Is there a way to make an experimental magnetic head?
The simplest diy magnetic probe is a cassette tape reader head, wired to a 3.5mm audio plug. A computer or even cell phone audio jack can then be used to see the waveform output of the mag card. You simply need to position the head at the right height to read each of the 3 tracks possible on a standard credit card.

Some of the first generation of cell phone audio jack card readers like square and PayPal used, were just that. Prior to it being found out and exploited, forcing them to add hardware to stop it. https://hackaday.com/2012/04/18/reading-credit-cards-with-a-tape-head/