When do wires attract?

Parallel wires carrying current in the same direction attract each other. Wires carrying current in opposite directions repel. This is due to the interaction of their magnetic fields.

How strong is the force?

For typical household currents (10A) at 1cm separation, the force is about 2×10⁻⁴ N/m — very small. At high currents (kA) in busbars, the force can be significant enough to bend or break conductors.

μ₀ is the permeability of free space = 4π×10⁻⁷ T·m/A. It is a fundamental physical constant that describes how magnetic fields propagate in vacuum.

Is this force related to the definition of the ampere?

Historically, yes. The ampere was defined as the current producing 2×10⁻⁷ N/m between two wires 1m apart. Since 2019 the ampere is defined by fixing the electron charge, but the force equation remains the same.

Magnetic Force Between Wires Calculator

F/L = μ₀I₁I₂ / (2πd)

μ₀ = 4π×10²⁻&sup7; T·m/A

Force Between Two Parallel Conductors

I₁ Current 1

I₂ Current 2

d Separation

L Wire Length

For total force (default 1m for F/L)

Enter both currents and separation

Magnetic Force Results

Force per Length (F/L)
—
N/m

Total Force

—

Direction

—

Figure 1: Parallel wires carrying current in the same direction attract; opposite directions repel. The force is proportional to both currents and inversely proportional to separation distance.

Table of Contents

Fundamentals

What Is the Force Between Wires?
Ampère’s Force Law

Worked Examples

Household Wiring
Industrial Busbars
Fault Current Forces

Deep Dive

Busbar Design Considerations
The Ampere Definition

Reference

Frequently Asked Questions
Related Circuit Analysis Calculators

What Is the Force Between Wires?

Two parallel wires carrying electric current exert a force on each other through their magnetic fields. If the currents flow in the same direction, the wires attract; if in opposite directions, they repel. This force is usually tiny for household currents but becomes significant at the high currents found in power distribution, motor windings, and fault conditions.

The Magnetic Force on Wire Calculator computes the related force on a single wire in an external magnetic field. Both effects stem from the same electromagnetic interaction described by the Lorentz force law.

Ampère’s Force Law

F/L = μ₀ × I₁ × I₂ / (2πd)
Where μ₀ = 4π×10²⁻&sup7; T·m/A, I₁ and I₂ are the currents (A), d = separation (m), F/L = force per unit length (N/m).

Worked Example — Household Wiring

Given: I₁ = I₂ = 10 A, d = 1 cm, L = 1 m

F/L = (4π×10²⁻&sup7; × 10 × 10) / (2π × 0.01) = 2×10²⁻&sup4; N/m = 0.2 mN/m

At household current levels, the force is negligible — about the weight of a grain of rice per metre. This is why normal wiring does not need mechanical bracing. The Circuit Current Calculator can find the current for any given circuit.

Worked Example — Industrial Busbars

Given: I₁ = I₂ = 1000 A (1 kA), d = 5 cm, L = 2 m

F/L = (4π×10²⁻&sup7; × 1000 × 1000) / (2π × 0.05) = 4 N/m

F = 4 × 2 = 8 N — enough to bend unsupported busbars.

Worked Example — Fault Current Forces

Given: I = 50 kA fault current (both wires), d = 10 cm, L = 1 m

F/L = (4π×10²⁻&sup7; × 50000 × 50000) / (2π × 0.1) = 5000 N/m = 5 kN/m

During a short-circuit fault, magnetic forces can be enormous — enough to rip busbars from their supports. Switchgear and busbar systems must be designed to withstand these peak forces.

Busbar Design Considerations

Power distribution busbars must be mechanically braced to withstand magnetic forces during fault conditions. Support spacing depends on the maximum fault current, conductor separation, and busbar stiffness. Standards like IEC 61439 specify the mechanical withstand requirements. The Power Dissipation Calculator helps check the thermal rating of busbars under normal operating current.

The Ampere Definition

Until 2019, the ampere was defined as the current that produces a force of 2×10²⁻&sup7; N/m between two infinitely long parallel wires 1 metre apart. This made the force between wires the defining measurement for electrical current. Since 2019 the ampere is defined by fixing the elementary charge, but the force formula remains physically valid and unchanged.

Frequently Asked Questions

Why do same-direction currents attract?

Each wire creates a magnetic field that circles around it. Between same-direction wires, the fields partially cancel, creating lower pressure between them than outside. The wires are pushed together by the higher external field pressure. This can be derived from the Lorentz force on the moving charges.

Does this force exist in AC circuits?

Yes. The force is proportional to I₁×I₂. For AC, the instantaneous force oscillates at twice the line frequency. The average force on a single-phase circuit is zero (currents in opposite directions in go and return wires), but during faults both directions carry the same current momentarily.

How far apart should busbars be?

Busbar spacing is determined by insulation requirements (voltage clearance) and mechanical withstand (fault current forces). Typical low-voltage busbars are spaced 20–60 mm apart with supports every 300–600 mm.

Can this force be used for measurement?

Yes. Current balances (Ampere balances) measure current by weighing the magnetic force between coils. This was historically the primary method for calibrating current standards before electronic calibration methods.

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Last updated: March 2026