Laplacian operator, Poisson and Image method Flashcards
What is the Laplacian operator and what is it used for?
The Laplacian operator is the divergence of a gradient of a scalar field.
What is Poisson´s equation and Laplace´s equation?
Poisson´s equation states, that the Laplacian of the voltage is equal to volume charge density over the permittivity.
What is the uniqueness theorem in electrostatics?
Uniqueness theorem states that, if a solution to an electrostatic problem satisfies the boundary conditions than the solution irrespective to the method is the right solution.
What is the image method and why is it useful?
The image method is a way to solve difficult electrostatic problems that have difficult boundary conditions if Poisson´s or Laplace’s equation is to be solved.
Image method is done by replacing bounding surfaces by having an image (equivalent charge), this will make the method of finding the potential easier.
What is equipotential?
Since, in electrostatic problems the surface has only the normal component of the electric filed, then the potential is also constant because with same magnitude over whole surface.
