A wire carrying a current generates a magnetic field. A current carrying conductor in a magnetic field will experience a force. This implies that if two wires both carrying currents are brought near to each other, there will be a force between them. If the wires are parallel, the expression for this force takes a very simple form.
The field at the position of wire 2 due to the current in wire 1 is
where
is the permeability of the substance in which the wires are embedded.
The force felt by wire 2 is
where
is the length of wire 2. The force per unit length is then
This argument is symmetrical so the force per unit length on wire 1 is also
This equation is used to define the ampere, and the coulomb is then defined to be 1 ampere second. By taking two infinitely long parallel straight wires, each carrying a current of 1 ampere, separated by a distance of 1 metre, the force per unit length is
The ampere is defined to be the current that produces this force.