# Polarization Vector

The polarization vector helps describe how much the charges are polarized. The polarization vector $P$ is a smoothed point function and represents the volume density of the electric Dipole Moment. It is defined mathematically by $P=lim_{Δv→0}Δv1 ∑_{i=0}P_{i}$ where $p _{i}$ is the Dipole Moment.

We can write $P$ as linearly proportional to the electric field intensity (assuming the dielectric properties of the medium are linear and isotropic): $P=ϵ_{0}χ_{e}E$

$χ_{e}$ is Electric Susceptibility

After some derivation from this above equation knowing about the Electric Flux Displacement Vector, $P=ϵ_{0}(ϵ_{r}−1)E$