Polarization density and genomes
Overview1 2
Conductors contain a high concentration of free charges. This means that many electrons are not bound to any particular nucleus and freely roam the interior of the conductor. Conversely, in dielectrics or insulators, the situation is different. All electrons are bound to specific atoms (molecules). While they can move slightly within the molecule, they cannot move freely like free charges. An example of this slight movement is polarization.
Polarization
Consider a dielectric composed of neutral atoms (or nonpolar molecules) placed in an electric field. Even though one might think the dielectric, being neutral, would not be affected by the electric field, in reality, it is.
Viewed from the outside, an atom appears electrically neutral, but inside, the nucleus carries a charge of $+q$, and it is surrounded by an electron cloud carrying a charge of $-q$. Therefore, the nucleus and the electron cloud experience forces in opposite directions due to the external electric field $\mathbf{E}$.
If the external electric field is very strong, theoretically, the nucleus and electrons could separate, forming an ion. However, if the electric field is not too strong, the electron cloud and nucleus attract each other and remain slightly apart, maintaining equilibrium. Thus, it’s as if there are two point charges of equal magnitude but opposite sign, causing each neutral atom to have a dipole moment parallel to the electric field. This phenomenon, where the electron cloud of an atom (molecule) shifts to one side due to the external electric field, is called polarization.
Two charges of equal magnitude but opposite sign, as shown in the image above, are referred to as a physical dipole. The magnitude of the physical dipole’s dipole moment is equal to the product of the distance between the charges and the magnitude of the charge. The direction of the physical dipole’s dipole moment is the vector pointing from $-$ to $+$.
Atoms polarized by an external electric field have a very small dipole moment $\mathbf{p}$. Its magnitude, if the electric field is not too strong, is proportional to the external electric field, and its direction is the same as the external electric field.
$$ \mathbf{p}=\alpha \mathbf{E} $$
The proportionality constant $\alpha$ is called the atomic polarizability, which varies according to the internal structure of the atom. In three dimensions, this relationship is generally represented as the linear equation below.
$$ \begin{pmatrix} p_{x} \\ p_{y} \\ p_{z} \end{pmatrix} = \begin{pmatrix} \alpha_{xx} & \alpha_{xy} & \alpha_{xz} \\ \alpha_{yx} & \alpha_{yy} & \alpha_{yz} \\ \alpha_{zx} & \alpha_{zy} & \alpha_{zz} \end{pmatrix} \begin{pmatrix} E_{x} \\ E_{y} \\ E_{z} \end{pmatrix} $$
The matrix containing $\alpha_{ij}$ as elements is called the polarizability tensor. In the case of molecules, the situation is not as simple as described above, since molecules consist of multiple atoms. Depending on the molecular structure, there might be a direction that is polarized more easily. Therefore, the direction of the induced dipole moment of the molecule generally does not align with the external electric field $\mathbf{E}$.
Polarization Density
When measuring polarized charges, it’s impractical to count each individual atom. Hence, the polarization density $P$, a physical quantity used to gauge the degree of polarization, is defined as the dipole moment per unit volume.
$$ \mathbf{P} := \dfrac{ \text{dipole moment}}{\text{unit volume}} $$
In Griffiths’ Electrodynamics, “polarization” is translated as polarization density.