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



?Krishna,
This is not a solution, just a simplifying comment to your calculation:

No generality is lost if you define the x axis to be the line joining the charged circle and the field point.

This makes

1) y=0 for all field points and
2) by symmetry, makes the y component of the E field zero (your second integral).

Hope this is useful.
-Bob


Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/
-----Original Message----- From: Krishna Chowdary
Sent: Wednesday, January 12, 2011 4:52 PM
To: Forum for Physics Educators
Subject: [Phys-l] [phys-l] electric field due to uniform ring of charge, off-axis

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
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