This appendix develops the mathematical machinery of screening and Green’s functions needed for electrostatics and magnetostatics. Starting from the screened Coulomb potential, it computes its Fourier transform, takes the unscreened limit, and thereby derives the standard free-space Green’s function and its representation as a Fourier integral. The appendix then examines convergence issues and the definition of the delta function, showing how to regularize Fourier representations with exponential factors. Translational invariance is used to motivate partial Fourier transforms when only some coordinates are symmetric, reducing Poisson’s equation to an ordinary differential equation in the remaining variable. These methods are applied to construct the Green’s function for half-space bounded by a grounded conducting plane, from which one obtains the induced surface charge, the potential, and the force on a point charge near the conductor.

This chapter analyzes how conductors respond to external charges through induced charge densities, screening, and currents. It first reviews the picture of mobile and bound charge in a metal and derives the screening time by combining Ohm’s law with the continuity equation and Gauss’s law. The chapter then treats screening of charges outside a conductor, enforcing boundary conditions on the electric field and surface charge, and develops integral representations for the fields using the near-field approximation and surface charge distributions. These ideas are systematized with the Green’s function method for electrostatics, including Fourier-space constructions and the solution of canonical half-space and planar-boundary problems. Green’s theorem is then used to formulate general boundary value problems for the scalar potential in terms of Green’s functions, free charge, and induced surface charge on conducting bodies. Finally, the chapter derives and interprets the Shockley–Ramo theorem, which expresses the current induced on electrodes by moving charges, and applies it to parallel-plate capacitors and simple detector circuits.