the heating effects of low frequency fields that depend on slower molecular motion, such as those caused by ion-drag. Power Dielectric heating must be distinguished from Joule heating of conductive media, which is caused by induced electric currents in the media. For dielectric heating, the generated power density per volume is given by: where ω is the angular frequency of the exciting radiation, εr″ is the imaginary part of the complex relative permittivity of the absorbing material, ε0 is the permittivity of free space and E the electric field strength. The imaginary part of the (frequency-dependent) relative permittivity is a measure for the ability of a dielectric material to convert electromagnetic field energy into heat, also called dielectric loss. (The real part of the permittivity is the normal effect of capacitance and results in non-dissipative reactive power.) If the conductivity σ of the material is small, or the frequency is high, such that (with ), then Joule heating is low, and dielectric heating is the dominant mechanism of loss of energy from the electromagnetic field into the medium. Penetration Microwave frequencies penetrate conductive materials, including semi-solid substances like meat and living tissue. The penetration essentially stops where all the penetrating microwave energy has been converted to heat in the tissue. Microwave ovens used to heat food are not set to the frequency for optimal absorption by water. If they were, then the piece of food or liquid in question would absorb all microwave radiation in its outer layer, leading to a cool, unheated centre and a superheated surface. Instead, the frequency selected allows energy to penetrate deeper into the heated food. The frequency of a household microwave oven is 2.45 GHz, while the frequency for optimal absorbency by water is around 10 GHz. Radio-frequency heating The use of high-frequency electric fields for heating dielectric materials had been proposed in the 1930s. For example, (application by Bell Telephone Laboratories, dated 1937) states:"This invention relates to heating systems for dielectric materials and the object of the invention is to heat such materials uniformly and substantially simultaneously throughout their mass. It has been proposed therefore to heat such materials simultaneously throughout their mass by means of the dielectric loss produced in them when they are subjected to a high voltage, high frequency field."This patent proposed radio frequency (RF) heating at 10 to 20 megahertz (wavelength 15 to 30 meters). Such wavelengths were far