EXPERIMENTS 1 & 2: ELECTRIC FIELD MAPPING
NOTE: The procedure for Exp. 1 begins on page 2 and
the procedure for Exp. 2 begins on page 5.
Object: To determine the nature of the electric field and equipotentials of a dipole and
the relationship between them. In addition, time permitting to investigate the
same quantities for other charge arrangements.
Discussion: The region near a charged body will influence the motion of another
charge brought into that region. The nature of the influence is given by the
electric field E. The force on a charge in the presence of that electric field is will
do work to move the charge (force times distance). It can be shown that the
electric force is conservative, therefore a potential energy/unit charge can be
defined. This potential energy may be represented by a contour map of lines of
equal potential. The relationship between the potential and the field is given by
vector mathematics as the negative of the gradient of the potential is equal to the
field. (See the chapter on electric potential in your text.)
The map of an electric dipole is shown in the figure below. The solid lines
represent the electric field and the dashed lines represent the equipotentials.
Overview:
The laboratory is divided into two experiments. First is a computer simulation
of the field and equipotential plots for point charge distributions defined by the
experimenter. The second experiment is to use the Overbeck Field Mapping
apparatus to experimentally determine the equipotential lines, and then to
sketch the corresponding electric field.
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EXPERIMENT 1. Electric Field Plotting I
Computer Simulation Program (EM Field 6.4) Instructions
Prior to lab, solve the following problem: Given two charges, –1.0C at x = -1.0 cm,
y = 0 and +5.0 C at x = 2.0 cm, y =0, locate the position on the xy plane where
E = 0.
Computer Program Instructions: To start the plotting program:
1. Turn on the computer and monitor.
2. As shown below, find the Start ‘button in the lower left corner and click on it.
3. With the mouse select Physics Software, EM Field6 and EMField (Fig. 1)
Figure 1 Computer desktop showing selection of
EM Field.
Figure 2 EM Field start up screen.
4. After the startup screen (Fig. 2) appears click on it to bring up the next screen
(Fig. 3) which begins the program. Follow the instructions on the screen and
select 3D point charges from the menu bar (Fig. 4).
Figure 3 Instructions for selecting program
features.
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Figure 4 Selecting mapping of the field due to point
charges
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5. After the next screen appears, select the Display menu and choose Show grid
(Fig 5).
6. Select equal and opposite charges of magnitude 4 and place them 6 units apart
along a horizontal line (similar to Fig. 6).
Figure 5 Selecting Show grid.
Figure 6 Placing the charges for mapping the field
of a dipole.
7. Select Field lines under the Field and Potential menu (Fig. 7), then move the
mouse to the active area, and click to have the program draw a field line (Fig. 8).
Select several points on the active area and repeat until you have mapped the
entire area. For a few points near displayed field lines select Field vectors and
show the field vectors on the mapping.
Figure 7 Choosing to map Field lines.
Figure 8 Beginning to map the electric field lines
8. When finished, print your result by selecting “Landscape” under File and Page
Setup, then Print Screen under the File menu (Fig.9 on next page). On the
printed paper indicate the direction of the electric field lines.
9. Follow the instructions under Laboratory to complete the lab session.
10. When you have finished the lab session, select Quit under the File menu and
shut down the computer.
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Figure 9 Selecting the Print screen option from the
file menu.
Procedure:
1. Plot the electric field lines for a dipole as described above. Include the print out in your report
2. a, Select (your instructor may give you this distribution) a distribution of 3 unequal charges
located asymmetrically.
b. Place the charges on the screen and select print a copy in the landscape mode of this
charge distribution without the field lines,
c. Sketch what you expect to see for the electric field lines when you map them on the
printout from step b.
d. After your instructor has approved and initialed your sketch, use the program to
map the electric field for the distribution you selected. Include a few electric field
vectors.
e. Print the computer mapping and include it as well as your sketch in your report. Be sure to
label the direction of the electric field lines.
3. Solve the problem given at the beginning of the lab. Place this distribution into the program,
and determine if the zero field is where you predicted it to be. Print your map of the electric
field. Comment on the nature of the field in the area close to the zero field.
4. Under options, select Challenge game under Options and choose two charges. By locating
the field vectors, try to solve the problem. Print your result before revealing the charges by
selecting Reveal charges under Challenge. Note: You may select Judge at any time.
Include the print out in your report.
REPORT:
1. For your report comment on the accuracy of your predictions for steps 2,3 and 4. Comment
on any inadequacies in the computer program. Include all printed field mappings and
drawings in your report. Be sure to indicate the direction of the field lines on all mappings.
2. State what you learned about the nature of the electric field for point charges.
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EXPERIMENT 2. Electric Field Plotting II
Equipotential and Field Mapping Apparatus
Prior to lab: On a separate piece of paper sketch the equipotential lines and the
electric field lines for the following charge distribution. Both elements are charged
conductors.
