Coulomb Interaction and Bjerrum Length

The electric potential rjr (r) due to a point-charge ezi at a radial distance r = r from the center of the ion is given by the Coulomb law. 

Therefore, the electric potential (V 1/r) and the electric field E 1/r ) due to a charge are long-ranged. This is to be contrasted with the hydrophobic forces that operate only at monomeric distances and hence short-ranged. When another ion of charge ezj is placed at a distance r from the first ion, the 

Substituting Equation 3.2 for V (r) in the above equation, the electrostatic energy of a pair of ions of charges zte and zje, separated by a distance r, is given by the Coulomb energy, 

The strength of the interaction depends on the valencies of the ions and the dielectric constant of the medium, in addition to the fundamental constants e and eo. A convenient measure of the strength of the electrostatic interaction between two ions in a medium with uniform dielectric constant e is the Bjerrum 

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