Lab 3: Electric Fields and Potentials
To experimentally investigate the concept of the electric field and to map (represent
graphically) some field lines for particular charge configurations.
The electric field intensity is defined as the electrical force per unit of charge, or
E = F/q. Theoretically, the electric field is determined by using a positive test charge q
and determining the force acting on it at every point in space. The direction of the field
is found by the laws of vectors and the rule that tells you whether the force is
attractive or repulsive. Since a free charge moves in an electric field by the action of
the electric force, then work (W = F * d) is done by the field in moving charges from one
point to another (e.g., point a to point b ). To move a positive charge from "b"
to "a" against the electric field would require work supplied by an external
force. The ratio of the work done, W, to the charge, q, in moving the charge between two
points in an electric field is called the potential difference, Vab, between
the points: Vab = W/q. If a charge is moved along a path at right angles (i.e.,
perpendicular) to the field lines, there is no work done (W = 0) since there is no force
component along the path. No work means no potential difference from point to point.
Hence, the potential is constant along paths perpendicular to field lines. Such paths are
called equipotentials. Thus, an electric field set up by charges may be "mapped"
by determining the equipotential lines (equipotential surfaces in three dimensions) that
exist in the region around the charges. Potential difference is easily read by a
voltmeter, whereas the measurement of forces would present numerous experimental problems.
Part 1: Measuring Equipotentials
The apparatus consists of a flat board on which is placed a sheet of carbonized
conducting paper imprinted with a grid. The sheet has electrode configurations of
conducting silver paint which provide an electric field when connected to a battery. The
standard electrode configurations provided are two circular dots representing point
charges of an electric dipole and two parallel linear electrodes representing a
two-dimensional cross section of parallel plates. Place one conducting sheet on the board
and connect the conductor wires from the battery terminals to the two electrodes. Make
connections to the electrodes with thumbtacks to hold spade lugs in contact with the
electrodes. The voltmeter measurements will be made using the Pasco Science Workshop data
acquisition program. Instructions for the use of the program will be given in the
Please do not write on the carbonized conducting paper.
- For each field investigation, sketch the electrode configuration on the paper provided
using the same coordinates as those of the painted electrodes on the grid of the
carbonized paper. You will plot your data directly on this paper.
- The wire from the computer interface that has a free end is to be used as a probe to
investigate how the potential changes in the region between the two electrodes. Since you
will be graphing equipotential lines, first choose which equipotential line you will
locate, for example, one might choose 0.3 volts. Double-click on the Voltage window and
change the display to 2 digits to the right of the decimal.
- Place the tip of the probe against the conducting paper at various positions between the
electrodes until you find a position such that the meter reads 0.3 volts. Each time it
does, you have found another point on that equipotential. Plot the points' coordinates on
the paper provided. About 6 to 8 points throughout the region will be sufficient
for each equipotential value.
- Repeat the process for at least three other potential choices that are spread throughout
the approximate 1.5 volt range, e.g., 0.6 volts, 0.9 volts, and 1.2 volts. The choices of
the potential values may need to be different to suit your apparatus.
- Once you have finished plotting all your points on your paper, draw a smooth curve
through each set of points that have the same potential and label each with its potential.
You now have mapped the equipotentials around the electrodes.
- Since the electric field lines must be perpendicular to the equipotential lines, sketch
smooth dashed lines to represent the electric field.
Part 2: Computer-Aided Field Mapping
We are now going to use two software programs that calculate the potential and electric
fields for various two- and three-dimensional distributions of charge. The programs can
then plot the potentials and the electric fields and help you visualize them and their
Run the mapping program EMField by using the following operations: open PY
Software, then EMField.win, then Ctwinx.exe, and then open EMField.ctb.
- Under Sources, choose 3D Point Charges. Then drag two equal and opposite
point charges into the region so that their configuration resembles the point charges from
the electric dipole of Exercise 1. Then under Field and Potential choose Field
vectors. At any point in the region you can click and the magnitude and direction of
the electric field at that point will be displayed. Click enough points so that you have a
good feel for the structure of the electric field in this region.
- Now choose Display and Clean up screen.
- Under Field and Potential choose Field Lines. Map a dozen or more field
lines to show you the field in the region. Then choose Equipotentials and map a
dozen or more equipotential lines.
- Print the screen by using the PrintKey software. Open MS Word and paste the
picture into it. Now you are ready to annotate and/or print the picture.
- Give an explanation for the nature of the equipotential lines and electric field vectors
near the charges. Is the angle between the field and equipotential lines 90 degrees?
- While still in the Equipotentials mode, click on the mouse to see the value of
the potential. Where is the potential highest and lowest? Where is it zero?
Run the mapping program Poisson by double-clicking on the following folders or
files in order: "Py Software", "cups", "Cupsem",
"Poisson", "Poisson.exe". If the program asks you for a place to store
temporary files, just type c:\temp\ and hit enter.
- Sketch a parallel plate capacitor (there is an icon with two lines on the toolbar) near
the center of the screen. The top plate will have the potential selected by the slider,
and the lower plate will have the same magnitude but opposite sign. Construct it to look
like the one you mapped in Exercise 1. Note that the "Modify" box selection will
allow you to change, move, or delete parts of the drawing until it is suitable. Click on Plot
How, then Contour map of potential. Then Run the program to calculate
the equipotential lines.
- Print the screen as follows:
Please first change the background color to white so that the printing process
does not use such an enormous amount of toner.
Click on the following in order: File, Configuration, Path Temporary Files Directory,
Accept, Change Colors, Reverse, OK.
Now use the PrintKey software. You now have a picture of what you have just done on the
Windows clipboard. Press the Alt and Tab keys at the same time to return to
the Windows desktop. Run the MS Word processor and "paste" the picture into the
blank document. Now you are ready to annotate and/or print.
Remember, in order to get back into the mapping program, you now can hold down Alt
and cycle through the open files with the Tab key until the MSDos icon is selected.
Alternately, you may simply click the MSDos icon C:\Software\
on the bar at the
bottom of the screen.
- Describe the equipotential lines near the middle of the plates.
- Click on the Plot How menu item and select Plot Electric Field Vectors.
Print the screen. What is the direction of the E field near the plate (on the
inside and the outside)?
- Give an explanation for the nature of the equipotential lines and E vectors near
- Choose Field Line Through a Point from the Extras menu. Click on about a
dozen points on the equipotential plot and notice the relationship between the field lines
and the equipotential lines. Print the screen. Is the angle between the field and
equipotential lines 90 degrees?
- Choose Crossection of E & V from the Extras menu. Move the mouse
around to see the value of the potential at various points. Where is it highest and
lowest? Where is it zero?
In your discussion section, comment on what you found, including how the manual mapping
compared to the computer mapping.
- Experiment with some other electrode configurations. For example, at +100 volts, draw a
line on the screen by clicking on the line tool and then click-dragging near the center of
the screen. Change the voltage slider to -100 volts and draw a circle on the screen. Click
on the RUN option. Does this mapping also match the conclusions you drew from the standard