+
Object: To determine the nature of equipotential lines and electric field lines for
several electrode configurations, and to determine the behavior of a insulator and
conductor in the presence of an electric field.
Theory: Since the electric potential is the result of integrating the electric field along
a displacement, the inverse operation would be that the rate that the electric
potential changes with position would yield the electric field strength in.
We may regard the equipotential lines to be similar to the lines of constant
elevation on a topographical map. The electric field lines then must be indicated by
the rate and direction that the ‘elevation’ changes. The closer the equipotential
lines are the steeper the slope or the faster the rate of change; i.e., the larger the
electric field. In addition we find that the electric field must be perpendicular to
the equipotential lines, thus we have the following rules for electric field lines,
electric fields and equipotentials.
General Rules for Electric Field Lines and Equipotentials:
1. The electric field (vector) is tangent to the electric field line.
2. Electric field lines start on positive charges and point toward negative charges.
Electric field lines terminate on negative charges.
3. Electric field lines are perpendicular to equipotential surface.
4. The number of electric field lines in an area is proportional to the magnitude of
the electric field in that region.
5. Electric filed lines never cross.
6. The closer equipotential surfaces are to each other, the stronger the electric field
is in that region.
PROCEDURE:
1. Install an electrode board on the bottom of the apparatus using the bolts and
washers provided (see Fig. 1), place a piece of plain white paper on the top of the
apparatus by pushing down on the board and slipping the paper under the rubber
washers that are the tops of the legs. Using the correct template mark the location
and sign of the charges. (Fig. 2)
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WARNING: NEVER PLUG IN OR TURN ON ANY POWER SUPPLY OR VOLTAGE
SOURCE UNTIL YOUR CIRCUIT HAS BEEN APPROVED BY YOUR LAB
INSTRUCTOR!
2. Connect the battery eliminator to the battery terminals of the board (Figs. 3 and 4).
Set the voltage of the battery eliminator for 3 volts, but do not plug in the battery
eliminator. Note that the red terminal on the battery eliminator is positive and the
black terminal is negative.
Figure 1 The bottom of the field mapping apparatus
illustrating the correct installation of a electrode board
(dipole in this case) for mapping.
Figure 2 The top of the field mapping apparatus
illustrating the placement of a sheet of plain paper
and the electrode template for determining the
location of the electrodes of the board installed on the
bottom of the apparatus.
Battery
Eliminator
Mapping Apparatus
DMM
Probe
Figure 3 The field mapping apparatus correctly wired
and ready to measure the locations of points of
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Figure 4. A wiring diagram of the apparatus. The lines
connecting the various labeled rectangles are wires,
the circles represent connections, and the labeled
rectangles represent the various pieces of apparatus
that are wired together.
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equipotential. The wire from the top of the board to
the digital multimeter (DMM) is connected at E4
which is the starting point to check that the
apparatus if working correctly.
3. Connect the terminal of the U-shaped probe to the COM terminal of the digital
multimeter (DMM). Connect the V- terminal to E4 on the board. Turn the selector
switch on the DMM to 2.0 VDC (Figs. 3 and 4).
4. Have your instructor check your connections. Only after your instructor has
checked you wiring are you allowed to plug in the battery eliminator.
5. Slip the electrode board, base and paper between the arms of the U-shaped probe.
Locate positions with a constant potential reading (voltage) and mark these
positions on the paper by making a small circle in the hole of the U-shaped probe.
Your locations should be one to two centimeters apart. (It is helpful to begin with
the 0 Volts potential (voltage) reading to check out the apparatus to see if it is
working properly.)
6. Move the probe to determine another potential approximately one centimeter from
the first, and find another set of locations as you did in step 5. (If necessary, you
may need to map equipotentials closer together to clearly map the entire area.)
7. Repeat 6 until you have mapped the entire area including areas to the left and
right of the charges (electrodes).
LABORATORY:
1. Plot the equipotential lines for a dipole (this is a repeat of step 7 above).
2. Unplug the battery eliminator. Replace the dipole board with the board that includes the
conductor and insulator. Have your instructor recheck your circuit, then plug in the battery
eliminator. Repeat the above procedure for the electrode arrangement that includes a
conductor and non conductor within the area of the field.
ANALYSIS: Make copies of the map you and your partner generated. Each partner then must
draw a smooth curve through the dots to represent the equipotential lines. After the
equipotential lines are drawn, using another color sketch the electric field lines. The field
lines must be perpendicular to the equipotential lines when they cross. Remember to
indicated the direction of the field lines.
REPORT: Describe and evaluate your results. Be sure to comment on any comparison
between the computer simulation or the mapping and deviations from the ideal map, etc.
For the electrode board mapped in step 2, describe the orientation of equipotential lines
and electric field lines near the surface of the conductor and non conductor.
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