# RE: Sphere Capacitance - John and Terry

• To: "John H. Couture" <couturejh-at-worldnet.att-dot-net>, tesla-at-pupman-dot-com
• Subject: RE: Sphere Capacitance - John and Terry
• From: Terry Fritz <twftesla-at-uswest-dot-net>
• Date: Sun, 10 Sep 2000 19:02:28 -0600
• Delivered-To: fixup-tesla-at-pupman-dot-com-at-fixme
• References: <4.1.20000909180905.009f33d0-at-pop.dnvr.uswest-dot-net>

```Hi All,  John and I have been discussing the capacitance of terminals off
list.  I originally rejected this thread, but it has drifted back into
pertinence.  You'll want to read this from bottom to top. - Terry

Hi John,

At 04:52 PM 9/10/00 -0700, you wrote:
>
>Terry -
>
>Note that capacitance (C) does not change but charge (Q) and voltage (V)
>does change when a  charged sphere is brought close to a grounded surface.

Q does not change but does get redistributed with the charge favoring the
side toward the grounded plane.  As the fields compress, the voltage
decreases.  As the sphere is brought closer and closer to the ground plane,
the voltage on the sphere drops and the capacitance between the two
increases following C=q/v.

>The capacitance of a sphere is
>
>  C (pf) = 1.4 * D       D = diameter in inches.
>
>Separation d is not involved with this equation. The diameter D is fixed so
>the capacitance (C) does not change when brought close to a grounded
>surface.

The above equation is derived from C = 4 x pi x Eo x r which is the
capacitance of a sphere in free space.  As your bring the sphere close to a
ground plane, the assumptions of the equation are violated (no longer in
free space) and it no longer applies.  It then becomes a fields analysis
problem.  Programs like E-tesla5 can then be used to find the capacitance
given the diameter of the sphere and distance to the ground plane.  As Jim
originally pointed out, this capacitance change is not very significant if
the distance is greater than 5 radii.

>If the sphere is charged only the charge and potential (voltage)
>will change because of electrostatic induction. But these changes will leave
>the capacitance the same.

The total charge on the sphere will not change.  In free space the voltage
distribution is uniform and the sphere is at it's lowest possible
capacitance.  As you bring it near a ground plane, the charge distribution
will change which increases the capacitance.

>
>So with a sphere in space where is the other plate? The answer is the other
>plate is at infinity! This is based on the theory of a charge in space.
>Refer to the Tesla Coil Design Manual page 10-1. There is much more to Tesla
>coil capacitances like the toroid problem.
>
>I think you should put this information on the List. Many coilers apparently
>do not know these facts about capacitance.

Ok, I'll forward this to the list.

Cheers,

Terry

>
>John Couture
>
>----------------------------
>
>
>-----Original Message-----
>From: Terry Fritz [mailto:twftesla-at-uswest-dot-net]
>Sent: Saturday, September 09, 2000 5:15 PM
>To: John H. Couture
>Subject: RE: Sphere Capacitance (was "human" topload )
>
>
>But john,
>
>	As you move the sphere closer and closer to the ground plane, d becomes
>less and less.  Thus, C increases!  The field stress is higher nearer a
>ground plane and thus a greater charge is needed to raise the sphere to a
>given voltage compared to the same sphere in free space.
>
>	Terry
>
>
>At 04:38 PM 9/9/00 -0700, you wrote:
>>
>>Terry -
>>
>>My physics book says that the capacitance of a certain capacitor is fixed
>by
>>    C = eo * A/d  =  q/V
>>   A = area    d = separation    eo = constant
>>Since the eo, A, and d are constants for a certain capacitor the
>capacitance
>>is FIXED and INDEPENDENT of the charge on the capacitor.
>>
>>To me that means that the sphere or TC toroid, charged or uncharged, does
>>not change capacitance when placed near a grounded surface. However, the
>>charge or voltage may change depending on whether the surface is charged or
>>uncharged.
>>
>>I believe Jim was incorrect when he said the capacitance of a sphere would
>>rise when close to a grounded surface.
>>
>>John Couture
>>
>>-----------------------------
>>
>>
>>-----Original Message-----
>>From: Terry Fritz [mailto:twftesla-at-uswest-dot-net]
>>Sent: Friday, September 08, 2000 6:00 PM
>>To: John H. Couture
>>
>>
>>Hi John,
>>
>>	This was not posted to the Tesla Coil Mailing List.
>>
>>The capacitance of on uncharged object is undefined.  But uncharged
>>terminals are not pertinent to the discussion here.
>>
>>Thanks,
>>
>>	Terry
>>
>>
>>At 05:33 PM 9/8/00 -0700, you wrote:
>>>
>>>Jim -
>>>
>>>You said that the capacitance would rise when the sphere was close to a
>>>grounded object. However, you did not indicate whether the sphere was
>>>charged or uncharged. It is my understanding the uncharged sphere would
>not
>>>change in capacitance. For example the capacitance of the uncharged toroid
>>>would not change when placed on top of the secondary coil. In fact some
>>>tests indicate the capacitance would decrease. Would you please clarify
>>your
>>>remark?
>>>
>>>John Couture
>>>
>>>---------------------------
>>>
>>>-----Original Message-----
>>>From: Tesla list [mailto:tesla-at-pupman-dot-com]
>>>Sent: Thursday, September 07, 2000 4:17 PM
>>>To: tesla-at-pupman-dot-com
>>>
>>>
>>>Original poster: "Jim Lux" <jimlux-at-jpl.nasa.gov>
>>>
>>>The biggest factor affecting body C is going to be distance from ground.
>>>
>>>-------------------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
>>>
>>
>>
>

```