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Distribution of charge on a conductor.

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  Distribution of charge on a conductor. Justin Thyme <JustinThyme@nowhere.com> - 2015-08-25 14:08 +0100
    Re: Distribution of charge on a conductor. Sam Wormley <swormley1@gmail.com> - 2015-08-25 08:37 -0500
      Re: Distribution of charge on a conductor. Justin Thyme <JustinThyme@nowhere.com> - 2015-08-25 15:31 +0100
        Re: Distribution of charge on a conductor. Odd Bodkin <bodkinodd@gmail.com> - 2015-08-25 10:12 -0500
          Re: Distribution of charge on a conductor. Justin Thyme <JustinThyme@nowhere.com> - 2015-08-25 16:50 +0100
            Re: Distribution of charge on a conductor. Poutnik <Poutnik4NNTP@gmail.com> - 2015-08-25 18:19 +0200
            Re: Distribution of charge on a conductor. Odd Bodkin <bodkinodd@gmail.com> - 2015-08-25 11:35 -0500
              Re: Distribution of charge on a conductor. Odd Bodkin <bodkinodd@gmail.com> - 2015-08-25 12:24 -0500
                Re: Distribution of charge on a conductor. Odd Bodkin <bodkinodd@gmail.com> - 2015-08-25 12:25 -0500
                  Re: Distribution of charge on a conductor. noTthaTguY <abu.kuanysh05@gmail.com> - 2015-08-25 10:30 -0700

#516736 — Distribution of charge on a conductor.

I know, or at least I think I do, that the charge on a hollow conductor 
(say a sphere) is all on the outside, and the charge on a spike is 
concentrated at the tip (I think the charge density increases with the 
curvature of the surface).  So naturally I wonder where the change on a 
sphere with a spike in the inside will accumulate...
-- 
Shall we only threaten and be angry for an hour?
   When the storm is ended shall we find
How softly but how swiftly they have sidled back to power
   By the favour and contrivance of their kind?

 From /Mesopotamia/ by Rudyard Kipling

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#516743

On 8/25/15 8:08 AM, Justin Thyme wrote:
> I know, or at least I think I do, that the charge on a hollow conductor
> (say a sphere) is all on the outside, and the charge on a spike is
> concentrated at the tip (I think the charge density increases with the
> curvature of the surface).  So naturally I wonder where the change on a
> sphere with a spike in the inside will accumulate...

   Nope -- not at the tip.


-- 

sci.physics is an unmoderated newsgroup dedicated
to the discussion of physics, news from the physics
community, and physics-related social issues.

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#516751

Sam Wormley wrote:
> On 8/25/15 8:08 AM, Justin Thyme wrote:
>> I know, or at least I think I do, that the charge on a hollow conductor
>> (say a sphere) is all on the outside, and the charge on a spike is
>> concentrated at the tip (I think the charge density increases with the
>> curvature of the surface).  So naturally I wonder where the change on a
>> sphere with a spike in the inside will accumulate...
>
>    Nope -- not at the tip.
>

First, sorry for writing "change" where "charge" is meant.

Consider, to be more specific, the surface of revolution got by turning 
a cardioid about an axis that runs through its centre and the cusp. 
Where (and why) would the charge on that accumulate?

-- 
Shall we only threaten and be angry for an hour?
   When the storm is ended shall we find
How softly but how swiftly they have sidled back to power
   By the favour and contrivance of their kind?

 From /Mesopotamia/ by Rudyard Kipling

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#516760

On 8/25/2015 9:31 AM, Justin Thyme wrote:
> Sam Wormley wrote:
>> On 8/25/15 8:08 AM, Justin Thyme wrote:
>>> I know, or at least I think I do, that the charge on a hollow conductor
>>> (say a sphere) is all on the outside, and the charge on a spike is
>>> concentrated at the tip (I think the charge density increases with the
>>> curvature of the surface).  So naturally I wonder where the change on a
>>> sphere with a spike in the inside will accumulate...
>>
>>    Nope -- not at the tip.
>>
>
> First, sorry for writing "change" where "charge" is meant.
>
> Consider, to be more specific, the surface of revolution got by turning
> a cardioid about an axis that runs through its centre and the cusp.
> Where (and why) would the charge on that accumulate?
>

It's a good question, because the naive answer would be the most convex 
portion on the outside of the conductor. But the most convex portions 
are immediately adjacent to the _highly_ concave inward-facing cusp. So 
the maximal concentrations are likely on the "shoulder" of the 
heart-shaped revolute. I don't know if this is solvable analytically, 
and it may be that a mesh-relaxation computer program would be needed to 
find the charge density profile.

-- 
Odd Bodkin --- maker of fine toys, tools, tables

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#516773

Odd Bodkin wrote:
> On 8/25/2015 9:31 AM, Justin Thyme wrote:
>> Sam Wormley wrote:
>>> On 8/25/15 8:08 AM, Justin Thyme wrote:
>>>> I know, or at least I think I do, that the charge on a hollow conductor
>>>> (say a sphere) is all on the outside, and the charge on a spike is
>>>> concentrated at the tip (I think the charge density increases with the
>>>> curvature of the surface).  So naturally I wonder where the change on a
>>>> sphere with a spike in the inside will accumulate...
>>>
>>>    Nope -- not at the tip.
>>>
>>
>> First, sorry for writing "change" where "charge" is meant.
>>
>> Consider, to be more specific, the surface of revolution got by turning
>> a cardioid about an axis that runs through its centre and the cusp.
>> Where (and why) would the charge on that accumulate?
>>
>
> It's a good question, because the naive answer would be the most convex
> portion on the outside of the conductor. But the most convex portions
> are immediately adjacent to the _highly_ concave inward-facing cusp. So
> the maximal concentrations are likely on the "shoulder" of the
> heart-shaped revolute. I don't know if this is solvable analytically,
> and it may be that a mesh-relaxation computer program would be needed to
> find the charge density profile.

