Transcription of Poisson’sEquationinElectrostatics
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Poisson’sEquationinElectrostatics
poisson s Equation in ElectrostaticsJinn-Liang LiuInstitute of Computational and Modeling Science, NationalTsing Hua University,Hsinchu 300, Taiwan. E-mail: 2010, 2011, 2012, 2017 AbstractPoisson s equation is derived from Coulomb s law and Gauss s theorem. It is a par-tial differential equation with broad utility in electrostatics, mechanical engineer-ing, and theoretical physics. It is named after the French mathematician, geometerand physicist Sim eon-Denis poisson (1781-1840). CharlesAugustin Coulomb (1736-1806) was a French physicist who discovered an inverse relationship on the forcebetween charges and the square of its distance.
The term Q0 limr→0 4πr3 3 has no physical meaning and can only be abstractedmath-ematically by means of the Dirac delta function [1] (a distribution as called
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