Rationalized electrical units

In Eq. D.l a factor l/(4ir) is inserted, somewhat arbitrarily, for ease in solution of many electrical theorems (e.g., Gauss ). Units which are defined as rationalized electrical units include this factor of l/(4ir) unrationalized units would omit it. 

All equations are given on a dimensionally consistent basis and can be used with any dimensionally consistent units. The illustrative units given in the following are based on the MKSA system, using the rational basis for electrical units. For the cgs-esu (irrational) system, the corresponding cgs-esu units would be used and the permittivity, e, would have a value ofl/(47r). Universal constants and defined values are represented by a symbol in Gothic (sans serif) or in bold face type. 

As an alternative procedure to predict coefficients of a radial function p(x) for electric dipolar moment, one might attempt to convert the latter function from polynomial form, as in formula 91, which has unreliable properties beyond its range of validity from experimental data, into a rational function [13] that conforms to properties of electric dipolar moment as a function of intemuclear distance R towards limits of united and separate atoms. When such a rational function is constrained to yield the values of its derivatives the same as coefficients pj in a polynomial representation, that rational function becomes a Fade approximant. For CO an appropriate formula that conforms to properties described above would be... 

A vector quantity representing the dipole moment per unit volume of a dielectric medium. In rationalized units, the electric induction in a dielectric is given by D = cE, which can be written... 

A minor variant of the SI system, called MKS by experimentalists in nonlinear optics, is called SI here and defined below. Alas, there are also other systems "rationalized" or "unrationalized", Heaviside-Lorentz, "atomic" (where me = c = h = 1), and so on. The "rationalized" and "unrationalized" versions differ in how they apportion the pesky factor An (surface area of a sphere with unit radius that is involved in surface integrals) between the various electrical and the magnetic variables. 

Table G Definitions of the Electric Field E, the (Di)electric Polarization P, the Electric Displacement D, the Magnetic Field H, the Magnetization M, the Magnetic induction or flux density B, statement of the Maxwell equations, and of the Lorentz Force Equation in Various Systems of Units rat. = rationalized (no 477-), unrat. = the explicit factor 477- is used in the definition of dielectric polarization and magnetization c = speed of light) (using SI values for e, me, h, c) [J.D. Jackson, Classical Electrodynamics, 3rd edition, Wiley, New York, 1999.]. For Hartree atomic u nits of mag netism, two conventions exist (1) the "Gauss" or wave convention, which requires that E and H have the same magnitude for electromagnetic waves in vacuo (2) the Lorentz convention, which derives the magnetic field from the Lorentz force equation the ratio between these two sets of units is the Sommerfeld fine-structure constant a = 1/137.0359895...

Finally, the magnitude of the electrical quantities must be chosen. Often the ampere is taken as the defining unit, and from the definition of the ampere a term l/(p0c2) = e0 arises. In the rationalized mks system x0 = 4tt x 10-7 N/A2 and then e0 = 8.8542 x 1012. 

Heaviside-Lorentz units A system of units for electric and magnetic quantities based upon c.g.s. electrostatic and electromagnetic units. They are the rationalized forms of Gaussian units and, like the latter, are widely used in particle physics and relativity in preference to the S1 units now employed for general purposes in physics. They are named after Oliver Heaviside (1850-1925) and Hendrik Lorentz (1853-1928). 

Although the growth of commercial nuclear power has slowed in the United States, it still accounts for about 20% of the total electricity generated. The use of nuclear energy and the disposal of nuclear wastes, however, are extremely controversial social and political issues. Because these topics evoke such a strong emotional reaction, it is often difficult to sift fact from opinion to make rational decisions. It is imperative, therefore, that we have some understanding of nuclear reactions and the uses of radioactive substances. 

These tables use the recommended SI (Systeme International) units, with some indication of their relation to other units in the literature, including electromagnetic units (e.m.u.) and the less common electrostatic units (e.s.u.), both in the centimeter gram second system (CGS). The relationships are complex four systems of equations have been used, and each of these has been written in nonrationalized and now rationalized forms/ With rationalization, explicit values and dimensions are given to the permittivity Sq of a vacuum, which was taken as unity and dimensionless in the e.m.u. system, and to the permeability taken as unity and dimensionless in the e.s.u. system. (These two systems are mutually inconsistent on the Maxwell theory the product Sq/ o is equal to c , where c is the speed of light, approximately 3 10 ms ) The physical relationships of the different systems of electrical and magnetic units have been ably described. ... 

Finally, it should be emphasized diat the quantities dp/dQ contain in a radier obscure form the structural information sought. This is due to the very complex nature of normal coordinates. It is, therefore, essential to fiulher reduce the erqierimental dp/dQk. derivatives into quantities characterizing electrical properties of molecular sub-units atomic groupings, chemical bonds or individual atoms. Various theoretical formulations for analysis of vibrational intensities have bemi put forward. The approaches developed are quite analogous to the anal)rsis of vibrational frequencies in tarns of force constants. As known, force constants may be associated with properties of molecular sub-units. If such a rationalization of intensity data is successfully performed, anothm irrqrortant aim of spectroscopy studies may become possible quantitative prediction of vibrational intensities by transferring intensity parameters between molecules containing the same... 

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