Since the phrase "mesh-relaxation computer program" means nothing to me, 
any thoughts about where more may be learned?  sci.math.num-analysis, maybe?

-- 
Shall we only threaten and be angry for an hour?
   When the storm is ended shall we find
How softly but how swiftly they have sidled back to power
   By the favour and contrivance of their kind?

 From /Mesopotamia/ by Rudyard Kipling

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#516788

On 08/25/2015 05:50 PM, Justin Thyme wrote:
>>>
>>> Consider, to be more specific, the surface of revolution got by turning
>>> a cardioid about an axis that runs through its centre and the cusp.
>>> Where (and why) would the charge on that accumulate?
>>>
>>
>> It's a good question, because the naive answer would be the most convex
>> portion on the outside of the conductor. But the most convex portions
>> are immediately adjacent to the _highly_ concave inward-facing cusp. So
>> the maximal concentrations are likely on the "shoulder" of the
>> heart-shaped revolute. I don't know if this is solvable analytically,
>> and it may be that a mesh-relaxation computer program would be needed to
>> find the charge density profile.
> 
> Since the phrase "mesh-relaxation computer program" means nothing to me, 
> any thoughts about where more may be learned?  sci.math.num-analysis, maybe?
> 
For conductors, charges and electrostatics,
there are few rules :

1/ there is no charge inside conductor,
as it would lead to non zero internal intensity and electric current.

2/ therefore all the charge is on surface.

3/ surface charge distribution follows the requirement
of surface being quipotential 3D area,
otherwise it would lead to current as at 1/


By mesh relaxation program is , I guess, thought
a numerical solution, replacing surface into mesh of points,
and calculating suface charge densities needed to constant surface
potential.

-- 
Poutnik ( the Czech word for a wanderer )

Knowledge makes a great man humble, but a small man arrogant.

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#516793

On 8/25/2015 10:50 AM, Justin Thyme wrote:
> Odd Bodkin wrote:
>> On 8/25/2015 9:31 AM, Justin Thyme wrote:
>>> Sam Wormley wrote:
>>>> On 8/25/15 8:08 AM, Justin Thyme wrote:
>>>>> I know, or at least I think I do, that the charge on a hollow
>>>>> conductor
>>>>> (say a sphere) is all on the outside, and the charge on a spike is
>>>>> concentrated at the tip (I think the charge density increases with the
>>>>> curvature of the surface).  So naturally I wonder where the change
>>>>> on a
>>>>> sphere with a spike in the inside will accumulate...
>>>>
>>>>    Nope -- not at the tip.
>>>>
>>>
>>> First, sorry for writing "change" where "charge" is meant.
>>>
>>> Consider, to be more specific, the surface of revolution got by turning
>>> a cardioid about an axis that runs through its centre and the cusp.
>>> Where (and why) would the charge on that accumulate?
>>>
>>
>> It's a good question, because the naive answer would be the most convex
>> portion on the outside of the conductor. But the most convex portions
>> are immediately adjacent to the _highly_ concave inward-facing cusp. So
>> the maximal concentrations are likely on the "shoulder" of the
>> heart-shaped revolute. I don't know if this is solvable analytically,
>> and it may be that a mesh-relaxation computer program would be needed to
>> find the charge density profile.
>
> Since the phrase "mesh-relaxation computer program" means nothing to me,
> any thoughts about where more may be learned?  sci.math.num-analysis,
> maybe?
>

Google first.


-- 
Odd Bodkin --- maker of fine toys, tools, tables

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#516815

On 8/25/2015 11:35 AM, Odd Bodkin wrote:
> On 8/25/2015 10:50 AM, Justin Thyme wrote:

>>
>> Since the phrase "mesh-relaxation computer program" means nothing to me,
>> any thoughts about where more may be learned?  sci.math.num-analysis,
>> maybe?
>>
>
> Google first.
>
>
https://en.wikipedia.org/wiki/Relaxation_%28iterative_method%29

-- 
Odd Bodkin --- maker of fine toys, tools, tables

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#516817

On 8/25/2015 12:24 PM, Odd Bodkin wrote:
> On 8/25/2015 11:35 AM, Odd Bodkin wrote:
>> On 8/25/2015 10:50 AM, Justin Thyme wrote:
>
>>>
>>> Since the phrase "mesh-relaxation computer program" means nothing to me,
>>> any thoughts about where more may be learned?  sci.math.num-analysis,
>>> maybe?
>>>
>>
>> Google first.
>>
>>
> https://en.wikipedia.org/wiki/Relaxation_%28iterative_method%29
>
http://home.gwu.edu/~hgrie/lectures/edyn12/comp-physII12.project1.pdf

-- 
Odd Bodkin --- maker of fine toys, tools, tables

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#516818

charge on cardioid-of-revolution is interesting, although
there ought to be a nicve, non-revolved, spatial shape, two

> http://home.gwu.edu/~hgrie/lectures/edyn12/comp-physII12.project1.pdf
> 
> -- 
> Odd Bodkin --- maker of fine toys, tools, tables

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