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Re: Bar magnets, was magnetic circuits

At 02:45 2/19/01 -0500, John Denker wrote:
///
Over 350 years ago there appeared a book called "Discourses on Two New
Sciences". One of the new sciences was the laws of motion. What was the
other one? Scaling laws!

Here is the index:
I First New Science, Treating of the Resistance which Solid Bodies
Offer to Fracture. First Day.

II Concerning the Cause of Cohesion. Second Day.

III Second New Science, Treating of Motion. Third Day.
Uniform Motion.
Naturally Accelerated Motion

IV Violent Motions. Projectiles. Fourth Day.

I think scaling laws are very important. The field of a point charge
scales like 1/r^2. The field of a line charge scales like 1/r. The field
of a surface charge scales like r^0.

This is a strikingly helpful observation. For people who find it useful
to visualize field intensity by means of 'line' density (Like Faraday did),
it is easy to see the variation of line density emanating from a point
source through a spherical surface at some radius r as proportional to
the surface of that sphere.
A linear source maintains its 'line' density in directions parallel
to the source, so the 'lines' spread proportionately to the circumference
of a circle of radius r.
A plane (but not just any surface) source maintains parallel 'lines' at
any distance.

Unfortunately, this visualization prop does not always guarantee useful
intuition. One might visualize all lines emanating from one pole
being captured by an opposing pole - a situation of constant line
density.
And the well known result that the field strength of a bar magnet
is halved when it is rotated from a polar to an equatorial orientation
to the sensor is not well visualized by the 'line' method.

brian whatcott <inet@intellisys.net> Altus OK
Eureka!