Homogeneous electric field power

If a molecule is placed in a homogeneous electric field, its energy changes as a result of orientation and polarization. The new energy E can be expressed as a power series of the field strength S ... 

The electric power P passing from a homogeneous electric field to a dielectric (which uniformly fills the field), is in the general case... 

The proportionality constant at the third-power term (the powers of electric field intensity) in the expression for the energy of a molecule in a homogeneous electric field is ... 

The incorporation of turntables and mode mixers to the domestic oven have been employed to reduce non-uniformity within the cavity and consequently reduce the number of hot and cold spots. On scale-up it is important that homogeneity is maintained and the temperature within the bulk medium is consistent. With a single mode reactor, the sample can be located precisely within the cavity where the electric field strength will be maximal. This in turn allows tuning of the power input into the sample and very high internal heat transfer. 

These domestic ovens (with limited power at 800-1000 W) are characterized by a non-homogeneous distribution of electric field due to several reflections on the metallic walls of the oven. Their use for synthetic purposes requires a previous cartography to determine the hot spots of high energy using a filter paper sheet impregnated with a solution of cobalt chloride [113] (Scheme 24). 

These drawbacks led to the development of monomode applicators that focus the electromagnetic waves in an accurately dimensioned wave-guide. This allows a homogeneous distribution of the electric field and can be used with a low emitted power with a high energetic yield (Scheme 25). 

Electrosurgery is based upon the heat effect of the current, and this is proportional to tissue conductivity a and the square of the current density (and the electric field). The power volume density Wy is falling extremely rapidly with distance from the electrode, as shown by the equation for a voltage driven half sphere electrode at the surface of a half infinite homogeneous medium Eq. 10.12. With constant ampUmde current i the power volume density Wy is ... 

The above calculation represents an example of the application to an atom of what is called the finite field method. In this method we solve the Schrodinger equation for the system in a given homogeneous (weak) electric field. Say, we are interested in the approximate values of Uqq/ for a molecule. First, we choose a coordinate system, fix the positions of the nuelei in space (the Born-Oppenheimer approximation) and ealeulate the number of electrons in the molecule. These are the data needed for the input into the reliable method we choose to calculate E S). Then, using eqs. (12.38) and (12.24) we calculate the permanent dipole moment, the dipole polarizability, the dipole hyperpolarizabilities, etc. by approximating E(S) by a power series of Sq A. 

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