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

[John Denker <jsd@av8n.com>]

On 11/30/2013 02:15 PM, LaMontagne, Bob wrote:
> 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.

That's the right idea.

It would be a slight overstatement to say the charge is "unrelated"
to the voltage, but Bob's meaning is clear anyway:  The charge is
nowhere near being proportional to the voltage.  The charge comes
nowhere near behaving the way _M&I_ says it should, even in the
simplest situations.

In some sense it doesn't matter where misconceptions come from,
but sometimes when there is a persistent misconception it pays to
dig around a little bit.  Here is my best guess at the moment:

Once upon a time, Sommerfeld cobbled up a situation where the 
wire had constant capacitance per unit length, and zero field 
in the far distant asymptote.  He published a formula for the 
charge distribution, valid in one special situation only.

Now the _M&I_ book boldly applies this formula to situations where 
the wire has nowhere near constant capacitance per unit length, and
there are large stray fields running around.  Wackiness ensues.
When students do this sort of thing, we call it "equation hunting".
It's a bad thing.

At this point, some people must be asking whether I am complaining
about too much detail or not enough.  Answer:  Both!  We are 
being asked to construct a model of DC circuits that is detailed
enough to show the surface charge distribution, but not detailed
enough to show the correct surface charge distribution.

I say that is an unhappy medium.  Between two stools one sits in the 
ashes.  If it's worth doing, it's worth doing right ... especially
when it's easily doable.

I say that if you claim it is important to understand the microscopic
circuit behavior in terms of surface charges, and then you find that
the wrong charge distribution serves the purpose just as well as the
right one, then it can't really be all that important.  You can't
have it both ways.

I would be happy with less detail, perhaps mentioning the existence 
of surface charges without detailing their location.  I would also 
be happy with more detail, or at least more correctness, showing the 
charges in more-or-less correct locations.  I can even imagine less 
detail in the introductory course along with correct details in the 
later courses.