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]) .
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.
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