Re: Spheres vs Toroids

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

Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net> 

 > Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
 >
 > As most of the charge will be located at the outer side of the toroid,
 > a thick toroid has more capacitance than a thin toroid with the same
 > major diameter. A very thin toroid has zero capacitance, but it must
 > be -very- thin.

I interprete thin to mean small minor diameter and not thin conducting
surface.  Also,  I'm presuming that as the minor diameter goes to zero and
the
toroid/capacitance vanishes, that there is no interconnecting surface that
would normally make connection from the center to the inner surface of the
toroid contributing to your capacitance calculation.  Would this be correct?

Is the distribution of charge on the outer surface of the toroid (for a
typical and FIXED geometry that we use for TCs) uniform or (for example) is
there a
gaussian like distribution across this outer surface.  Does this
distribution (whatever it is) affect the capacitance calculation?

My thinking is maybe yes.  The distribution of charge may affect the surface
potential {integral (from left infinity lets say, to the toroid outer left
surface) (e.dl)} and C = Q/V.  On the otherhand, the surface potential any
where on the conducting toroid surface should be the same (for static
fields) meaning that for any infinity start point and any surface end point,
the potential integral should be the same and independent of the path of
integration.  Maybe this is an argument that the capacitance is not a
function of charge distribution on the surface of a fixed geometry toroid.

Comments

Gerry R