🚀 go-pugleaf

Having gotten a few (very constructive) personal replies to my posting
about the nature of repulsion/(attraction) of like/(unlike) charges,
I'd like to bring the discussion of a larger question to the forum, as
I think it hints at a difficult issue (conceptual -vs- computational
teaching), in which I would certainly benefit from the collective
experience here.

Basically the reply was: "While a deep description of why like charges
repel in terms of relativistic quantum theory is all very nice for
researchers and practicing physicists, it's useless at best, and and
most probably dangerous, to give this answer to students". Or in a
broader sense, one simply has to say: "The answer to your question (dear
student), is beyond the scope of this course" [and we will now have a
rousing reading from Problem Set 35].

In the first case, let me say that I agree. My previous posting was to
fellow physicists and physics educators, trying to gear it to those
with some familiarity with relativity, waves, and Maxwell's
equations. It was NOT meant to be passed on verbatim to students,
unless they too are familiar with the above areas and would benefit. I
also tried to contrast the question with some (interesting?) similar
questions in modern physics, namely the color charges of quarks and
gravitational attraction in general relativity. It was simply meant
for synthesis into the lore.

On the second point, what to do about deep questions from students, I
don't agree; or at least I don't think the axiomatic approach is
constructive to learning (conceptual) physics. I would say that it is
PERHAPS constructive to learning engineering, and similar applied
physics disciplines involving the manipulation and application of
formulas.  Don't get me wrong here; engineering has it's own
conceptual agenda to advance, involving VERY high art, the alleviation
of suffering, the advance of culture, etc., borrowing well tested
equations from physics to meet these aims.

But a question like "why do like charges repel" is a beautiful and
clear question of basic physics. It's akin to "what does a photon
`see', while traveling at the speed of light" which led Einstein to
relativity, or "why don't atoms collapse" which was part of those that
ushered in quantum mechanics, or "why is Mars' orbit an ellipse", or
"why does PV = nRT", or...

These questions need to be recognised, encouraged, fostered, and
guided toward the answer whenever possible. Fortunately one of the
gems of the engineer's high art, this electronic network, will help us
all with this as we exchange our views and thoughts.

Clearly I have a bias toward the conceptual aspect physics, whereby I
mean that it is (for me) much easier to intuit the computation
required for a problem given a conceptual understanding, than it is to
intuit the conceptual picture having done some computations (assuming
I got the right answer). Nonetheless, both are extremely important
parts of the process of learning physics, and we must balance our
presentation as educators.  Furthermore I haven't said anything about
the experimental/demonstration part of teaching which is certainly
indispensible (although I would align demonstrations with the teaching
the conceptual aspects of physics, while experiments/labs go under
computational physics).

How do others of you divide your curricula among conceptual and
computational modes? What is a good set of guidelines for what must be
accomplished in the 'First Course In Physics' say at the high school
level and at the college level (since this list seems to stride
K-12-16+)? What must a A- student be able to compute, and what
concepts of physics must she know? Do you assume you're giving the
last (and perhaps first) class in physics that students will take, or
do you lay the groundwork for the next one?

For instance, I've heard it said that students who couldn't compute
the emeging speed of a 2 kg block from a 30^o frictionless inclined
plane on the Moon haven't learned any physics. Yet I would say
students who can determine the falling accelerations of weights on
convoluted pulleys but don't know the quark model or the evidence for
the Big Bang are really missing out, and doubly so since these are
discoveries of their own, ie. part of the present science of their own
lifetimes. This is even more true if it's the one and only physics
class that the student takes.

To clear some waters which I may have muddied, let me return to
(un)like charges. The point of my last post was to show that the
lack of minus sign in the electrostatic potential

	V = k q q'/r         (1)

as opposed to the gravitational case (G=1, m,m' > 0)

	V = -G m m'/r

and the fact that q and q' can be positive and negative makes like
charges repel and opposites attract. The lack of minus in (1), and the
binary nature of electric charge (+ and -) comes from deeper levels in
relativistic quantum field theory. From a simpler point of view, this
is responsible for the fact that electric field lines begin on +
charges and end on - ones. Notice that this is NOT the case for
gravitational field lines from one mass to another, and as pointed out
previously, very different from the behavior of color field lines
between quarks.

Given that the field lines begin on + charges and end on - ones, it's
fairly easy I think to convince one's self that like charges repel and
unlike ones attract. Draw the E field lines of two opposite charges
(+,-) close to each other (the classic dipole). As the charges come
closer, more and more of the field lines go into the - charge from the
+. Since test charges follow field lines, considering the + to be a
test charge, it will fly into the -. In fact the closer the charges
get, the fewer field lines actually escape to infinity, hence the
attracton is stronger. Also the potential energy in the field is
reduced (made more negative).

Now for like charges, all field lines must escape to infinity. As the
charges are brought closer the field lines become more dense and point
in opposite directions. Thus letting one charge go, as a test charge,
it will be repelled from the other, lowering the energy density
in the field (as per eq. (1)).

But remember there are no such things as test charges and solid little
grey electrons. It's VERY important that this too be told to students.

Cheers,  --Jim




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      James E. Hetrick            Institute for Theoretical Physics
     hetrick@phys.uva.nl               University of Amsterdam