**2. Electromagnetic waves in everyday life**

#### **2.1 Elementary experiments with induction stove and microwave oven**

The active part of an induction hob is a spiral supplied with around 25 kHz and located just below the hob. The energy is not radiated, but it decreases exponentially as it moves away from the spiral. It generates a Foucault current in the surrounding conductors, which tends to move away from the inductor, i.e., from the plate.

To be convinced, one can place a sheet of household aluminum on the plate in operation. If the electrical force is greater than the weight of this aluminum sheet, the sheet will fly away and leaves the field. However, if the experimenter puts the finger on the sheet to hold it, he notices heat release. Heat generation is nature's answer of last resort. It is interesting to tear the sheet and bring the two pieces together: an electric arc appears to ensure the current continuity. This arc sometimes denominates the extra-current of rupture.

To test a microwave oven, the experimenter can heat a soup plate slightly moistened and covered with a well-joined kitchen film. He will quickly see the film inflate like a balloon. Water evaporates and naturally finds with steam a mechanical application. Obviously, one should not use valuable plates or plates decorated with conductive paint.

The experimenter could dry a piece of bread put on the same plate but pre-cooled in a refrigerator and always covered with a kitchen film. He will extract drops of liquid water and then analyze them because they include a lot of salts and other components coming from the bread itself. It is indeed very useful to analyze the evaporated drop to highlight a possible peculiarity of microwave heating and try to find out if it is due to internal friction.

It is also interesting to test the widely marketed metal trays. If the tray is placed on the metal grid of the oven, an arc will appear with the vibrations during operation. The arc can also be maintained by directly capturing microwave energy. One must follow the experiment by standing a few meters from the oven because the door grid is not completely impermeable. However, it is made to see since there is a lamp in the oven!

It is instructive to experiment with metal trays filled with common foods to test the quality of heating. The considered domestic experiments also give an order of magnitude of the masses and volumes, power, and time encountered in microwave heating, for example, one liter of water, one microwave kW, and one minute of heating. These proportions are used in the simulation program presented below. Mass and volume are related to the number of dipoles chosen since 18 cm3 of water contains *N*, Avogadro's number of molecules, and weighs 18 g. Time is measured by the period of the incident microwave field since period *T* is the inverse of the chosen frequency.

#### **2.2 Magnetron and power supply**

The magnetron is an electromagnetic wave generator, very similar, in its operating principle, to a 50 Hz alternator but which emits at very high frequencies, for example, 2.45 GHz. The magnetron constitutes a cylindrical vacuum diode formed of an electron-emitting cathode and a stator receiving anode. A continuous magnetic field is applied in the axis to spin the electrons. The rotor appears because the anode generates an alternating circular electric field, sometimes in one direction, sometimes in the other to the group–ungroup the electrons in the beam and thus find the characteristics of a real alternator winding. The electrons finish their route and reach the anode by producing heat which must be eliminated by ventilation or circulation of fluid. The electron beam, in a vacuum, can rotate very quickly (much faster than a rotor) and thus generate a high-frequency current. The anode also has an antenna that collects and emits produced electromagnetic energy.

One can find magnetrons in industrial microwave heating and radars, on roads, and in kitchens. The kitchen magnetron has a special power supply: the first 50 Hz alternation (60 in some countries) charges a capacitor, and this charge will be added to the second. Therefore, the magnetron transmits half-time and even less if the user wishes to reduce the power of his oven. Thus, the heated food makes the average value and leaves a little of the thermal energy of the hot regions to diffuse towards the cold regions. In the elementary experiments proposed above, the observer should detect that the balloon above the plate inflates and deflates in time with the power supply.
