What will happen if you put a lighted match stick in a microwave oven?

When it is already lighted it only has the burned ash and the paper stick. Nothing is likely to happen (except with metal impurity particles in the paper stick) when those are exposed to a household microwave field.

A DRIED not-yet-lighted high quality match stick, or even a glass cup of gasoline liquid, should in theory not burn in the household microwave field. WARNING: DO NOT TRY THIS AT HOME. A TINY METAL IMPURITY PARTICLE IN THE MATCH HEAD OR IN THE GASOLINE SHALL, HOWEVER, BE HEATED INSTANTLY TO CAUSE THE WHOLE THING TO BURN AND EXPLODE.

The induction heating of a typical household microwave was designed targeting the polarization and molecular-bond elastic strength of the water molecules. For each water molecule, the two hydrogen atoms are not symmetrically bonded to the oxygen atom causing a dipoleā€”a nanostructure that has separated positively and negatively charged ends. The alternating electromagnetic filed of the household microwave oven agitates those water molecule dipoles back and forth causing a raising of bulk temperature.

Any non-electrically conductive solid or any liquid that cannot dissolve with water (non-polarized liquids) cannot be heated by a household microwave oven.

Electrically conductive materials, such as metals, have free charge carriers which are much easier moved by an electric field than the dipoles of the water molecules and hence would aggressively collide to one another and would explode the bulk when excited by a (water-optimized) household microwave.

There are other industry or laboratory induction heating chambers that target metals and other polarized non-metals. Some of those chambers can melt tonnes of steel but might not warm up a small bowl of water-based soup.
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