Re: [Phys-l] [phys-l] electric field due to uniform ring of charge, off-axis

[curtis osterhoudt <flutzpah@yahoo.com>]

I doubt that there's a very simple analytical form for the off-axis result (I 
and a colleague are doing some off-axis scattering calculations which turn out 
to be awfully complicated), but this might help, especially the approximations:

http://link.aip.org/link/?AJPIAS/74/295/1 

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________________________________
From: brian whatcott <betwys1@sbcglobal.net>
To: phys-l@carnot.physics.buffalo.edu
Sent: Wed, January 12, 2011 5:25:37 PM
Subject: Re: [Phys-l] [phys-l] electric field due to uniform ring of charge, 
off-axis

On 1/12/2011 3:52 PM, Krishna Chowdary wrote:
> Dear colleagues
>
> Is there a closed form expression for the electric field due to a
> uniform ring of charge (charge Q, radius a) at points in the plane of
> the ring (but not on the ring itself), or even more generally anywhere
> in space (but not on the ring itself)? If yes, I'd appreciate
> suggestions on how to proceed.
>
> It's a standard exercise to determine the field for such a ring on its
> axis. What about not on the axis?
>
> I can do this numerically with a straightforward spreadsheet
> implementation. I can't yet do it analytically (I couldn't find an
> elementary anti-derivative, and Mathematica and WolframAlpha invoke
> the Appell Hypergeometric Function of two variables, which is far
> outside my experience).
>
> If you're interested, here are the integrals I'm trying to evaluate,
> where (x,y) is the coordinate of the field point and a is the radius
> of the ring (centered on the origin):
>
> http://tinyurl.com/4c5fp3x
>
> http://tinyurl.com/4gnmd99
>
> I appreciate your insights.
>
> sincerely,
> Krishna