A modern, rapid and simple investigation of Ampère’s law

Classical physics results are often taught purely from the theoretical side. Key results, especially in electromagnetism, are typically not explored experimentally, and in applications students are then expected to leap straight into more complex scenarios that make use of these principles in electronics, sensors and instrumentation. This is unfortunate because not all individuals are equally able to learn well purely from the mathematical angle, and even those who do are not exposed to exploring the magnitude of competing effects, for example isolating a particular magnetic field signal from the background of the Earth's field. An experiment is presented here to test Ampère’s law with a setup that can be assembled out of everyday materials with minimal components - a smartphone, a DC power supply, wires - in a procedure that can be completed in just a few hours. The data from the three magnetic field sensors of the phones, together with the gyroscope sensors providing position, are recorded and numerically integrated. The experiment is also demonstrated using sensors collected by an Arduino board instead of a smartphone. The experiment allows to measure the net current carried by wires inside the closed path over which the magnetic field is integrated, i.e. Ampere's law. This experimental approach to exploring Ampere's Law can be adapted towards high school or university demonstrations, depending on the level of accuracy and detail that one aims to pursue.