Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Equipotential lines

Thanks again JohnM (see his message at the end). Your picture
was extremely useful to me; it revealed something so wrong in my
thinking that I do not want to express it again. The equipotential
lines I described yesterday now make sense to me. Many years
ago I took a workshop conducted by Bruce Sherwood and, like
many others, was shocked by the idea of surface charges. I
never had motivation for returning to this topic till last night.

It seems to me that Pasco sheets offer a method for studying
space charges. Let me justify this quickly; I am looking at my
item 2 (straight horizontal silver strip) at y=10 (from x=5 cm
to x=23 cm). The equipotential lines are more or less as for
an ideal dipole.

At x=14 the angle between the equipotential line and the strip
is 90 degrees; it means the gradient of surface charge density
is zero. Not surprisingly; x=14 is the center of the strip.
Going away from the center the equipotential lines are no
longer perpendicular to the strip. They are more and more
tilted. It means that the corresponding gradients become
larger, as on pictures shown by C&S. The local angle of
the E vector (always perpendicular to the U=const line) is
likely to be (?) proportional to the local gradient of the
surface charge density.

Even the zig-zag strip pattern of lines makes sense to me
now. The only problem with this "new lab (?)" is the
difficulty of painting really uniform R strips. But suppose
that sheets for this lab come from the manufacturer who
has a machine for uniform silver-painting (or depositing
it by another way). Then students can perform measurements
on ready made sheets and, if properly guided, learn something.
I am tempted to write a short note on this for The Physics
Teacher. Would you like to be a coauthor John? If so I would
like to compose the first draft. I have nothing against doing
this openly on this forum. What do you think? I hope it is
only a beginning of an instructive thread.

I recall asking Bruce about experimental demonstrations of
surface charges. He confirmed that this has been done. Can
somebody be specific on this? Please share what you know
about this and share the references.

Joseph Bellina wrote:

If you search the archives of AJP you will find articles on
the role of surface charges. This is a very carefully written
insightful text and deserves your careful reading.

Can you post the specific URL Jopseph? I am not yet very
good in searching for things in archives.

John Mallinckrodt wrote:

On Fri, 15 Feb 2002, Ludwik Kowalski wrote:

... here is a challenge to those who like to make predictions.

What kind of equipotential lines would you expect for the
silver strip painted on a carbon-impregnated paper if the
shape of the strip was an uncurling flat spiral. Suppose the
length is 100 cm, the DOP between the terminals is 1 V, the
uniformly distributed resistance of the strip is 1 ohm.cm and
the angle is 1800 degrees (5 round trips from the grounded
terminal at the center to the positive terminal at outer end).
Draw equipotential lines for U=0.5 V and U=0.25 V. Assume that
the resistance of the carbon paper, (for example ohms/cm^2) is
1000 times larger than that of the silver layer. Ludwik
Kowalski

Here's my entry.

<http://www.csupomona.edu/~ajm/special/spiral_ep.gif>

You'll see that I ran out of patience at two cycles, changed the
total DOP to "10", totally ignored the specific values of
resistivity, but included representative E-field vectors to
indicate the general character of the field.

Note in particular the dipole like field external to the spiral
and the related existence of a cusp in the equipotential lines
emerging from the interior as they choose which way to head
around the exterior.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm