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 S₁ and S₂ is expressed by the formula:

Magnetic vector potential

The expression of the magnitude of the vector potential created by a current I₁ in a point M of coordinates (x₀, y₀, z₀) 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 I₁ on the conductor and provided with a current I₂.

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 l₃ = 0.

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