Ampère's Force Law: Force between Parallel Currents

Ampère's force law for parallel currents can be regarded as an analog of Coulomb's law for charges. The force per unit length between two current elements separated by a distance is given by , where is the permeability of free space. In contrast to Coulomb's law, parallel current elements attract (signified by the minus sign) while opposing currents repel. The formal SI definition of the ampere is "the constant current which will produce an attractive force of 2⨯10^{-7} newtons per meter of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one meter apart in a vacuum."

Ampère's force law is a consequence of the Lorentz force on the moving charge in each current element acted upon by the magnetic field produced by the other current element: .