Coulombs Law and Permittivity

Coulomb s law was published in 1785 and is thus much older than the Maxwell equations. It contained a revolutionary new parameter for an electrical property of a dielectric, the permittivity e. Coulomb s law describes the mechanical force F between two electric charges qi and q2 at a distance L  

In our context, it is of course not the properties of vacuum but the permittivity of biological materials that are of interest. It is not always clear whether s is the relative permittivity 8r (dimensionless, often called the dielectric constant) or, as in this book, the complete expression Sj. bq. For vacuum, Sj = 1. There are a lot of subscripts in use for different cases, bq does not mean permittivity at zero frequency, but the permittivity of vacuum. 8s means static permittivity. This is not the same as 8dc because static is electrostatic with no current flow, whereas DC means current flow but at zero frequency. 8m is the permittivity at very high frequencies. And indeed here it may be high frequencies up in the optical range. The relationship between the optical refractive index n and the permittivity is roughly n = /b.  

The Coulomb force will try to unite charges of opposite sign (even if other forces hinder it at close distance in an atom). Note that coulomb forces are smaller the larger the permittivity of the medium. If the medium is water with the large relative permittivity of around 80, the forces are relatively small, and water will tend to break up (dissociate) solute molecules held together by Coulomb forces. 

As seen from Table 3.1, the permittivity of water is reduced by the addition of electrolytes. This dielectric decrement Ae is for 1 mol/L concentration —17 for HT , —8 for Na and K, —3 for CP, and —13 for OH . It is directly related to the hydration of the ion, because these water molecules are more tightly bound and therefore not so easily polarized as free water molecules. The number of hydrated water molecules around a monovalent ion is of the order of 5 (see Table 2.4). 

The concept of electric field is derived from Coulomb s law. There is an electric field at a location if a charge there is influenced by a mechanical force f (space vector) proportional to the charge  

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