Download (voltage). Recall that the potential difference at a given location is

Equipotential Surfaces Computer Lab
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An equipotential surface is the set of all points around a group of charges that are at the same
potential difference (voltage). Recall that the potential difference at a given location is the
potential energy per charge at that location for a positive charge.
The purpose of this activity is to make you familiar with the shape of equipotential surfaces and
electric fields for simple charge arrangements, and to learn the relationship between the electric
field vector and the equipotential surfaces.
1. Load the simulation “Charges and Fields” from http://phet.colorado.edu/new/simulations/
sims.php?sim=Charges_and_Fields. You will see an area for grabbing charges
that can be placed in the primary area on the screen, a green box that allows
you to change certain aspects of the area, and a movable voltage tool (Shown
right). It is used to find the value of the potential at any point in space and will
plot lines of equipotential surfaces. The circle at the top changes color to reflect
the relative magnitude and polarity of the potential at the point in the cross
hairs. You will be using this tool to measure and plot the lines of equal voltage.
2. Check the box in the green window labeled “Grid.” Notice that the major lines of the grid are
at intervals of 0.5 meter. In the same window check the box labeled "Show E-Field." Once
a charge is placed in the test area, you will see arrows that represent the direction electric
field due to the charge(s) and the intensity (darkness) of the arrows provide a rough
indication of the magnitude of the electric field. Check the “show numbers” box.
3. Place one of the positive charges in the center of the test area. Notice the electric field?
Move the charge around and note what the field does.
a. What is the general direction of the electric field at any point?
b. In general, where is the electric field the strongest and weakest?
c. Grab an orange electric field sensor and move it around. Does its behavior agree with
your observation in b above?
d. In the diagram on the next page, draw the electric fields of a positive point charge.
e. If the charge is doubled, (placing a second charge on top of the first), what happens to
the size of the electric field?
f.
Use the electric field sensor to measure the electric field at 0.5 m intervals from a single
charge (put one back!). Fill in the table below:
Distance (m)
0.5
1.0
1.5
2.0
2.5
3.0
Electric Field (V/m)
g. Does the electric field due to a point charge vary directly or inversely with distance from
the charge? Is the relationship to the first or second power?
4. Move the equipotential tool around the test area.
a. How is the color in the cross hairs related to the voltage measured in the field?
b. Where is the voltage the highest? Where is it lowest?
c. If the size of the charge is doubled, what happens to the voltage value?
d. Use the voltage tool to plot the equipotential lines at 0.5 m intervals from a single
charge. Fill in the table below:
Distance (m)
0.5
1.0
1.5
2.0
2.5
3.0
Potential Difference (V)
e. Does the voltage due to a point charge vary directly or inversely with distance from the
charge? Is the relationship to the first or second power?
f.
Draw in the equipotential lines around your charge in your diagram in 3d above.
g. How is the electric field oriented relative to the equipotential lines (random angles,
perpendicular, parallel, etc.)? Is this similar to the relationship between the gravity field
(vertical) and equipotential (horizontal) surface?
5. Clear the test area then place a negative charge in the test area. On the diagram below,
draw in the electric field lines and equipotential lines for a negative charge. How are the
field lines oriented relative to the equipotential lines?
6. Clear the test area. Place two positive charges a distance of 1.5 m apart in the test area.
Use the diagram below to draw in the electric field and equipotential lines:
a. Where is the place where the electric field is zero? Is the potential zero at that same
place?
7. Repeat for a positive and a negative charge. This configuration is what is called an “electric
dipole.”
a. Where is the place where the potential is zero, what is the happening to the electric field
at that location?
8. For all the charge configurations, the following can be true statements. Circle the boldfaced
choice that will make each statement true.
a. Electric field vectors point in the direction of increasing / decreasing voltage.
b. The electric field vectors point parallel / perpendicular to the equipotential surfaces.
c. If the size of a single charge is doubled, the electric field and the voltage at a given
location are both doubled / halved.
d. The electric field is a scalar / vector quantity and the potential is a scalar / vector.
e. For the electric dipole charge configuration, at the exact center point between the
charges, the voltage / electric field is zero.
f.
For the two positive charges, at the exact center point between the charges, the electric
field / potential is zero.
g. For a single charge, the electric field at twice the distance is halved / quartered.