Two wires carrying currents push or pull on each other: parallel currents attract, opposite currents repel. Until 2019 this effect defined the ampere – 1 A in each wire 1 m apart gives exactly 2 × 10⁻⁷ N per metre.
How to use the Magnetic Force Between Wires Calculator
- Current I₁
- Current I₂
- Distance between wires d
- Wire length L
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter both currents (negative for the opposite direction), the separation and the wire length.
Inputs explained
| Field | What to enter |
|---|---|
| Current I₁ | Units: A, mA, µA, kA |
| Current I₂ | Units: A, mA, µA, kA |
| Distance between wires d | Units: cm, mm, m, in, ft |
| Wire length L | Units: m, cm, mm, km, in, ft … |
What each result means
- Force per unit length = abs(1.25663706212e-06×[Current I₁]×[Current I₂]÷(2×pi×[Distance between wires d]))
- Total force = abs(1.25663706212e-06×[Current I₁]×[Current I₂]÷(2×pi×[Distance between wires d]))×[Wire length L]
Example values
How the main result changes when Current I₁ changes and everything else stays at the example values above:
| Current I₁ (A) | Total force (mN) |
|---|---|
| 5 | 1 |
| 7.5 | 1.5 |
| 10 | 2 |
| 12.5 | 2.5 |
| 15 | 3 |
| 20 | 4 |
Formula
F/L = μ₀·I₁·I₂ / (2π·d)
Worked example
Inputs — Current I₁: 10 A; Current I₂: 10 A; Distance between wires d: 1 cm; Wire length L: 1 m.
Results — Force per unit length = 0.002 N/m; Total force = 2 mN; Interaction = Attraction (same direction).
Key terms
- Ampère's force law
- Force between current-carrying conductors.
Frequently asked questions
Why do parallel currents attract?
Each wire sits in the other's magnetic field and feels a Lorentz force.
How was the ampere defined?
By this force: 2 × 10⁻⁷ N/m for 1 A at 1 m (until 2019).
Can the force be large?
Yes – short-circuit currents can bend busbars.
Does it apply to short wires?
Approximately, if the length is much greater than the separation.