Density near the Central Ion Is Determined by Electrostatics Poissons Equation

Charge Density near the Central Ion Is Determined by Electrostatics Poisson s Equation 

Consider an infinitesimally small volume element dVsituated at a distance r from the arbitrarily selected central ion, upon which attention is to be fixed during the discussion (Fig. 3.8), and let the net charge density inside the volume element be g,. Further, let the average electrostatic potential in the volume element be y/. The question is What is the relation between the excess density g in the volume element and the time-averaged electrostatic potential y/  

One relation between g and is given by Poisson s equation (Appendix 3.1). There is no reason to doubt that there is spherically symmetrical distribution ofpositive and negative charge and therefore excess charge density around a given central ion. Hence, Poisson s equation can be written as 

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