Magnetic Force⚠ unverified
Physics / Electromagnetics · Compute the magnetic force between two parallel current-carrying wires
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| I1 | I1 | A | 1.0 | Current |
| I2 | I2 | A | 1.0 | Current |
| L | L | m | 1.0 | Length of the wires over which the force acts |
| r | r | m | 1.0 | Separation distance between the wires |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | F | N | Magnitude of the force between the wires, in newtons (N). Returns 0.0 when ``r`` is not positive |
The science & history
Understanding the Parameters
- $I_1$, $I_2$ — force $\propto I_1 I_2$.
- $L$ — longer parallel run → larger total force.
- $r$ — closer wires → stronger force ($1/r$).
- $F$ — basis of the SI ampere definition historically (force between currents).
Derivation (Approaching a Proof)
Wire 1 produces $B_1 = \mu_0 I_1/(2\pi r)$ at wire 2 (Magnetic Field Wire). Force on wire 2: $F = I_2 L B_1$ (currents parallel, $B\perp I$), hence $F = \mu_0 I_1 I_2 L /(2\pi r)$. Equivalent to the Lorentz force on moving charges in the wire.
History
Ampère’s force law between currents founded classical electrodynamics and the ampere as a base unit.
Related Concepts: Magnetic Field Wire, Lorentz Force, Poynting Vector
Notes: Registry calculator magnetic-force (unverified). Infinite parallel wires; free space.