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



Here is the situation I was trying to set up: If the field is zero in the wire, then some charges must have polarized and set up a field of their own to cancel the external field such that there is no net field in the wire. But if the wire has the same potential at both ends, then the existence of surface charges is unrelated to a potential difference.

I later realized that the grounding is not actually needed - the simple General Physics conductor in a uniform field suffices. A straight wire place parallel to the field will have surface charges on its ends - but since the field is zero, the wire is an equipotential. So again, the existence of surface charge appears unrelated to Voltage difference. The fields are the entities that produce (and are produced by) the surface charges - not the Voltages.

Bob at PC

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John
Mallinckrodt
Sent: Saturday, November 30, 2013 2:11 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] circular definition of "success" .... was: standard DC
circuits

The "grounding" part is potentially (pun virtually unavoidable) problematic
because we don't know HOW it is grounded, i.e., what OTHER conductors
might be involved. Better simply to say that we will ensure that it carries an
appropriate amount of charge to BE at whatever potential we are calling
"ground" potential. Then, all one needs to do is understand that the wire
WILL come to some constant potential along its length by distributing
whatever charge it has so as to accomplish that result. Clearly there will be
no field IN the wire because it's a conductor. You can quickly visualize what
the filed must look like simply by imagining a downward sloping sheet with a
linear section of it distorted into a constant horizontal level.

I made some images using a spreadsheet I put together long time ago to
solve Poisson's law problems using the relaxation method. You can look at
the results here.

https://dl.dropboxusercontent.com/u/409806/WireInUniformField.pdf

John Mallinckrodt
Cal Poly Pomona

On Nov 29, 2013, at 7:44 PM, LaMontagne, Bob wrote:

Sorry, meant to say that the wire is parallel to the field.

Bob
________________________________________
From: Phys-l [phys-l-bounces@phys-l.org] on behalf of LaMontagne, Bob
Sent: Friday, November 29, 2013 10:36 PM
To: Phys-L@Phys-L.org; Bruce_Sherwood@ncsu.edu
Subject: Re: [Phys-L] circular definition of "success" .... was: standard DC
circuits

Suppose we have a uniform electric field and we place in the field a finite
length straight wire which is grounded at both ends. What is the field in the
wire and what do the surface charges look like?

Bob at PC
________________________________________
From: Phys-l [phys-l-bounces@phys-l.org] on behalf of Bruce Sherwood
[Bruce_Sherwood@ncsu.edu]
Sent: Friday, November 29, 2013 7:39 PM
To: Phys-L@Phys-L.org
Subject: 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 Erings.py, available in the "Lecture-demo
materials" section of matterandinteractions.org, and there's now a
GlowScript version that may run in your browser, depending on your
browser and your graphics card:


http://www.glowscript.org/#/user/Bruce_Sherwood/folder/MI/program/19
-E
rings

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


http://www.glowscript.org/#/user/GlowScriptDemos/folder/Examples/prog
r
am/MatterAndInteractions

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.

Bruce
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Forum for Physics Educators
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