You can multiplex them. Look into port expanding.

would I really need to? I was just thinking about it, and I can use the same PWM output to energize more than one electromagnet at a time and acheive a pull/push that way. I.e if I have one magnet on one end of the pad, and another directly across, I can orient them in such a way that the field would point towards one of the magnets, and would attract the mouse to it.

 

You will need a reverse bias Schottky Diode across the coil - aka a snubber.

PWM with an inductor works to allow an average current to flow.

During the on phase the current builds a magnetic field.

During the off phase, the magnetic field collapses while the inductor conducts through the snubber.

Without the snubber the coil would raise up a high voltage of CEMF.

If you understood all of this already then that is fine, but I thought I might as well make certain that you were aware.

Would I also need a resistor in series with the reverse bias shottky so that it could discharge the buildup to the resistor?

Thank you.