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Re: [Phys-L] circular definition of "success" .... was: standard DC circuits

"What's appropriate for the general run of high-school juniors is not
necessarily the same as for engineering and science majors in the second
year of the calculus-based college physics course. A 16 year old kid grows
up a lot in three or four years. Not to mention the selection effects."
Students may well have taken HS physics as seniors. It would be lovely if
engineering and science students took two years of physics in college, but
many years ago the physics requirement was reduced to two semesters almost
everywhere, and often the mechanics course is taken at the same time as the
intro calculus course, in the first semester of the freshman year, so that
E&M comes in the second semester of the freshman year (otherwise, in the
first semester of the sophomore year, if calculus is a prerequisite rather
than a corequisite for the mechanics course). Also, at NC state about 15%
of the engineering and science students in the intro physics course have
never studied any physics before coming to college. The "three or four
years" is just wrong; often it is one year, or none. Not highly relevant to
the discussion, but needs correction. I'll also mention that E&M often
doesn't get much attention in HS physics, as can be seen that college
pretest scores for BEMA are close to random guessing in all universities
(except in special courses for honors students or physics majors), unlike
the situation with the FCI.

"In contrast, it is a misconception to think that the charge determines the
change in voltage, or determines the field itself (which is the gradient of
the voltage)." Huh? The source of the field isn't charges? Field is only to
be thought of as gradient of voltage and charges play no role? That's
precisely the problem we have tried to address, that in intro physics
courses there is no connection between electrostatics and circuits, that in
the discussion of circuits there are only voltages and (macro) currents,
and charges and fields either don't exist or are irrelevant now that we've
gotten to the chapters on circuits. In fact, early in our attempts to bring
surface charge to the attention of physicists, we would ask them,
"Evidently there is a nonzero field in the wires, so where are the charges
that are the sources of those fields?" Almost always the answer was, "The
field is made by the gradient of the potential." When we pointed out that
this is a tautology in the context of calculating potential difference as a
line integral of the field, and that there have to be charges somewhere,
they had no answer to the question of where the source charges might be.

Some physicists even denied the existence of surface charges! John is
correct that the charge distribution in our Figure 19.17 is flawed, but
that diagram is not the heart of the discussion in which it appears, a
discussion we invented out of frustration at trying to convince physicists
that the existence of surface charges is an essential part of how a circuit
works. By doing a qualitative analysis of a "snaky" circuit, in which
polarization leads to contributions to the field in addition to the field
of the battery (an argument of a kind similar to the reasoning in John's
section 5b), we finally were able to convince physicists of the role and
relevance of surface charges, and this then also served to introduce the
basic idea to students.

One element of our approach is that, as discussed in A. Sommerfeld,
Electrodynamics (Academic Press, New York, 1952), 125-130, and A. Marcus,
“The electric field associated with a steady current in long cylindrical
conductor,” Am. J. Phys. 9, 225-226 (1941), a constant gradient of surface
charge along a finite long straight wire produces a uniform field inside
the wire, both along the wire and across the cross section of the wire (the
charges of course also produce a field outside the wire, but as John
comments, what matters is the field inside the wire, because that's where
the mobile charges are). This suggests that for simple circuits, where
wires don't lie near other wires (unlike the situation in Figure 19.17), we
can expect a rather smooth variation of surface charge along such a wire.
We show in class a simple 3D model that illustrates the point: rings of
charge with linearly varying amounts of charge along a straight line
produce inside the rings a surprisingly uniform field, even of a rather
short line of charged rings. This is relevant to John's complaints about
the discussion on p. 761. This model may be seen in the VPython program, available in the "Lecture-demo materials" section of, and there's now a GlowScript version that may
run in your browser, depending on your browser and your graphics card:

More of these little demo programs can be run from here:

I'll try saying again in different words what I've said before. The title
of our chapter 19 is not "Surface Charge" but "Electric Field and
Circuits". We are basically not teaching about how to determine the
distribution of surface charge in a circuit but rather about how to
determine the distribution of electric field, and tying that electric field
to the fundamental point that electric field in the absence of a
time-varying magnetic field has charges as its source. That there is
surface charge is very important, but for our purposes the details are not.
That there is a transient that leads through polarization to a steady state
is important for understanding how and why there is a steady state; the
details of the transient are not important.

John, you're providing useful ideas that are relevant to teaching E&M, but
they are ideas that are appropriate to upper-level E&M courses, not the
intro course, and I insist that without teaching that course, and knowing
from experience what are the background and capability of these students,
you're not in a good position to judge what is appropriate and what can or
cannot work. Your advice to me can be taken as "what you're doing is so
awful that you shouldn't say anything about surface charge at all", but to
the extent that anything is measurable in education we've found that it
makes a significant difference in intro-level students' understanding of
some important aspects of circuits.

And not only circuits: linking electrostatics and circuits deepens and
extends student understanding of polarization phenomena, which are of
central importance yet very nearly completely absent from traditional intro
textbooks. These textbooks tell you how to calculate the fields made by
charges, but are very nearly (or sometimes totally) silent on what fields
do to matter. This glaring omission is presumably due to the fact that it
is not permissible in the intro physics course to mention that matter is
made of atoms, in which case it's difficult to talk about many aspects of
polarization, thereby losing a splendid opportunity to deepen student
understanding of the nanoworld.