Gravitational and Electric Potential Energy
What is meant by Electric Potential, Electric Potential Energy and Change in
Electric Potential Energy?
Definition of Potential
#1 (from Webster's Ideal Dictionary): Something that can
develop or become actual
Many times when a coach of a sport is interviewed on television, if the interview is before the season starts, he or she indicates that the team has "potential". They usually do not say that their teams are "Weak, Slow and Chicken" ! What does it mean when a coach says, "the team has potential? "
Gravitational Potential Energy
Early in the course you probably discussed the acceleration of gravity, the force of gravity and Newton's Law of Universal Gravitation. Later in this course, you probably studied potential energy.
You have a text book. Hold this book in this room (up off the table or desk). Assuming the gravitational potential energy at the level of the floor of this room is zero, what is the gravitational potential energy of your book? Express your answer in joules.
Change in Gravitational Potential Energy
Assume that the level of the floor in this room has gravitational potential energy of zero joules. Place your textbook on one of the chairs in the room. Calculate its gravitational potential energy in joules. Now move the book horizontally to a similar chair elsewhere in the room. Did you do work "on the book"? Explain your answer. (Review the definition of work, if needed.)
Now move the book from the chair to a laboratory table in the room. With the book lying on the table, calculate the book's gravitational potential energy. Was there a change in gravitational potential energy? If so, what was the change in gravitational potential energy? Express your answer in joules.
Was work done "on the book" in moving it from the chair to the table? Explain your answer.
Gravitational Potential Difference
In the previous activity, you have used the fact that the change in gravitational potential energy is equal to the mass of the object multiplied by the acceleration due to the earth's gravitational field multiplied by the change in the height of the object. ( DPE = mgDh) If we were to divide both side s of the equation by the mass, then DPE/m =gDh. This is called the difference in gravitational potential or the gravitational potential
At the surface of the earth there is a gravitational potential difference of about 9.8 joules/kilogram for every one meter increase in elevation. Potential difference describes how much the potential energy changes if a unit test object is moved from one point to another in a force field. The object does not have to move for
the potential difference to exist. The potential difference is created by the source that is producing the force field, not by the test object.
A) A potential exists at any point as a result of a field. A gravitational potential (gh) exists at any point in the space associated with a gravitational field. Similarly, an electrical potential (Ed) exists at any point in the space associated with an electric field.
B) If we place "our" charge 'q' in an electric field it will have an
electric potential energy (PE = Fd = qEd). This is analogous to
gravitational potential energy (PE=Fd=mgh).
C) The effect of moving a mass in a gravitational field creates a change in potential energy of "our" mass 'm' such that DPE=mgDh. When work is done in moving our charge 'q' in the electric field, there is a change in the electric potential energy such that DPE = qEDd. If we find the change in the electric potential energy for each unit of "our" electric charge, then DPE / q = EDd.
D) This change in electric potential energy/charge is measured in units of volts ( 1 volt = 1 joule / 1 coulomb)
Notice that this quantity is also the change (or difference) in electric potential (E Dd) sometimes called the electric potential difference.
E) A battery functions by creating a difference in electric potential
energy between two points. Definition of Potential # 2 (from Webster's Ideal Dictionary): the degree of electrification with reference to a standard
Experiment #1 -
How can electric potential differences be detected?
Pyrex baking pan or clear plastic tray, voltmeter, connecting wires with alligator
clips, two electrical conductors that sink in water, power supply, graph paper and salt.
1. Place the graph paper on a table and center the baking dish on the grid. Hook one alligator lead to the positive terminal and another wire to the negative terminal of the supply. Attach each of the wire ends to one of the conductors, and separate the conductors in the dish.
2. Fill the dish one forth full with water.
3. Connect the power supply to the electrodes as illustrated and adjust the
potential to approximately 10 volts. Attach one lead of the voltmeter to one of
the electrodes and let the other lead of the voltmeter be the "probe" that will be
used to plot the equipotentials. As a preliminary check, place the probe on the "+" electrode and not the full scale reading. then move the probe into the salt water very near the "+" electrode. You should note only a small change int he reading in the voltmeter. If a large change is observed, this means either the water is not sufficiently conductive or you should use a voltmeter with a higher internal
resistance. Now move the probe between the electrodes and you should observe a
fairly linear change in voltage with distance for the "-" electrode. You are now
ready to plot equipotentials.
