Define electric dipole and polarization

Electric dipole

An electric dipole consists of two equal and opposite point charges, +Q and −Q, separated by a small distance d. Its dipole moment is the vector

p = Q d   (C·m), directed from −Q to +Q

Far from the dipole, the potential is V = p cosθ/(4πε₀r²) and the field falls off as 1/r³. A dipole placed in a field E experiences a torque T = p × E.

Polarization

Polarization P is the dipole moment per unit volume of a dielectric:

P = lim(Δv→0) (Σ pᵢ)/Δv    (C/m²)

When an electric field is applied to a dielectric, its atoms or molecules form (or align) electric dipoles, so the material becomes polarized. For a linear, isotropic dielectric,

P = ε₀ χ_e E = ε₀(ε_r − 1)E
D = ε₀E + P = ε₀ε_r E