Re: [Phys-l] tutorial on scaling laws

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

I just read a nice scaling argument in Section 6-11 of Vol. II of the
Feynman Lectures on Physics.  Feynman, for the static case of two
charged conducting spheres connected by a long straight conducting wire,

determines how the magnitude of the electric field at the surface of one
sphere compares with that at the surface of the other in terms of the
radii of the spheres.  He approximates the charge distribution on each
sphere as being symmetric.  In this approximation the potential at the
surface of a sphere of radius r is that the same as that which would be
produced (in the absence of the sphere) at a point a distance r from the
location of the center of the sphere by a point charge at the location
of the center of the sphere.  Likewise for the electric field.  Since
the potential for the entire conductor is the same everywhere on the
conductor, and the potential at the surface of a sphere is proportional
to q/r, the charge on a sphere scales with r.  (That is, if the bigger
sphere has twice the radius of the smaller sphere, then the bigger
sphere has twice the charge.)  Since E is proportional to q/r^2, this
means that E scales with r/r^2 or simply 1/r.  So if the smaller sphere
has half the radius that the larger sphere has, the magnitude of the
electric field at the surface of the smaller sphere will be twice that
at the surface of the larger sphere.

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
> Sent: Thursday, July 26, 2007 4:21 PM
> To: Forum for Physics Educators
> Subject: [Junk released by Allow List] [Phys-l] tutorial on scaling
> laws
>
> I recently put together a tutorial on scaling laws:
>   http://www.av8n.com/physics/scaling.htm