Re: Etesla6 math questions

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Paul Nicholson by way of Terry Fritz <teslalist-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

Peter Lawrence wrote:

 > 6... but we don't know either the voltage or the E-field
 > at the sphere.

Ah, slight misunderstanding here.  The outer boundary in E-Tesla is
a cylinder, formed from floor, walls and ceiling.  Declared to be
at zero volts.

The sphere is an imaginary sphere over which the flux is integrated
to determine the total E flux leaving the resonator.  This 'Gaussian'
sphere sits (hopefully) entirely within the outer cylinder, and is
large enough to entirely enclose the resonator, thus catching all
its external flux.  The Gaussian sphere takes no part in the
relaxation process, and is instead an extra step applied after the
field has been computed.

 > 7. I always assumed Coulombs law was inverse square...

Yes, inverse square when written in terms of the field strength,
   E = q/(4 * pi * epsilon * r^2)
but only inverse when expressed using the electric potential,
   V = q/(4 * pi * epsilon * r)

Differentiate the second equation to get the first.  The first
describes the Coulomb field in terms of the force on a test particle,
whereas the second describes the field in terms of the potential
energy of a test particle.
--
Paul Nicholson
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