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  2. Laplace's equation - Wikipedia

    en.wikipedia.org/wiki/Laplace's_equation

    In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties.This is often written as = or =, where = = is the Laplace operator, [note 1] is the divergence operator (also symbolized "div"), is the gradient operator (also symbolized "grad"), and (,,) is a twice-differentiable real-valued function.

  3. Method of image charges - Wikipedia

    en.wikipedia.org/wiki/Method_of_image_charges

    Diagram illustrating the image method for Laplace's equation for a sphere of radius R. The green point is a charge q lying inside the sphere at a distance p from the origin, the red point is the image of that point, having charge −qR/p, lying outside the sphere at a distance of R 2 /p from the origin. The potential produced by the two charges ...

  4. Electrostatics - Wikipedia

    en.wikipedia.org/wiki/Electrostatics

    Download as PDF; Printable version; ... Electrostatics is a branch of physics that studies slow-moving or stationary electric ... the equation becomes Laplace's equation:

  5. Green's function - Wikipedia

    en.wikipedia.org/wiki/Green's_function

    In other words, the solution of equation 2, u(x), can be determined by the integration given in equation 3. Although f ( x ) is known, this integration cannot be performed unless G is also known. The problem now lies in finding the Green's function G that satisfies equation 1 .

  6. Potential theory - Wikipedia

    en.wikipedia.org/wiki/Potential_theory

    In mathematics and mathematical physics, potential theory is the study of harmonic functions.. The term "potential theory" was coined in 19th-century physics when it was realized that two fundamental forces of nature known at the time, namely gravity and the electrostatic force, could be modeled using functions called the gravitational potential and electrostatic potential, both of which ...

  7. Green's function for the three-variable Laplace equation

    en.wikipedia.org/wiki/Green's_function_for_the...

    Using the Green's function for the three-variable Laplace operator, one can integrate the Poisson equation in order to determine the potential function. Green's functions can be expanded in terms of the basis elements (harmonic functions) which are determined using the separable coordinate systems for the linear partial differential equation ...

  8. Double layer potential - Wikipedia

    en.wikipedia.org/wiki/Double_layer_potential

    In potential theory, an area of mathematics, a double layer potential is a solution of Laplace's equation corresponding to the electrostatic or magnetic potential associated to a dipole distribution on a closed surface S in three-dimensions.

  9. Electrostatic levitation - Wikipedia

    en.wikipedia.org/wiki/Electrostatic_levitation

    Electrostatic levitation is the process of using an electric field to levitate a charged object and counteract the effects of gravity. It was used, for instance, in Robert Millikan 's oil drop experiment and is used to suspend the gyroscopes in Gravity Probe B during launch.