# Simplified case: filiform conductors

## Introduction

This paragraph gives the analytical expression of partial inductance in the simplified case of two filiform parallel conductors (negligible cross-section area).

Reminder: The partial inductance between segments S_{1} and S_{2} is
expressed by the formula:

## Magnetic vector potential

The expression of the magnitude of the vector potential created by a current
I_{1} in a point M of coordinates (x_{0}, y_{0},
z_{0}) is given by the following formula:

## Partial inductance between two conductors

In order to obtain partial inductance between two parallel filiform conductors, we
integrate the vector potential created by the current I_{1} on the conductor and
provided with a current I_{2}.

The following analytical expression is obtained:

where:

## Partial inductance of a conductor

The partial inductance of a filiform conductor can be more difficult to obtain because
the previous formula diverges when ρ = 0 and l_{3} = 0.

It is then necessary to apply the volume formula given in § Real case: volume conductors.