What is the formula for Force Between Parallel Wires?

The Force Between Parallel Wires formula is F/L = µ₀ × I1 × I2 / (2π × d), where F/L—Force per unit length (N/m); I1, I2—Currents in the two wires (A); d—Separation between wires (m); µ₀ = 4π×10⁻⁷ H/m.

What does F/L mean in the Force Between Parallel Wires formula?

F/L is Force per unit length (N/m).

Force Between Parallel Wires

Q: How do you calculate Force Between Parallel Wires?

Use the formula F/L = µ₀ × I1 × I2 / (2π × d). Two parallel current-carrying conductors exert a force per unit length on each other through their magnetic fields. Enter the values you know in the calculator above and it solves for the remaining variable.

F/L = µ0 · I1 · I2 / (2π · d)

Calculator

Force per Length

Current 1

Current 2

Separation

Result

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Formula

F/L = µ₀ × I1 × I2 / (2π × d)

Description

Two parallel current-carrying conductors exert a force per unit length on each other through their magnetic fields. Currents in the same direction attract; opposite currents repel. This effect once defined the ampere itself and is the source of the mechanical stress that high-current busbars and fault currents place on conductors.

Variables

F/L — Force per unit length (N/m)
I1, I2 — Currents in the two wires (A)
d — Separation between wires (m)
µ₀ = 4π×10⁻⁷ H/m —

Practical Notes

During a short-circuit fault, busbars can see thousands of amps and large attractive/repulsive forces—mechanical bracing must be rated for it. Twisting or transposing conductors reduces the net force.

Related Concepts

All Fields & Electromagnetism formulas →

Coulomb’s Law Electric Field of a Point Charge Electric Potential of a Point Charge Gauss’s Law (Electric Flux) Lorentz Magnetic Force Force on a Current-Carrying Wire Force Between Parallel Wires Magnetic Field of a Straight Wire

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