$$\require{cancel}$$
$E_{r}=-\frac{d V}{d r}, \nonumber$
where $$E_r$$ is the component of the electric field along the direction specified by dr. The exception referred to above occurs at a layer of dipoles; see the example problem discussed below. Let a surface carry a density of dipoles $$\vec P_d$$ per unit area (dimensions of Coulombs/m) oriented such that the dipole density is perpendicular to the plane. Such an electrical dipole layer, or electrical double layer, generates no external electric field, but it does generate a jump in potential given by
$\Delta V=\left|\overrightarrow{\mathrm{P}}_{d}\right| / \epsilon_{0}. \label{2.24}$