Re: [Phys-L] amusing electrostatics exercise

[John Denker <jsd@av8n.com>]

On 02/28/2013 08:43 PM, Bruce Sherwood wrote:
> ... My own
> analysis was to calculate at an arbitrary location in space the field that
> would be produced by a solid wire, and the field that would be produced
> instead by a wire whose diameter is the same as that of the hole and which
> carries current in the opposite direction. The currents for these two
> different current distributions are adjusted appropriately so that the
> vector sum of the two calculated fields is equal to the field at that
> location in space for the actual wire that has a (longitudinal) hole in it.
> Since the sources are the same, the field must be the same, at all
> locations in space. No?

That analysis works fine if you are playing by ivory-tower 
rules.  It assumes a great many "spherical cow" symmetries
that are not actually given as part of the original problem
statement.

In contrast, in the real world, it is verrrry common to find
wires that meet all the requirements of the problem statement
yet have much lower symmetry than the two-wire model, in which
case the model does not even begin to describe what's going
on.  See the note I posted in the "spherical cow" thread 
on 02/28/2013 08:40 PM.

This raises serious doubts about the validity of the question, 
insofar as the more you know about real wires, the less likely 
you are to come up with what is apparently the desired answer.