Why does aluminium foil spark in the microwave? I don't understand fully why aluminium foil sparks in a microwave oven? 
I think what is happening is the oven sets up an electric field, and the field induces a current in the foil (how?), and current in the foil then produces a very strong electric field which causes dielectric breakdown of the air, which is why we see sparks.
I think I'm confusing some electromagnetism concepts or something.
 A: The reason for the sparking is the photo-electric effect.  The microwaves energize outer orbital electrons in metals and causes emission.  Due to the conductive nature of the Al and insulting nature of the air (it's a dielectric), the electron charge can build.  However, recombination of electrons into the orbitals is possible, but very slow compared to the discharge rate. The resulting charge becomes strong enough to ionize the air and create a conductive path to the walls of the microwave.  
The electro-magnetic fields are highly dependent on the topology of the metal object.  Where you have a sharp edge, there is a significant concentration of electric potential and therefore, the edge is more likely to discharge the electrical charge build-up.  
Another example of this topological effect are tesla coils, where you'll often observe that folks place a rod on the torus to force the arc to originate that the end of the rod.  The charging mechanism of electrons to the torus is completely different in this case, however.
A: I have read no less than six different explanations of why aluminum foil sometimes sparks in a microwave.  This is my best guess: Microwave ovens operate at about 2.45 Ghz.  Water absorbs the non-ionizing radiation and becomes more active, creating heat.  But aluminum foil, like all shiny metal, does not absorb microwaves - it reflects them.
Because the microwave energy is limited to the surface of reflective metal, only the surface electrons of the aluminum foil are excited (although if the foil is REALLY thin, it could transfer surface excitation heat to the food beneath).
Loosely bound to their nuclei, mobile among molecules (which is why metal carries electric current well), and driven by the microwave magnetron, these excited surface electrons set up currents and electric fields.
If there are sharp edges and crinkles in the metal, the fields intensify there.  This is because electrons, which all have like charge, want to avoid each other, so in the absence of a positive charge to attract them, they flow to narrow sharp edges where the electron population is not as numerous as on the flat surfaces.  Intensifying fields at sharp edges may create enough potential difference to cause a current to jump to the microwave oven's metal walls.
Microwave ovens are designed to discourage such antenna-like behavior, but if a current does jump through the air within the oven, it may exceed the dielectric breakdown strength of the air molecules (30 Kv per centimeter) and strip electrons from them, ionizing the air through which current travels.  When the air becomes a conductor, it creates a spark.  If the circuit breaker doesn't blow, an electric arc may appear.
