Calculation
F/l = μ0·I1·I2/(2π·a)
Conductors carrying current in the same direction attract; force per length grows with both currents and falls with conductor spacing.
Busch 2006, Abschnitt 2.7.2, Gl. (2.72) Leiter im Feld eines anderen Leiters
Force between two parallel current-carrying conductors
Conductors carrying current in the same direction attract; force per length grows with both currents and falls with conductor spacing.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Force per length F/l — Attractive (same current direction) or repulsive force per metre of conductor length.
- Current in first conductor I1 — Current magnitude in the first of the two parallel conductors.
- Current in second conductor I2 — Current magnitude in the second of the two parallel conductors.
- Conductor spacing a — Distance between the two conductors' centre axes.
Example
I1=I2=10 A at 1 cm spacing give F/l=2 mN/m.
Assumptions and limits
Infinitely long, thin, parallel conductors in vacuum or air (μr≈1); real conductor cross-sections, finite length and ferromagnetic surroundings are excluded.
Understand Force between two parallel current-carrying conductors
This calculator determines the force per unit length between two parallel current-carrying conductors, the basic magnetic force effect that once underpinned the definition of the ampere.
What does this quantity describe?
Two parallel conductors spaced a apart carrying currents I1 and I2 exert force per length F/l=μ0·I1·I2/(2π·a) on each other. They attract when currents flow the same direction and repel when opposite.
Formula and variables
F/l = μ0·I1·I2/(2π·a)
F/l = μ0·I1·I2/(2π·a)
| Symbol / input | Meaning |
|---|---|
| Force per length F/l | Attractive (same current direction) or repulsive force per metre of conductor length. |
| Current in first conductor I1 | Current magnitude in the first of the two parallel conductors. |
| Current in second conductor I2 | Current magnitude in the second of the two parallel conductors. |
| Conductor spacing a | Distance between the two conductors' centre axes. |
Choose the inputs correctly
I1 and I2 are the currents in the two conductors, a is the distance between their centre axes.
How to use the calculator
Take currents and spacing from the actual wiring layout; for multi-core cables use the spacing of the cores considered.
Worked example
I1=I2=10 A at 1 cm spacing give F/l=2 mN/m.
Understand the result and units
Force grows with the product of both currents and falls inversely with spacing; at fault currents this can produce substantial mechanical loading on busbars.
I1 and I2 are currents, a a length. F/l is output as force per length.
Typical applications
Estimating mechanical short-circuit forces on parallel busbars and conductors, and illustrating magnetic force effects in teaching.
Assumptions, limits and common mistakes
Ideal infinitely long, thin, parallel conductors in vacuum or air; finite conductor length, real cross-sections and ferromagnetic surroundings are excluded.
Common mistake: Do not forget that opposite current direction produces a repulsive rather than attractive force; the formula's magnitude is unchanged.
Frequently asked questions
What is “Force between two parallel current-carrying conductors” used for?
Estimating mechanical short-circuit forces on parallel busbars and conductors, and illustrating magnetic force effects in teaching.
Where do the input values come from?
I1 and I2 are the currents in the two conductors, a is the distance between their centre axes.
What does the result not cover?
Ideal infinitely long, thin, parallel conductors in vacuum or air; finite conductor length, real cross-sections and ferromagnetic surroundings are excluded.