Re: Flat conductors

[Brian Whatcott <inet@INTELLISYS.NET>]

At 04:17 AM 3/8/02, Ludwik responded in this way to a detail of my earlier note
when he wrote:

> [bw]
> > ... But the ratio between the magnetic permeability of a
> > sheet of material and free air is much lower than the
> > electric permeability (conductivity) ratio between
> > resistance paper and free air.

[lk]
> I am a little confused by equating (?) permeability with
> resistivity. You are probably saying that in electrostatics
> "bending of E lines" at boundaries depends on the ratios
> of the dielectric constants of two media while in
> electrodynamics it depends of the ratio of resistivities?
> Is this correct?

This was my train of thought: students are exposed to two
graphical field plots: magnetic flux with iron filings, and
isopotentials with resistance paper. It will be natural to compare
the graphical forms - I made explicit how I believe the two
presentations differ.

 Now to answer your two questions above.
I WAS equating the phrase "electric permeability" to electrical
conductivity. Conductivity ratios as between many conductors
and air are much larger than ratios of magnetic permeability
between any materials and air.
I was not commenting on ratios of electric permittivity, where
a relation between incident and transmitted ray angle holds.

> I am probably abusing the term "electrodynamics"; what
> is the correct word for the "physics of current" when
> magnetic fields are ignored?
> Ludwik Kowalski

Treating this as a philological question, one muses on the
roots of the term offered: 'electro-'    which refers to
an elementary charge carrier, and 'dynamics' which has to
do with the forces involved with motion. It seems to me that
the magnetic force is a consequence of the electric force in motion,
so that ignoring magnetism is to ignore a motional force - and so
perhaps electrokinetic might be a better term (except it is
 unorthodox and thereby mystifying)

Brian W

[bw]
> > There is an interesting comparison between the educational approach
> > to visualizing magnetic fields ("flux lines") and visualizing electric
> fields
> > (with isopotential contours).
> > If there were overwhelming comparability, the magnetic flux lines would
> > *not depart the "magneto-permeable" surface; or in the other case, the
> > isoelectric lines *would depart the surface at the edges.
> >   But the ratio between the magnetic permeability of a sheet of material
> > and free air is much lower than the electric permeability (conductivity)
> > ratio between resistance paper and free air.
> > I believe that's one factor.
> >
> > The second factor is the contrasting plot lines - iso lines versus
> field lines.
> >
> > The third factor is the 'common sense' argument.
> > It's not difficult to agree that for any circuit contained in a compact
> > plane, the
> > current if any, MUST be parallel to the edge, at the edge, if the
> exterior is
> > non conducting.
> > So no matter the current direction away from the edge, close to the edge,
> > it becomes increasingly aligned in the direction of the edge. And this
> seems
> >   to apply to any edge shape at all.
> >
> >
> > > [jm]
> > > > Your experimental data generally reflect the type of distortion
> > > > that would necessarily be caused by the existence of the
> > > > boundaries, but they also appear to be in pretty significant
> > > > disagreement with the theoretical requirement that the
> > > > equipotentials be perpendicular to the edges of the paper.
> > > > Did you measure carefully right out to the edge to see if
> > > > the lines become perpendicular?

> > > [lk]
> > >Yes, the lines are perpendicular to the paper borders. I just
> > >conducted an experiment whose purpose was to demonstrate
> > >the opposite. The silver dots were at (6,2) and (22,18); these
> > >are Pasco paper coordinates in cm. With this geometry the
> > >central bisecting equiupotential line is at 45 degrees with
> > >respect to the x and y axes. I expected this line to cross the
> > >paper boundary at 45 degrees. And that what I observed,
> > >all the way up to last cm or less. Then the line turned
> > >toward the margin and intercepted it at about 90 degrees.
> > >Other equipotential lines were also examined carefully
> > >near the boundary (mm by mm) and were found to be
> > >practically perpendicular as well.
> > >
> > >If I had more time I would repeat the measurements
> > >after cutting left and right margins to make the a square
> > >sheet. How would the central equipotetential know to
> > >which margin to turn near the corner. The one I observed
> > >turned toward the nearest lower margin. So much so far.
> > >
> > >Why should the gradient be parallel to the paper boundary
> > >everywhere, as it seems to be?  I know why the E lines are
> > >perpendicular to conductive surfaces in electrostatics but I
> > >do not know why should they be parallel to the surface
> > >inside a conductor connected to a battery.
> > >Ludwik Kowalski

Brian Whatcott
  Altus OK                      Eureka!