**1. Introduction**

Domestic microwave ovens first appeared in American homes at the end of World War II; the American company Raytheon, which manufactured the radars for the Liberty Ships, was redirecting its production towards civilian applications. This is the case in this chapter which deals with microwave heating. The present chapter is interested in a simple water drop reduced to its electric dipoles, masses, and charges. The drop contains 1536 of them in a 3.585 nm edge cube. These dipoles are in permanent interaction and move according to a brownian movement or similar. For these dipoles, receiving an electromagnetic wave means receiving an external force additional to those they receive from the other dipoles of the drop. Their movement generates friction and thus transforms part of the captured energy into heat. We must also keep in mind the adage: "a cold-cooked carrot is no longer raw". Thus, heat produces irreversible changes. However, the cloud of dipoles similar to those of water is not a drop of water. It makes it easy to calculate its collective behavior in a microwave field, displacement, and speed of particles but does not put in thermal memory the sequence of events. Only a human program can transform the kinetic energy acquired by dipoles into thermal energy captured by water and invent a temperature scale that accumulates the sequence of events.

The expression "microwave heating" means that the material itself transforms into heat according to the equality *W = J.Q*, the electromagnetic energy it captures (1 calorie = 4.185 Joule, where *W* is mechanical energy, *J* is a universal constant, Q is a heat).

Internal movement of two electrical charges of the dipole also results in a current different from that of the free carriers in a metal or ions in the water itself, i. e., *J = σE* (where σ is electric conductivity and *E* is an electric field) is displacement current,

*<sup>∂</sup>D=∂<sup>t</sup>* introduced by Maxwell completes Ampère's equation rot *<sup>H</sup>* <sup>¼</sup> *<sup>J</sup>*, which becomes rot *<sup>H</sup>* <sup>¼</sup> *<sup>σ</sup><sup>E</sup>* <sup>þ</sup> *<sup>∂</sup>D=∂t*. This current was introduced to satisfy its continuity between capacitor terminals, even in a vacuum. The last equation is used interchangeably in metals and dielectrics to translate any heat production type. Therefore, the expression "microwave heating" is completely different from wood, gas, or coal heating, which burns and radiates the energy produced by combustion or diffuses it by conduction on the material surface to be heated. There are significant differences between the two types of heating:

