Re: Isotropic Capacitance

At 12:02 PM 5/25/96 -0600, you wrote:
>>From brzozoww-at-rchland.vnet.ibm-dot-comSat May 25 11:56:06 1996
>Date: Fri, 24 May 1996 15:54:18 -0400 (EST)
>From: Wesley Brzozowski <brzozoww-at-rchland.vnet.ibm-dot-com>
>To: tesla-at-pupman-dot-com
>Subject: Isotropic Capacitance
> Richard Hull <hullr-at-whitlock-dot-com> wrote: 
>> The charge figured relative to a point infinitely distant is a nice 
>> concept.  But, to aquire a charge, anywhere in the real world, work must 
>> be performed in a dielectric (space in this case) by sparating this 
>> charge relative to something (the point far off).  Metals can't have 
>Ahhh... but the point that originally sparked this exchange was your quite 
>correct comment that the formula used for the capacitance of a sphere does 
>not match the measured values. And the reason for this is that the  
>assumptions made to derive the capacitance do not match anything that can 
>be done in the real world. Since most real-world problems don't have any  
>exact, closed-form mathematical solution, (at least that we've yet been  
>able to find) we are forced to either work with approximations or go with 
>computer-based numerical solutions. These are still approximations, but we 
>can usually make them very, very close to what's really measured. 

[big snip]

The capacitance of an isolated sphere in the real world is affected by close
(and not so close) objects and the earth itself.  Tesla spent several pages
(207 - 210) of his Colorado notes examining the capacitance of an elevated
sphere at different heights above the ground.  You have undoubtedly seen the
pictures of the Colorado Springs lab with the external tower with the
hanging sphere - this was the raised capacitive test setup.

It is interesting to note that tesla spent a lot of time and work making an
exhaustive study of elevated capcitances, it therefore was of great
importance to him.  You would think that the higher the sphere was above the
earth, the lower the capacitance, but if you plot the values Tesla got, then
you see this is not the case.  There is a trend toward lower capacitances,
but only at the maximum altitudes.