4. Draw the locations of the conductors on the graph paper an d label them with the voltage readings of your voltmeter.
5. With your positive voltme ter probe in the water, note the voltage reading. Move the probe in the water, keeping the voltage reading at the same value. How far does this path go? Sketch this pattern on your graph paper and label the line with the voltage you chose.
6. Choose other voltage values and similarly sketch their patterns on the graph paper until you mapped out the area between and around the conductors.
7. With another color pen or pencil draw a point any place on your map to
represent a moveable positive charge. Predict the path it would take by
drawing a line with your colored pen or pencil.
8. Now place a large metal ring in the tank between the electrodes. You will
notice that the potential will change as you move the probe in the region
outside of the ring but that it will remain the same when the probe is
moved around in the region inside of the metal ring. Hence a conductor placed in
an electric field will have the same potential everywhere.
1. What generalizations ca n you make from this exploration?
2. Where would a positive test charge have the least potential energy?
3. How much energy must be added to the system to move 1 electron, 1 meter in a direction along one of the equal potential lines.
4. If lightning strikes a tree 20 meters away, would it be better to stand facing the
tree, your back to the tree, or your side to the tree? Assume your feet are a
comfortable shoulder width apart. Explain your answer.
Summing Up (Comments):
1. Students' generalizations will vary. They may recognize that equal potential lines
are more concentrated near surfaces that have a smaller radius of curvature. Some
students may recognize that the force on a charge will be at right angles to the
equal potential lines, but don't push this point until after the students have made
their generalizations. This activity should be most appropriate to build the concept
of an electric field.
2. A positive test charge would have the least potential energy next to the conductor
established at 0 volts.
3. If an electron is moved any distance along the two volt equal potential line, no
work will be needed.
4. If the person stood with the side facing the tree, the feet would be at difference
potentials and a dangerous shock could be the result. If the field around the tree is
uniform, then facing or your back to the tree would place both feet on an equal
potential line and result in no shock. Facing away from the tree would probably be
the preferable option because the face would be protected from flying debris and
the flash of light.
Note: This experiment is not an electrostatic experiment. As electric current passes
through the salt water, an IR drop is established and you are using the voltmeter to
measure this IR drop. As you move the probe, keeping the readings on the
voltmeter constant, you will be moving along regions of constant IR drop.
Therefore, you will be identifying lines of constant potential difference. In this
electric current situation, lines of constant potential difference correspond to
equipotentials in the region surrounding the charges in an electrostatic situation.
Experiment # 2-
To show the electric field around a simple charge configuration and to relate these electric lines to the equipotential lines in the previous experiment.
This experiment uses the same equipment as Experiment #1 on plotting equipotentials except that the probe will now be in two contacts held a fixed distance apart. This can be accomplished with nails through a small piece of wood or plastic (clear plastic will give a better view). A separation between the nails of about 3 cm usually works well.
Procedure and Notes:
Wire the apparatus exactly as in Experiment #1 except that this time the voltmeter will not be attached to the "-" electrode, instead it will be across the double probe . Place the double probe in the salt water somewhere between the electrodes. Notice that, when you rotate the double probe, there will be a particular orientation which will give a maximum reading on the voltmeter. In this position the line between the two probes will indicate the direction of the electric field. If you start near the negative electrode, rotate the double probe until you find the maximum reading. Then move it so that the first nail is now in the position of the second nail and again rotate to find the maximum reading. This process will map out the electric field between the two electrodes. Repeating this procedure with the map in another position will result in plotting out another field line. After you have plotted several field lines, compare these results with those of Experiment #1 and notice that the
equipotentials are always perpendicular to the electric field lines.
The apparatus is to be connected to map out the electric field lines in the region between the two electrodes. Rotating the double probe to give a maximum voltage reading will indicate the direction of the electric field.
1. Give specific values in volts of changes in electric potential in the tray.
2. Explain what is meant by the term, "Electric Field Lines".
When you move along an equipotential with a test charge, you will do no work. In an external electric field this would be possible only if the charge were moved perpendicular to the field. By the same token, if you move in a direction of maximum potential difference, you will be moving along a electric field line and you do work. Rotating the double probe until the voltage across it is maximum results in finding the maximum potential change and, consequently, the direction of the electric field.
NOTE: This experiment is not an electrostatic experiment. As electric current
passes through the salt water, an IR drop is established and you are using the volunteer to measure this IR drop.