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HOW TO DO IT ? Was Potential of a point charge



HOW I WOULD DO IT

If I were asked to write a textbook for the
first physics course I would try to reduce
electrostatics to a minimum. I would start with
Coulomb's law, then with E produced by one
point charge and by two point charges. The
idea of field lines, representing "downhill"
directions for a positive probe charge would
culminate that short traditional sequence.

Then, skipping Gauss law, I would introduce
the formula for E near a very large uniformly
charged plane (E=2*Pi*sigma*k), where k is
the Coulomb law constant and sigma is the
charge density. The formula would be
introduced as an experimental fact, not as
a logical consequence of Gauss' Law. The
formula is intuitively acceptable; E must be
perpendicular to the plane and must be
proportional to sigma. The 2*Pi*k factor has
to do with units (*) not with phenomenology.
This would be a quick introduction to the
concept of a uniform field between the plates
of a capacitor (E=4*Pi*k*sigma). This time
sigma can be replaced by Q/A.

In the uniform field potential energy would be
treated in the same way PE=m*g*h is treated
in mechanics. Motion of charged particles in
uniform field would be the next topic. Then I
would remind students that, as in mechanics,
some problems are solved more easily by
using the energy approach. The concept of
electric potential (in the uniform field only)
would be introduced to finish with electrostatics
and to proceed to capacitors, currents, wires,
etc. Spending too much time on electrostatics
usually means that no time is left for topics
which are more "practically important."
Ludwik Kowalski
P.S.

(*) Many years ago I published a short note about
history of electric units. Those who have access
to old issues of The Physics Teacher can find it
as:

"A Short History of the Si Units in Electricity."
The Physics Teacher, February, 1986, 97. In
1993 (?) this publication was reproduced (with
many others) as an item in the "Physics
Teachers CD-ROM Toolkit".

I do not have this CD_ROM. If somebody sends
me the electronic version of the note I will be
happy to post it on my web site immediately.
Then you will be able to give the URL to students.
Ludwik Kowalski

On Thursday, Feb 26, 2004, I wrote:

In my opinion it is desirable to start
(in an introductory course) with a
uniform electric field and generalize
later, not the other way around.

Another desirable think is to make
sure that students are aware that
electric field lines show the downhill
direction for positive q and uphill
directions for negative q. Downhill
means that electric potential energy
is decreasing (negative delta_U).
Once they accept this they are less
likely to be confused by the definition:

delta(U) == -q0 * sum of dot products
of E and ds.

Each dot product is positive on a
downhill segment and negative on an
uphill segment (positive or negative
cosine). That is why we need the minus
sign in the definition of delta U. Without
it delta U would not be negative in
downhill segments, as we want it to be.
Ludwik Kowalski