Re: Capacitance of domed topload

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

Original poster: "Jim Lux by way of Terry Fritz <teslalist-at-qwest-dot-net>" <jimlux-at-earthlink-dot-net>

The Medhurst approximation (used for self C of a secondary) is really an 
approximation of the C of a cylinder over a ground plane, and will be 
fairly close.

Another approach to approximate is to divide the cylinder up into little 
rings, and calculate the capacitance to ground of each ring, then sum.  If 
the distance from cylinder to ground is >> dimensions of cylinder, you can 
probably just approximate with the surface area of the cylinder and the 
"average" distance to ground.

An analytical approach is to consider it as a modified case of two 
concentric cylinders (or, cones, more precisely) where one of the cones is 
opened all the way out.

Attempts to come up with an analytical solution will quickly get you into 
Bessel functions and elliptic integrals (after all, it has all those 
circular symmetries).  Fun for some, as an intellectual exercise.  (Find 
someone to assign it as a homework problem in a class!)  Given that you're 
at Surrey, you might ask someone in the antennas/microwave area who deal 
with this sort of thing all the time: David Jeffries is an antenna guy with 
a pedagogical bent, judging from his web page(s)). I don't have his phone 
number handy, but I'm sure he's in the faculty directory.


At 07:44 AM 4/2/2003 -0700, you wrote:
>Original poster: "Dr Brian H Le Page by way of Terry Fritz 
><teslalist-at-qwest-dot-net>" <b.h.le-page-at-surrey.ac.uk>
>
>Hi All
>
>I have a problem working out the capacitance of a topload.  The shape is an
>aluminium cylinder with a diameter of 715mm and a height of 280mm.  On top
>of this is a hemisphere with the same diameter as the cylinder.  Can anyone
>suggest a way to calculate the capacitance of this shape?  I can find an
>expression for the capacitance of a sphere, but not for the cylinder.
>
>Thanks
>
>Dr B