Result
Force between parallel wires
(E8.2.1) E8.2 · Force Between Parallel Conductors →Statement
The force per unit length between two long, parallel current-carrying wires separated by distance d.
Symbols and units
| force per unit length | N/m | |
| currents in the two wires | A | |
| separation | m | |
| permeability of free space | 4π×10⁻⁷ T·m/A |
When it applies
Two long, straight, parallel wires with steady currents.
Don't use when
Only for long, straight, parallel wires — non-parallel or short wires need a full Biot-Savart calculation.
Derivation
One wire's field, from the straight-wire result, acts on the current in the other wire via the force law for a current-carrying wire:
Watch out for
Currents in the SAME direction attract; currents in OPPOSITE directions repel — the reverse of the intuition many carry over from bar magnets.
Connects to