Potential Gradient, Field and Field Gradient; Image Charges and Boundaries

This chapter provides some basic insights into the relationship between the electric field and the potential gradient at any point in space, as obtained by solving Laplace's equation. It describes the conditions that apply to the behaviour of D‐field and E‐field lines of force at the boundary surface between two dielectrics, together with the concept of an electric field gradient. Derive a general solution of Laplace's equation that can be used to solve the electrostatic potential V(r, Θ, Φ) in a situation where there is spherical symmetry. The method of image charges, also known as the method of images or the method of mirror charges, is a useful tool for solving problems in electrostatics. Basically, imaginary point electric charges are introduced within a conductor to replace a distribution of charges along the conductor's surface. The validity of this method depends on uniqueness theorems.