A to B
to be positive. Note the order is important. We would say the potential difference from
B to A is negative.
Step 8: Measure the electrical potential difference from point A to point B by placing the tip
of the negative probe on point A, and the tip of the positive probe on B. Enter your
measured value in the Table 1. Hold the probes so that the wires are vertical. If they are
angled you will get inaccurate readings.
Potential Difference
Work on 2 × 10−6 C charge.
A to B
B to C
C to D
Table 1:
Step 9: Now measure the electrical potential difference from point B to point C, placing the
negative probe on B, and the positive probe on C. Enter your measured value in Table 1.
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Continue by measuring the potential difference from C to D and enter your value into
Table 1.
Question 1.8 How large is the total potential difference from point A to point D?
Question 1.9 How much work would be needed to move a particle with charge 2 × 10−6
C from point A to point B? B to C? C to D? Calculate the amounts of work, and enter
them in Table 1.
Question 1.10 What would be the total work needed to move a particle with charge 2 ×
10−6 C from point A to point D?
Total work A to D =
Joules
Question 1.11 As the charged particle is moved from A to D, does its potential energy
increase or decrease? By how much does the potential energy change?
Prediction 1.1 Suppose you were to move the charged particle from A to D along the
straight line going from A through points E and F to D. Would the total amount of work
be the same? Would you determine the same potential difference between points A and
D?
Step 10: Check your predictions. Using the same technique as in steps 8 and 9, measure the
potential difference from A to E, E to F, and F to D, and enter your measured values in
Table 2.
Potential Difference
Work on 2 × 10−6 C charge.
A to E
E to F
F to D
Table 2:
Question 1.12 What is the total potential difference from A to D along the path through
E and F. Does your measurement agree with your prediction? Because of the limits in
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precision of the equipment, you should consider any discrepancies smaller than a few
hundredths of a volt to be insignificant. Is it reasonable to expect that the amount of work
needed to move a particle from A to D would be the same along any path? Why or why
not?
Prediction 1.2 What is the electrical potential difference from B to E? Realize that the
precision of the equipment is no better than about a tenth of a volt. Can you tell with
certainty which point, B or E, has the higher potential?
Step 11: Check your prediction using the probes to measure the potential difference from B
to E.
Question 1.13 Does your measurement agree with your prediction? Because of the limits in precision of the equipment, you should consider any reading smaller than a few
hundredths of a volt to be a potential difference of 0.
Prediction 1.3 What is the electrical potential difference from C to F? Can you tell with
certainty which point, C or F, has the higher potential?
Step 12: Check your prediction using the probes to measure the potential difference from C
to F.
Question 1.14 Does your measurement agree with your prediction? Because of the limits in precision of the equipment, you should consider any reading smaller than a few
hundredths of a volt to be a potential difference of 0.
Question 1.15 From your measurements in this activity will the difference of potential
be maximum when the particle moves along the field or perpendicular to the field?
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Question 1.16 From your measurements in this activity will the difference of potential
be zero when the particle moves along the field or perpendicular to the field?
Investigation 2:
Exploring Equipotentials
In any arrangement of charges there are many points that have the same electric potential. We
call the set of all these points an equipotential. These equipotentials give us one way to map
out the electric field set up by the arrangement of charges.
In this investigation you will explore the equipotentials for few different arrangements of
electric charge represented by different electrodes.
Activity 2.1: Sketches of equipotentials
Question 2.1 Suppose that you are a test charge and you start moving at some distance from
the charge in Fig. 3 (such as 1 cm). (a) What path could you move along without doing any
work? That is, what path would you take so that the work is always zero? (hint: check your
answer to Questions 1.15 and 1.16)
(b) Using the answer to (a) indicate what the shape of the equipotential surfaces around
the point charge represented in Fig. 3 is. Remember that in general you can move in three
dimensions.
Question 2.2 Sketch some equipotential surfaces for the configuration of two charged parallel
plates shown in Fig. 4, which consists of two charged metal plates placed parallel to each other.
What is the shape of the equipotential surfaces?
Question 2.3 Sketch some equipotential surfaces for the electric dipole charge configuration
shown in Fig. 5
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+
Figure 3: Electric Field from a Point Charge
−
−
−
−
−
−
−
−
−
−
+
+
+
+
+
+
+
+
+
+
Figure 4: Electric Field Between Parallel Conducting Plates
Question 2.4 In general, what is the relationship between the direction of 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?
