Ampere extended Oersted's observations. If a current could generate a magnetic field, then presumably, two wires carrying currents in close proximity should be able to interact magnetically.
He showed that this interaction existed, and that the wires exerted forces on each other. Parallel – or like - currents attract and antiparallel – or unlike - currents repel.
In addition there exists a simple formula expressing the force between the wires. It is proportional to each current separately, so also to their product and inversely proportional to the distance between them. We may write
The definition of the unit of current is called Ampere and is derived from the above formula. It is that constant current in each of two infinite, straight, parallel wires of negligible cross section that will produce an attractive force of
newton per metre of length when placed in a vacuum.
The constant of proportionality is then
In fact we include constants
and a 2 to give
In addition Ampere also derived a useful relationship between the integral of the magetic field around a closed loop and the current passing through the loop, which is very useful in cases where there is a lot of smmetry, allowing the magentic field to be easily calculated.