# 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

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Contributed by: S. M. Blinder (August 2020)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

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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