A rigorous and simpler method of image charges
Autor: | G Donoso, C L Ladera |
---|---|
Rok vydání: | 2016 |
Předmět: |
Physics
Laplace transform Differential equation General Physics and Astronomy Method of image charges 01 natural sciences 010305 fluids & plasmas Image (mathematics) Method of images Quantum mechanics 0103 physical sciences Calculus Uniqueness Boundary value problem 010306 general physics Constant (mathematics) |
Zdroj: | European Journal of Physics. 37:045208 |
ISSN: | 1361-6404 0143-0807 |
DOI: | 10.1088/0143-0807/37/4/045208 |
Popis: | The method of image charges relies on the proven uniqueness of the solution of the Laplace differential equation for an electrostatic potential which satisfies some specified boundary conditions. Granted by that uniqueness, the method of images is rightly described as nothing but shrewdly guessing which and where image charges are to be placed to solve the given electrostatics problem. Here we present an alternative image charges method that is based not on guessing but on rigorous and simpler theoretical grounds, namely the constant potential inside any conductor and the application of powerful geometric symmetries. The aforementioned required uniqueness and, more importantly, guessing are therefore both altogether dispensed with. Our two new theoretical fundaments also allow the image charges method to be introduced in earlier physics courses for engineering and sciences students, instead of its present and usual introduction in electromagnetic theory courses that demand familiarity with the Laplace differential equation and its boundary conditions. |
Databáze: | OpenAIRE |
Externí odkaz: |