Calculate the magnetic force per unit length between two parallel current-carrying wires using F/L = μ₀I₁I₂/(2πd). Includes AWG reference table.
Two parallel wires carrying electric currents exert a magnetic force on each other — attractive if the currents flow in the same direction, repulsive if they flow in opposite directions. This phenomenon, described by Ampère's force law, provides the physical basis for the SI definition of the ampere and is fundamental to understanding electromagnetic force in power systems, busbars, and electrical machinery.
This Magnetic Force Between Wires Calculator computes the force per unit length F/L = μ₀I₁I₂/(2πd), total force over a given wire length, and the magnetic field each wire produces at the other's location. The force-vs-distance chart visualizes the inverse relationship, and presets cover scenarios from household wiring to high-voltage power lines.
The AWG wire gauge reference table helps relate calculated forces to real wiring scenarios, making this tool useful for electrical engineers, physics students, and anyone designing systems where parallel conductors carry significant current. Check the example with realistic values before reporting.
The force between parallel conductors is often surprising — even modest household currents at close spacing produce measurable forces. This calculator instantly shows the force magnitude, field strength, and how rapidly force drops with distance, helping engineers design busbar supports and verify that wiring routes can handle electromagnetic loads. Keep these notes focused on your operational context.
Force per unit length (Ampère's law): F/L = μ₀I₁I₂ / (2πd) Total Force: F = (F/L) × L Magnetic Field from Wire: B = μ₀I / (2πr) Where: μ₀ = 4π × 10⁻⁷ T·m/A (permeability of free space) I₁, I₂ = currents (A) d = distance between wires (m) L = wire length (m)
Result: F/L = 4.5 × 10⁻⁴ N/m, Total = 1.35 × 10⁻³ N
Two 15 A household wires separated by 1 cm over 3 meters exert about 1.35 mN of force on each other. The force is small but real — in high-current busbars (1000+ A), these forces require mechanical support.
The force between current-carrying wires was first demonstrated by André-Marie Ampère in 1820, shortly after Ørsted discovered the connection between electricity and magnetism. Ampère showed that parallel currents attract and antiparallel currents repel — establishing electrodynamics as a quantitative science and earning him the honor of having the unit of current named after him.
In electrical switchgear and power distribution, copper or aluminum busbars carry thousands of amps. The electromagnetic forces between parallel busbars must be calculated for both normal operation and worst-case fault conditions. Peak fault forces can exceed 10 kN/m, requiring substantial insulating spacers, bracing, and structural analysis.
Since 2019, the SI ampere is defined by fixing the elementary charge e = 1.602176634 × 10⁻¹⁹ C exactly. This replaced the old definition based on the force between two wires, but the force formula remains physically correct and is still used for practical engineering calculations.
Each wire creates a magnetic field that exerts a Lorentz force on the moving charges in the other wire. By Ampère's right-hand rule, the geometry works out so same-direction currents attract and opposite-direction currents repel.
The old SI definition (pre-2019) defined the ampere as the current that produces 2 × 10⁻⁷ N/m of force per meter between two infinitely long, parallel wires 1 meter apart. The modern definition uses a fixed value of the elementary charge.
For household currents (15 A), forces are millinewtons per meter — negligible. For industrial busbars carrying thousands of amps, forces can be hundreds of N/m and require robust mechanical support, especially during fault currents.
Fault currents can be 10–100× normal current, and the force scales as I². A 10× current increase means 100× force — busbar systems must be designed to withstand these brief but enormous mechanical loads.
No — the magnetic force depends only on current and geometry, not wire material. However, wire resistance (material-dependent) affects power loss and heating.
This formula assumes parallel, infinitely long wires. For non-parallel or finite wires, numerical integration of the Biot-Savart law is required.