Potential and Lines of Force for Two Parallel Infinite Line Charges

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The electrostatic potential in an \[Hyphen]
plane for an infinite line charge in the
direction with linear density
is given by
Contributed by: S. M. Blinder (August 2020)
Open content licensed under CC BY-NC-SA
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The orthogonal networks of equipotentials and lines of force must satisfy the equation
,
or, more explicitly,
.
This is analogous to the mappings of the real and imaginary parts of a complex function. For the problem of parallel line charges, consider the complex function
,
where . Working out the real and imaginary parts of
, we obtain the functions
and
given in the caption.
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