A simple experiment is described to verify the current dependence of Ampère's law for a long straight current-carrying conductor. A narrow and long rectangular multi-loop design is used to increase the strength of the magnetic field in between the long sides. As expected, the magnetic field is found to be linearly proportional to the electric current. The current dependence of the magnetic field is used to determine the value of a fundamental constant--the permeability of free space--with acceptable experimental error. Theory predicts that the effect of narrow sides is only 2% for a width-to-length ratio of 0.2, hence smaller dimensions, down to 20 cm × 4 cm, can be employed conveniently for good results.