Table of Contents
Force Between Parallel Wires
Two parallel current-carrying wires exert a magnetic force on each other. If the currents flow in the same direction, the wires attract; if in opposite directions, they repel. This force arises because each wire sits in the magnetic field created by the other wire, and the Lorentz force acts on its moving charges. This phenomenon was discovered by Ampere and was historically used to define the ampere, the SI unit of electric current.
The force per unit length between the wires is proportional to the product of the two currents and inversely proportional to their separation distance. This fundamental electromagnetic interaction is the basis for the Ampere force law and has practical implications for the design of bus bars, power cables, and electromagnetic launchers (railguns).
The Formula
Where F/L is force per unit length (N/m), μ0 is the permeability of free space, I1 and I2 are the currents, and d is the distance between wires.
Definition of the Ampere
Until 2019, the ampere was defined as the constant current which, flowing through two straight parallel conductors of infinite length and negligible cross-section, placed 1 meter apart in vacuum, produces a force of exactly 2 × 10-7 N per meter of length. This definition directly uses the force between wires formula.
| Configuration | I1 | I2 | d | F/L |
|---|---|---|---|---|
| Definition | 1 A | 1 A | 1 m | 2 × 10-7 N/m |
| Power bus bar | 1000 A | 1000 A | 5 cm | 4 N/m |
| Household wire | 15 A | 15 A | 1 cm | 0.45 mN/m |
Frequently Asked Questions
Why do same-direction currents attract?
Wire 1 creates a magnetic field at Wire 2. Using the right-hand rule, the field from Wire 1 pushes the charges in Wire 2 toward Wire 1 (via the Lorentz force qv x B). The net effect is an attractive force when currents are parallel. For anti-parallel currents, the Lorentz force points away, causing repulsion. This is analogous to how aligned magnetic dipoles attract.
Is this force significant in practice?
For household currents and typical wire spacing, the force is negligible (micro-newtons). But in high-current applications like bus bars in power plants (thousands of amperes), the force can be hundreds of newtons per meter, requiring robust mechanical supports. In short-circuit faults, momentary currents of 50,000+ A create explosive forces that can destroy equipment.
How is this related to railguns?
A railgun uses two parallel conducting rails with a sliding armature. Enormous currents (millions of amperes) flow through the rails in opposite directions through the armature. The repulsive magnetic force accelerates the armature and projectile to extreme velocities (Mach 6+), demonstrating the force between parallel conductors at extreme scale.