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Suppose we have a collection of charged line segments in 2D. I'd like to be able to do two things :

  • from an arbitrary point in the plane, follow the electric field and find where it meets the collection of line segments (and how far we traveled along the electric field line)
  • from a point on one of the line segments, follow the electric field for a given distance and report the point.

Is there some analytic solution to this problem or a special case of it, say involving functions of complex variables?

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  • $\begingroup$ Here is a paper on just one charged segment. Robert Rowley, "Finite line of charge," American Journal of Physics, 2006 Volume 74, Issue 12, pp. 1120. From the Absract: "The equipotentials are shown to be prolate ellipsoids and the electric field lines follow hyperboloids confocal to the ellipsoids. The common foci are shown to be the endpoints of the charged line segment." $\endgroup$
    – Joseph O'Rourke
    Commented Apr 6, 2011 at 12:09

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