Ampère's force law
Also known as the Force between parallel conductors.
Two long parallel conductors carrying currents attract each other when the currents flow in the same direction and repel when they flow in opposite directions, with a force per unit length proportional to the product of the currents and inversely proportional to the distance between them.
F/l = μ₀ × I₁I₂ / (2πd)
- F/l
- force per unit length on each conductor (newtons per metre)
- I₁, I₂
- the two currents (amperes)
- d
- distance between the conductors (metres)
- μ₀
- permeability of free space = 4π × 10⁻⁷ H/m
In plain English: Parallel currents pull together, antiparallel currents push apart — each wire sits in the other's magnetic field. Two wires 1 m apart carrying 1 A each feel exactly 2 × 10⁻⁷ N per metre; that tidy number is no accident — it's how the ampere itself was defined until 2019.
Where you'll meet it: The old SI definition of the ampere, busbar bracing in switchgear (fault currents slam parallel conductors together violently), and the standard 'force between parallel conductors' exam numerical.