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Terry, Jim, All -

I believe the following is correct but electric field analysis is not a
simple subject.

The electric field analysis for a charged sphere that is moved close to a
grounded plane would normally not be of interest to coilers. However, this
has a direct bearing on the toroid that is placed on the classical or
magnifier Tesla coil. How should the capacitance of the toroid be
calculated?

When moving a charged sphere close to a grounded plane the amount of the
charge does not change. However, the distribution of the charge on the
surface of the sphere does change. Also the electric intensity in the space
around the sphere would be redistributed as the charge is redistributed.

The distance (d) between the sphere and the grounded plane determines the
redistribution of the electric field intensity around the sphere according
to Gauss's law. The simplified equation is
E = D * A    where E = electric field intensity
A = area involved with distance (d)
D = constant involving several parameters
Because area is involved the electric field intensity varies inversly as the
square of the distance (d). However, changing the distance does not change
the capacitance of the sphere. The capacitance of the sphere depends only on
the radius of the sphere and a constant.

A graph showing distance (d) versus electric field intensity (E) would show
a non linear curve. A 3 dimensional graph would be even more interesting to
show. The electric field intensity at the point of the sphere away from the
plane would extend to infinity. A real challenge for any simulator.

John Couture

--------------------------

-----Original Message-----
From: Tesla list [mailto:tesla-at-pupman-dot-com]
Sent: Sunday, September 10, 2000 6:37 PM
To: tesla-at-pupman-dot-com

Original poster: Terry Fritz <twftesla-at-uswest-dot-net>

Hi Jim,

At 01:59 PM 9/7/00 -0700, Jim Lux wrote:
snip...
>For what it's worth, a sphere 1 meter radius in free space has a
capacitance
>of about 110 pF.  If it is close (within 5 radii) of a grounded surface,
the
>C is going to rise.  The mathematically inclined (and masochistic) can do
>this by considering the ground as a reflector and calculating the
>capacitance between two spheres separated by 2d, where d is the distance to
>ground.  This in itself is non trivial (there isn't a closed form
solution).
snip...

Actually, a single graph would do it all.  The only defining aspect to the
capacitance of a sphere above an infinite plane is the diameter to distance
factor.  So if you knew the capacitance of a 1 meter ball 1 meter above a
plane, the capacitance if a 1/2 meter ball 1/2 meter above the plane would
simply be 1/2 of the 1 meter ball's capacitance.  A chart with a normalized
1 meter ball's capacitance vs. distance above the plane could be used for
any diameter sphere just by multiplying the capacitance by the diameter
factor.  A toroid is a bit different, but the answers would probably still
be close.

The terminals we use are far enough above ground that this effect would
probably not be significant.  E-Tesla5 does this stuff already taking into
account the other TC variables, so the generation of such a chart would
probably not be useful to us...

Cheers,

Terry

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