surfacecharge

Surface charge refers to the net electric charge per unit area residing on a surface that separates different media or on the surface of a conductor. It is commonly denoted by the symbol σ. Surface charge can be free (not bound to atoms) or bound, as in polarization charges that arise at dielectric interfaces. In conductors, excess charges accumulate on the outer surface in electrostatic equilibrium, while in dielectrics the distribution is influenced by the material’s polarization.

A key relation in electrostatics is the boundary condition for the normal component of the electric field across a surface. The discontinuity of the normal field is determined by the free surface charge density: E2⊥ − E1⊥ = σ_free/ε0, where ε0 is the vacuum permittivity and n̂ is the unit normal to the surface. In a conductor, the field inside is zero, so the field just outside the surface is determined by the surface charge as E⊥ = σ/ε0.

In dielectric materials, polarization can produce bound surface charge. The bound surface charge density is σ_b = P·n̂, where P is the polarization vector and n̂ is the normal to the surface. At interfaces, both free and bound charges contribute to the total charge distribution, and the electric field is influenced by polarization through the bound charges even as the boundary condition references the free surface charge.

Applications of surface charge include the operation of capacitors, where opposite surfaces acquire equal and opposite σ, and the formation of electric double layers at electrolyte interfaces, which affect interfacial potential and capacitance.