How can you have heat without fire? It's not magic, it's science. Specifically, the science of induction, where strong electric fields can create heat. Induction cooktops use this to heat food without any flames or direct heat, cooking more efficiently than their gas or conventional electric cousins. And this lack of direct heat makes them safer, too: you can even put paper between an induction cooktop and a pan, and it won't catch light.
Induction cooktops are also more efficient than other types of cooking methods. Because the heat is generated inside the base of the pan, they use less electricity than conventional electric cooktops, and can heat things quicker. They are also easier to clean, because the flat glass or ceramic surface has no gaps or grills to collect spilled food, and the food doesn't get burned onto the surface. If you spill something, one quick swipe with a damp cloth will clean it up. They are also quicker to control and more precise, again because the heat is generated inside the cookware, and so react quicker when you turn the dial up or down.
So why aren't they more common? It's partly a comfort thing; most US consumers don't like them because they grew up on gas rings. Samsung has recently introduced an interesting solution to this problem: a cooktop that, and indicates the heating level. Induction cooktops are also more expensive, because they are more complex than the more common gas type.
But the main issue is with which cookware you can use with them. Because of the way they work, many types of pans just don't heat up with induction cooktops. If you have copper bottom, glass or aluminum pans, they don't get hot when you put them on an induction cooktop.
How they work
Induction cooktops use one of the odd quirks of electromagnetism: if you put certain materials into a rapidly alternating magnetic field, the material absorbs the energy and heats up. That's because the field creates electrical currents inside the material, and the resistance of the material converts this electrical energy into heat, which is transferred to the food inside the pan.
Right underneath the cooking area of an induction cooktop is a tight spiral of cables, usually made of copper. The cooktop controller pushes an alternating current through this coil, which changes direction usually 20 to 30 times a second. This current flow creates a magnetic field above the coil. As the current alternates back and forth, the magnetic field does the same. If you put a pan on the surface (so it is just above the coil), this magnetic field induces (hence the name) an electrical current in the metal base of the pan. As the magnetic field alternates, this current flows back and forth (which is why it is often called an eddy current, as it swirls around like an eddy in a river). The metal resists this flow, and, like an electric heater, creates heat, which is conducted into the food through the metal of the pan. If you want to gently heat the food, the cooktop pumps a lower current through the coil, so the cookware generates less heat, and the food warms slower.
The limitations of induction
The Achilles heel of this process is that it only works with pans made of certain materials that have specific properties. In order to be heated by the magnetic field, the cookware has to be made of a ferromagnetic material, such as stainless steel or iron.
Electrons have a property called spin, where they can behave like a tiny magnet pointing in a specific direction. The reasons for this are complex (it gets into the crazy world of quantum mathematics and the strange nature of sub-atomic particles), but the basic idea is that, depending on where they are surrounding the nucleus of an atom, electrons spin on one direction (called up) or the other, called down. Ferromagnetic materials have an unbalanced set of electrons, where there are more up-spin electrons than down ones in each atom, or vice versa. This means that the atoms that make up the material can behave like a tiny magnet, and can be influenced by magnetic fields. The larger crystal structure of the material also helps by keeping the atoms aligned so this effect is increased.
Non-ferrous materials like zinc and most non-metals have a balanced set of electrons, where every up-spin electron is matched to a down-spin one. So, they aren't affected by magnetic fields nearly as much as the ferrous ones: the magnetic field only creates very small eddy currents that aren't enough to heat things up.
This does mean that there is an easy way to check if your pans will work with an induction stovetop. If you touch them with a magnet and it sticks to the bottom of the pan, they can be used on an induction cooktop. If the magnet doesn't stick, they won't work with induction. Many pan manufacturers are also now introducing a special mark on the pan that shows they are suitable for use on an induction cooktop: the Induction Mark.
The future of induction
Induction cooktops remain a niche market: according to the Association of Home Appliance Manufacturers (AHAM), only 7 percent of the cooktops sold in the first quarter of 2014 in the USA were induction models. That isn't true in other countries, thoug': the percentage of induction cooktops in Germany is 17 percent, and is even higher in other parts of Europe.
There have been attempts to get around the limitations of induction cooking: Panasonic introduced a model in 2009 that they claimed worked with all metal cookware, widening the range of pans that could be used. This worked by increasing the frequency of the alternating magnetic field, so the current in the pans flowed faster, and produced the heating effect in a wider range of metals. However, this model does not seem to be available outside of Japan, and it was more expensive than normal induction cooktops, so it doesn't seem to have been a success. According to some reports, this high-frequency field caused the pans to levitate slightly, so the manual recommended that the pans should always be fairly full, otherwise the pans had a habit of sliding off the cooktop.
So it seems that induction cooktops are likely to remain a niche market in the US. Which is a pity, as they are definitely a cool example of appliance science.
(One interesting note here: most chemicals, including water, have a property called dimagnetism, where molecules can act like very small magnets. With a strong enough magnetic field, this property can make objects levitate. This was the effect used by M Berry and Andre Geiym when they levitated a frog in 1997. But don't try this at home, because the type of magnetic field used was incredibly strong, at over 16 Teslas. That's millions of times more powerful than the magnetic field from an induction cooktop, and it required over 4 megawatts of electricity to generate. An induction cooktop only uses a few hundred watts at most. Plus, frog levitation should only be done by a qualified scientist with the appropriate safety precautions.)