Toroid capacitance reduction

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

Original poster: Paul Nicholson <paul-at-abelian.demon.co.uk> 

John Couture wrote (in 'First Light for 10" Coil'):

 > I do not believe anyone has ever explained this Toroid reduction
 > with Tesla coils. It should be an increase because the toroid is
 > closer to other objects. Maybe Paul or Antonio will look into it

John's comments about reduction of toroid capacitance when it is
in-situ over the coil are quite correct.  However, there is no
mystery to the reason why - it is a well known and understood
phenomena in electrostatics.

Generally if you have two objects A and B, having self capacitances
of Ca and Cb respectively when each is measured (or calculated) in
isolation, then when they are brought together, joined or just close
to one another, the combined capacitance of the two will always be
less than Ca + Cb.

You can think of it as each object shielding the other to some
extent.  The effective electrical 'surface area' of the two objects
combined is less than the sum of the two separate objects.  This is
because charge which would have been distributed fairly evenly over
each of the separate objects will be displaced away from the other
object when the two are brought together.

With fixed width font and some allowance for the ascii artwork,
the charge distribution around two isolated blobs is something
like:

      +  + +                      + + +
    +  ____  +                  + ____  +
   +  /    \  +               +  /    \  +
  +  |      |  +             +  |      |  +
   +  \____/  +               +  \____/  +
    +        +                  +       +
      + + +                       + + +

where the + indicate charges on the surface of each blob (not in
the air around it as the sketch might suggest!)

When they are brought close to each other, we get

           +  + +   + + +
         +  ____  +  ____  +
        +  /    \   /    \  +
       +  |      | |      |  +
        +  \____/   \____/  +
         +        +        +
           + + +     + + +

If you count the charges (ie measure the capacitance) you see
there are now fewer, because charge is not inclined to occupy the
surfaces of the objects which are close to each other.  Thus the
total charge needed to raise the combined objects to some given
potential is less than the sum of the amount needed for the two
separate objects.

Why doesn't charge want to sit on the adjacent surfaces?  Because
each charge can find a lower potential energy by moving elsewhere.

Each charge is immersed in the E-field generated by all the other
charges, and those that are free to move (ie not bound into atoms,
etc) will 'fall' through the field until they find their lowest
level.  In effect the charges are just trying to get as far away
from each other as they can.  The upshot is that less total charge
is needed to reach some potential because the adjacent surfaces
don't need to be covered.

It isn't too hard to calculate this behaviour, because at low
frequencies the only significant force on each charge is just the
Coulomb force.

Programs made available by Terry, Bart, and more recently Antonio,
will all take these effects into account quite accurately, because
one way or another they compute the actual charge distribution of
the in-situ objects.

And as a corollary, not only does C_toroid fall when in-situ, so
does C_secondary too.

Apparently my hands are waving so much they risk bringing down the
xmas decorations, but hope that helps!

Greetings All,
--
Paul Nicholson
--