Electric Potential
The Physics Hypertextbook™
© 1998-2008 by Glenn Elert -- A Work in Progress
All Rights Reserved -- Fair Use Encouraged
Discussion
introduction
Recall the developmental history of electrostatics.
- Charges exist.
- Charges exert forces on each other.
- This force appears to exert itself across distances of any size.
You and I have no problem with this idea, but in the day, this was derisively called "action at a distance". To get around the action at a distance problem and to avoid the conceptual and mathematical problems of dealing with this otherworldly force, Michael Faraday invented the electric field and the world was satisfied.
Well, satisfied for awhile. Once Faraday invented the idea of the field, it became a great conceptual hit and everybody was happy for until … Until somebody noticed that the field was a vector quantity and they remembered that vectors were cumbersome and difficult to deal with mathematically. Conceptual ease was gained, but practical ease was unchanged. Damn those scientists. Always looking for the best of all possible worlds. They wanted something both conceptually and mathematically simple to deal with. Such temerity!
Believe it or not, a solution was at hand. Of course we only know this to be the case with the fortune of hindsight. The problem has already been solved, which makes it seem to us like no big deal. But it took years of thinking and years of hard, deliberate work before the next step was taken.
What are field lines if not some kind of flow pattern? Field lines "flow" from positive charges to negative charges. They occupy space much like the flow lines associated with other phenomena. Think for a moment, of other phenomena that exhibit flow and think of what it is that causes them. This will be the answer to our conceptual problem.
Let's set up a table that compares similar phenomena. In all cases, there will be some thing that flows and some cause of the flow.
| the flow of … | is caused by a difference in … |
|---|---|
| a river (liquid water) | altitude |
| the wind (atmospheric gases) | atmospheric pressure |
| heat (internal energy) | temperature |
| dissolved substances (solutes) | concentration |
Surely, field lines (or charges, if you prefer) must flow under the influence of something. Well of course yes, why else would I be telling you any of this? What "causes" electric field lines to "flow"?
| the flow of … | is caused by a difference in … |
|---|---|
| electric field lines (test charges) | electric potential |
Now you have to ask yourself what "electric potential" is.
Random junk
- Alessandro Giuseppe Antonio Anastasio Volta (1745-1827) Italy (Lombardy)
- The heart: −80 mV to +20 mV
Summary
- bullet
Problems
practice
- A charge of -1.0 μC is located on the y-axis 1.0 m from the origin
at the coordinates (0,1) while a second charge of +1.0 μC is located on
the x-axis 1.0 m from the origin at the coordinates (1,0). Determine the value
of the following quantities at the origin …
- the magnitude of the electric field,
- the direction of the electric field,
- the electric potential (assuming the potential is zero at infinite distance), and
- the energy needed to bring a +1.0 μC charge to this position from infinitely far away.
- Answer it.
- A proton (mass m, charge +e)
and an alpha particle (mass 4m, charge
+2e) approach one another with the same initial
speed v from an initially large distance. How close will these two particles get to
one another before turning around?
- Answer it.
- sketch-v.pdf
The diagram on the accompanying pdf file shows the location and charge of four identical small spheres. Find the electric potential at the five points indicated with open circles. Use these results and symmetry to find the potential at as many points as possible without additional calculation. Write your results on or near the points. Sketch at least 4 equipotential lines. Pick round values seperated by a uniform interval. At least one of the lines should be disconnected.
Solutions …- Do the math for each of the five points.
- Record the numbers at as many symmetric locations as possible.
- Sketch in the equipotentials.
- Do the math for each of the five points.
- Write something completely different.
- Answer it.
numerical
- Write something.
Resources
- general
- Franklin: An Electrostatic Field Tracer for Macintosh Computers, Paul Peters
- The Mechanical Universe and Beyond (video on demand, login required)
- Potential and Capacitance, Franklin proposes a successful theory of the Leyden jar and invents the parallel plate capacitor.
- Voltage, Energy, and Force, When is electricity dangerous or benign, spectacular or useful?
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