The Quarter Shrinker was constructed by Rob Flickenger at Hackerbot Labs.
Quarter Shrinking has three steps.
1. make a coil of wire,
2. stick quarter inside it,
3. discharge an enormous amount of electric current through the coil.
Passing current through a coil of wire produces a magnetic field. In this case, with so much current, the magnetic field produced is gigantic: the coil becomes a magnificently powerful electromagnet.
The creation of a magnetic field in the coil-now-magnet induces a circling current to flow around the coin sitting inside the coil. This current in the coin also produces a magnetic field (i.e., the coin becomes another electromagnet). The kicker is that the coin’s magnetic field and the coil’s magnetic field point in opposite directions, so the coin and the coil repel each other furiously.
This repulsion creates forces which overcome the strength of the metal; the coil is expanded out and explodes, and the coin is pushed in and shrunk.
Theory of Operation of the Quarter Shrinker– http://capturedlightning.com/frames/shrinker.html
More information on the physics which make the coin deform– http://en.wikipedia.org/wiki/Pinch_(plasma_physics)