Interactive demonstration of magnetic force between parallel current-carrying wires
Two wires push each other without touching
Each wire creates a magnetic field; the other wire is a current-carrying conductor sitting inside it—the motor effect applied twice. Same-direction currents attract, opposite currents repel. Adjust each current and direction, then drag the separation slider to watch F/l = (μ₀/2π) I₁I₂/r respond live.
Parallel Wire Forces
Attract • 2.00×10⁻⁵ N/m
Adjust currents & directions — drag separation to see force change
Attract • F/l = 2.00×10⁻⁵ N/m
Wire 1 Current: 5.0 A
Wire 2 Current: 5.0 A
Separation: 0.50 m
Force per Metre
2.00×10⁻⁵
Field Strength
10.0 μT
The force per metre between parallel wires is F/l = (μ₀/2π) × I₁I₂/r, where μ₀ = 4π×10⁻⁷ T·m/A. Double either current and the force doubles—the relationship is perfectly linear. Double the separation and the force halves—inverse first power, not inverse square, because each wire creates a field that falls off as 1/r. Newton's third law guarantees the forces are equal and opposite: wire 1 pushes wire 2 exactly as hard as wire 2 pushes wire 1. This mutual force was once measured so precisely that from 1948 to 2019, it defined the ampere: one ampere was the current that produced exactly 2×10⁻⁷ newtons per metre between two infinitely long parallel wires one metre apart in vacuum.
Know This
Parallel wires carrying current in the same direction attract; opposite directions repel—because each wire sits in the circular field made by the other, experiencing the motor effect force F/l = (μ₀/2π) I₁I₂/r.