"When a molecule with a permanent dipole strength μ is surrounded by other particles, the inhomogeneous field of the permanent dipole polarizes its environment. In the surrounding particles moments proportional to the polarizability are induced, and if these particles have a permanent dipole moment their orientation is influenced. An exact calculation of the consequences of these two effects may in principle be made using the methods of statistical mechanics, but it is so difficult to take into account the interaction of the molecules and the microscopic structure of the material, that even for a gas at low pressure the statistical calculation must start from simplified models" C. J. F. BOTTCHER
To explain our interest in polarization, let us assume a liquid solution of water and ions as shown in the figure. Each water molecule is described as a spherical particle with embedded point dipole. It is well-known that the dipole moment of a water particle is about 1.85 D. Now, let us consider a reference water particle (the red sphere in the figure). The electric fields arising from other water particles and ions are going to induced a dipole moment on the reference particle. Our group has interest to determine how much the reference particle is induced as a result of nearby particles using a mean field approach. We have develop a general theory based on the self-consistent mean field theory for this purpose.