Dielectrics

Polarization Vector

The polarization vector helps describe how much the charges are polarized. The polarization vector $\vec{P}$ is a smoothed point function and represents the volume density of the electric Dipole Moment. It is defined mathematically by $\vec{P}={\lim }_{\Delta v\to 0}\frac{1}{\Delta v}{\sum }_{i=0}^{n\Delta v}{\vec{P}}_i$ where ${\vec{p}}_i$ is the Dipole Moment.

We can write $\vec{P}$ as linearly proportional to the electric field intensity (assuming the dielectric properties of the medium are linear and isotropic): $\vec{P}={ϵ}_0{\chi }_e\vec{E}$

${\chi }_e$ is Electric Susceptibility

After some derivation from this above equation knowing about the Electric Flux Displacement Vector, $\vec{P}={ϵ}_0({ϵ}_r-1)\vec{E}$

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