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*From*: brian whatcott <inet@INTELLISYS.NET>*Date*: Mon, 19 Feb 2001 09:23:15 -0600

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!

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