Editing Polarization density (section)

==Other expressions==

Let a volume {{math|d''V''}} be isolated inside the dielectric. Due to polarization the positive bound charge <math>\mathrm d q_b^+</math> will be displaced a distance <math>\mathbf d </math> relative to the negative bound charge <math>\mathrm d q_b^-</math>, giving rise to a dipole moment <math> \mathrm d \mathbf p = \mathrm d q_b\mathbf d</math>. Substitution of this expression in {{EquationNote|1|(1)}} yields
<math display="block">\mathbf P = {\mathrm d q_b \over \mathrm d V}\mathbf d </math>

Since the charge <math>\mathrm d q_b</math> bounded in the volume {{math|d''V''}} is equal to <math>\rho_b \mathrm d V</math> the equation for {{math|'''P'''}} becomes:<ref name="Irodov" />
{{NumBlk||<math display="block">\mathbf P = \rho_b \mathbf d </math>|{{EquationRef|2}}}}
where <math> \rho_b </math> is the density of the bound charge in the volume under consideration. It is clear from the definition above that the dipoles are overall neutral and thus <math> \rho_b </math> is balanced by an equal density of opposite charges within the volume. Charges that are not balanced are part of the free charge discussed below.