Activity 2.2: Mapping out equipotentials experimentally
In this activity you will use the voltage probes to map out the equipotentials for the arrangements that you worked with in Activity 2.1. You will use the same equipment as in Activity
1.2
Step 1: One of the sets of electrodes has a post at the center, surrounded by a brass ring on
a plastic grid as shown in Fig. 6.
The center post simulates a point charge. We will think of the outer ring as being ”far
away,” where it is customary to take the electrical potential to be zero (this is a slight
approximation). Since the center post will be made positive, the electric field lines should
be directed radially outward.
Place this set of electrodes in the tray, and make sure the tray has enough water to come
up about 1/4th of an inch over the plastic grid.
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+
−
Figure 5: Electric Dipole Field
−
+
Figure 6: Coaxial Conducting Shells
Step 2: You will use the same file as in Activity 1.2, file L3A1 2 (Potential Differences).
Step 3: Clip the leads of each of the voltage sensors together to assure that the potential
differences between the leads are zero. Click the zero button, and zero all sensors.
Step 4: Connect the positive (red) terminal of the signal generator to the center post, and
connect the negative (black) terminal to the outer brass ring. This way the center post
can be thought of as a positive point charge.
Step 5: Connect voltage sensor 2 with the negative lead of voltage sensor 2 to the outer ring,
and the positive lead to the center post. Turn on the signal generator and adjust the
frequency to 60 cycles per second. Then turn up the amplitude so that meter 2 reads 6
volts. Adjust the amplitude slowly enough that the meter reading can keep up.
Step 6: You will use voltage sensor 1 to locate points that have the same potential. Connect
the negative lead of voltage sensor 1 to the outer ring. Clip the positive lead to the bare
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copper end of one of the stiff wires.
Step 7: Use the stiff wire as a probe. Search in the area within the ring to locate a point
that has an electric potential of 1 Volt. Plot the position of the point on the graph paper
showing this arrangement of electrodes. (If you have difficulties finding a point with an
electric potential of 1 Volt try finding a point with electric potential of 2 Volt).
Step 8: Continue locating and plotting points with the same potential as in the previous
question. Until you have enough points to draw a curve that will represent all the points
having that same potential as in the previous question. This is the one (or two) volt
equipotential. Label the curve ”1 (or 2) Volt.” You should not have to find a lot of points,
if you recognize that there is symmetry.
Step 9: Repeat the process of locating and plotting points to draw the 2 Volt, 3 Volt, 4 Volt,
and 5 Volt equipotentials. Be sure you label the equipotentials.
Step 10: Now disconnect the leads to the voltage sensors from the electrodes, and replace the
electrodes with the set with two parallel bars.
+
−
Figure 7: Two parallel Bars
Adjust the amplitude of the signal generator so that voltage sensor 2 reads 6 volts. Repeat
the process of locating the 1, 2, 3, 4 and 5 Volt equipotentials, as in steps 7 through 9.
Plot them on graph paper showing the two parallel bars. You should focus primarily on
the region between the two bars, but locate some points beyond the end of the bars so
that you can see how the equipotentials spread out.
Step 11: Finally, replace the parallel bars with the set of electrodes consisting of two posts.
−
+
Figure 8: Two Posts: An Electric Dipole
This arrangement of electrodes gives us an electric dipole. Take care to note which post
is connected to the positive terminal of the power supply, and which is connected to the
negative. Mark them on the graph paper you will use to plot the equipotentials. Again
locate the 1, 2, 3, 4 and 5 volt potentials.
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Question 2.5 Compare your plots for each of these configurations with the sketches you
made to answer Questions 2.1, 2.2 and 2.3. Is there general agreement between the
sketches and your experimental plots? If there are differences, which plots are different,
and how are they different?
References
[1] David R. Sokoloff, Priscilla W. Laws, Ronald K. Thornton, and et.al. Real Time Physics,
Active Learning Laboratories, Module 3: Electric Circuits. John Wiley & Sons, Inc., New
York, NY, 1st edition, 2004.
[2] Priscilla W. Laws. Workshop Physics Activity Guide, Module 4: Electricity and Magnetism.
John Wiley & Sons, Inc., New York, NY, 1st edition, 2004.
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