The Green's function can be used to find the electric field or electrostatic potential for arbitrary charge distributions. You will learn that the polarization of a dipole in front of a flat metallic surface enormously affects the overall field.

The so-called boundary integral equation relates the values of the electrostatic potential in some domain to its values at that domain's boundary. In this problem we will derive this important statement which leads to the "Boundary Element Method", a discretized version with numerical applications throughout science and engineering.