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Lab 5: Equipotential Lines
THEORY
The electric field is the force per unit charge experienced by anything placed in the
vicinity of an electrically charged body. It is somewhat similar to the gravitational field,
g, which is the force per unit mass experienced by anything placed in the vicinity of
another mass. Unlike the gravitational field, the electric field is not equivalent to the
acceleration of a freely falling body in the field. If you measured the electrical force
acting on a charged body placed in an electric field, then divided that value by the amount
of charge on the body, you would have a value for the electric field in Newtons of force
per Coulomb of charge.
The electric potential is the potential energy per unit charge that anything has at a
particular location in an electric field. Lines of equal potential in an electric field are
analogous to the contour lines on a topographic map. The "fall line" is perpendicular to
those contour lines at any location on a map. The electric field ("line of force") is
perpendicular to the lines of equal potential - called equipotentials. Electric potential is
measured in Volts, which are equivalent to Joules of energy per Coulomb of charge. A
little arithmetic with the units will show that Newtons per Coulomb are very conveniently
equal to Volts per meter, so the spacing of equipotentials shows the magnitude of the
electric field.
Electric field, derived from force, is a vector quantity - it has a direction. Electric
potential, derived from energy, is not a vector quantity - it has only a magnitude at a
particular location.
We are going to explore some two-dimensional electric fields and their associated
equipotentials by mapping them.
SIMULATION
Using the simulation Charges and Fields,
simulate the situation shown to the right. This is as
close as we can get to a two line electrodes.
http://www.colorado.edu/physics/phet/simulations/
chargesandfields/ChargesAndFields.swf
Move the equipotential plotter around and.plot a
number of equipotential lines with the same ΔV
between them.
Print your results.
Repeat for two point electrodes.
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Your Text
Using your textbook (or similar resource), find diagrams that show equipotential lines for
the two ideal arrangements: parallel plates and electric dipole.
Think and Apply
Now show examples of each of the following, where they exist, on the diagrams from the
simulation and from your text.
 An area of larger Electric Field. (Look for a very steep section of a “potential
hill”)
 An area of very low, near zero, Electric Field. (Look for a place where the
potential is changing very gradually.)
 The gravitational equivalent of a below sea-level region. An area with
negative potential.
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Draw in electric field lines by hand. (You may check them on the computer.)
How do the electric field lines relate to the equipotential lines?
The simulation together with information from your book should give you enough
information to write out a theory section.
PROCEDURE “The Real Lab”
1. Place the sheet of black conductive paper with the dipole electrodes (two spots) on the
sheet of foam board, and press two pushpins into the electrode-spots. Connect the battery
to the pushpins using the clip-leads. Connect the + terminal to one pin and the - terminal
to the other. Set the meter to the 0-10 Volt range. Touch the meter probes to the
corresponding (+ or -) electrodes. This is the maximum V of the battery. It should be
around 6 V.
With the negative probe held in place, touch the positive probe to various places on the
conductive sheet. You should see readings on the meter between 0.0 and approximately 6
Volts. Now draw a map of the electrode layout in your lab book, using four small squares
in your notebook for each larger square printed on the conductive paper (2:1 in each
direction). With the negative probe held at the negative electrode, see if you can find a
line of points which all have the same potential - say, 1.0 Volts. As you find each point at
that potential, transfer its location to your map and label it with the measured potential.
You will find that you can conveniently space these points along a continuous curve, a
centimeter or so apart, so that they show the shape of the curve. Draw a smooth curve
through these dots. This is called an equipotential line since the potential is the same
(equal) at all points along its path. Try several other values of equipotentials between 0.0
and 6 Volts, evenly separated in potential, carrying each line as far as you can. Make
sure that you have enough values to draw several equipotential lines each an equal
V from the other.
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Looking at the pattern of lines drawn, come up with some general descriptive
statements about the shape of these equipotential lines.
Imagine that you have a positive test charge on the positive electrode. Along what
kinds of paths would this test charge travel if it were attracted along the shortest
path toward more and more negative potentials?
Starting from the positive electrode on your map, draw a dotted line outward,
perpendicular to the equipotentials you just drew, and arriving at the negative
electrode. An arrow on this line will show the direction of this electric field line.
Draw a few more electric field lines until you get the hang of it. How do these
lines compare to the paths the positive test charge would take? Explain. Check
your results with your instructor.
Follow the same procedure for a set of parallel line electrodes. Try measuring
several points along the electrodes themselves - what do you find? Describe the
shape and spacing of the equipotential lines between the electrodes. What
happens to this shape and spacing as you move out from between the electrodes?
ANALYSIS
Summarize the method to find the equipotential lines.
Now show examples of each of the following on the diagrams (where they exist):
* A very steep section of a “potential hill”
* A place where the potential is changing very gradually
* The gravitational equivalent of a below sea-level region.
* Draw in electric field lines by hand.
Comment on the patterns found for each electrode arrangement. Then summarize any
similarities to give a general description of equipotential lines for any electrode
arrangement.
Compare your “Real Lab” results with the simulation and with your text.
Explain the relationship between equipotential lines and field lines.
Gravitation field lines can be imagined as the direction a ball would roll on a particular
terrain, say from the top of a mountain, or into a hole. If you replaced the positive test
charge with a ball, what kind of terrain would give the ball the same motion as the test
charge? Describe the terrain for each of the electrode arrangements that you did.
CONCLUSION
Summarize your findings for equipotential lines and field lines for each electrode
arrangement. Be sure to compare to theory.
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