24.5 - Spreadsheet: electric potential graphs
At the right, you see a three-dimensional graph of the electric potential for the points in
a plane surrounding three charges. The graph was generated by a spreadsheet that
you can access from this textbook if you are using a computer that can open Microsoft®
Excel files. The electric potential at any point in the horizontal plane is indicated by the
graph’s distance above or below zero. Two positive charges of different magnitudes
cause the “peaks” you see at the right, while the “well” is caused by a negative charge.
The electric potential takes on extremely large positive or negative values at locations
very near the positive or negative charges. We do not show the most extreme values
because it would require a drastic change to the vertical scale of the graph.
The graph may remind you of very mountainous terrain. It serves as a map of electric
potential, showing the locations of peaks, plains and wells. The electric PE of a test
charge will increase as it “climbs up” the side of any peak. It requires positive work on
the test charge to cause it to approach the underlying charge generating the peak. On
the other hand, the PE of a test charge that is free to move will naturally “fall into” a
well, as the test charge is attracted by the underlying negative charge.
Click here to launch the spreadsheet. You can change the amounts and locations of
the charges, or add additional charges, and see the results. If the file does not open, on
Windows click with the right mouse button and choose the save option. On the
Macintosh, hold down the “control” key and click on the link, then choose the option to
download the file.
Click here to see a separate document that explains the programming of the
spreadsheet in case you want to modify it.
24.6 - Electric potential difference
Electric potential difference is the difference in electric
potential between two points. For example, if point B
has an electric potential of positive five volts, and
point A has an electric potential of positive three volts,
then the potential difference VBíVA is two volts.
You see this in Equation 1. Like electric potentials,
electric potential differences are measured in volts.
In the three illustrations to the right, you see two
plates. They are both charged: The plate on the left
(plate A) is negatively charged, and the plate on the
right (plate B) is positively charged. In the example
problem, we chose to make the electric potential of
plate A negative 0.5 V and of plate B positive 1.0 V.
The potential difference between the plates is 1.5 V.
The electric potential values just cited for the plates depend on some choice of a
reference point for zero potential. Often, in practical applications, the ground (the
electrically neutral Earth) is defined as having zero electric potential, and all values are
measured relative to this value. In an interactive problem in the introduction to this
chapter, the midpoint between the plates was selected as the location of zero potential.
Also at the right, you see a common source of electric potential difference: a battery. Its
two terminals have different electric potentials. Batteries are often described by the
potential difference between their terminals. For instance, the potential difference
between the terminals of a D cell is 1.5 V. This is often referred to as the battery’s
voltage. In the configuration at the right, the potential difference between the battery’s
terminals caused electrons to flow to plate A and away from plate B, thereby charging
the plates.
The potential difference between the terminals of the car battery is 12 V.
Between two contacts of a household outlet, ǻV averages 120 V.Electric potential difference
Difference in electric potential between
two points