The equation governing the potential distribution in the electrolyte becomes

Laplace's equation (for constant conductivity):

The mathematical theory regarding

Laplace's equation is often referred to as the potential theory, given the significance the equation holds for describing physical phenomena such as gravitational and electrical potentials.

When a dielectric microsphere is placed under an applied static axisymmetric electric field, the potential is defined by

Laplace's equation in spherical coordinates (r, [theta], [phi]) [21].

Numerical solutions of

Laplace's equation are done in various ways, Such as finite difference, finite volume, finite element, boundary element and natural element methods.

Laplace's equation describes the field in the non-ionized area

(1)

Laplace's equation, which describes the distribution of electrical potential within a food,

The resolution of

Laplace's Equation (1) in regions V, VI and VII by using the technique of separation of variables permits to get

In this case, the analysis reduces to an electrostatic problem and transmission lines can be modeled using the inhomogeneous

Laplace's equation instead of the more rigorous wave equation.

Conformal maps preserve guided-and radiated-wave characteristics of a two dimensional structure working in TEM mode, in which the longitudinal component of the field is zero and hence

Laplace's equation can be applied.

Zhang, "A method for solving

Laplace's equation with mixed boundary condition in electro magnetic flow meters," Journal of Physics D, vol.

Electrostatic problems essentially consist of finding the unknown potential function [PHI] that satisfies

Laplace's equation within a prescribed solution region D under certain boundary conditions.

Key Words: Electrostatics, Dimensions,

Laplace's Equation