We place four small magnetic needles around a vertical straight wire (or better a few wires in parallel), which is part of an electrical circuit. When the switch is in the open position, we see that the all compasses needles are in the north direction. (If they are too close they tend to couple one with another and to form a kind or ring even without the current in the wire).
When we close the switch and the wire carrying an electric current, the compass needles turns with respect to circles around the wire. In this experiment we show that electric current could be the source of a magnetic force, and that the lines form circles.
The Ampere’s part of the experiment is that the intensity of the field falls down as the inverse of the distance from the wire, and is proportional to the current  (1)
This follows from a general formulation of Ampere’s law applied for a circular symmetry. As the direction of the current matches as well, if current in two wires are opposite, the field is null.