Measuring the strength of a magnetic field with a microcontroller
so I believe the ADC is picking up the 50/60Hz AC sine wave from the wall, so it's detecting magnetic/electric field.


Electric field, but not magnetic field. The wire and the AC mains wire work like a low value capacitor, allowing the 50/60 Hz to pass through to the ADC.


  The problem is when I place my inductor circuit next to the microcontroller and trigger it, the micro-controllers ADC doesn't pick up anything


It cannot pick anything up. The frequencies required for any measureable inductive coupling into a 6cm wire are in the GHz range and waaay outside usable ADC frequencies on an AVR µC.