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Since the flow lines all lie in the plane of the paper, it seems to me
that the situation is a 2 dimensional one.
Let me describe an experiment I did some time ago which supports this
claim.
Construct a ring of conducting paint, and put a dot of conducting paint
in the center. Measure the potential as a function of distance from the
center, plot the curve, differentiate it by drawing some tangent lines,
and then plot the slopes as a function of distance on log-log paper. Of
course now you would do it with a computer. The slope of the
resulting line is -1, so the electric field falls off as 1/r, which is the
characteristic of an infinite rod. In this sense the paper can be
seen as a perpendicular cut in the space around a charged rod.
Now since the "difference of the logarithms is the logarithm
of the quotient" we can re-write the potential as
V = V_0 - C*ln(r_A / r_B).