Electromagnetic Theory #15 Poisson's & Laplace's Equations скачать в хорошем качестве

Electromagnetic Theory #15 Poisson's & Laplace's Equations

We derive Poisson's and Laplace's equations from Gauss's law, write the Laplacian in Cartesian, cylindrical, and spherical coordinates, present the 4-step solution procedure for boundary-value problems, and solve a full EHD pump example step by step. Topics covered: 0:00 Introduction 0:03 Recap (Polarization & Dielectrics) 0:42 Deriving Poisson's & Laplace's Equations 1:45 Laplacian in 3 Coordinate Systems & Solution Procedure 2:55 Example: Electrohydrodynamic Pump (step by step) 5:17 Summary Key equations: ∇²V = −ρᵥ/ε (Poisson's equation) ∇²V = 0 (Laplace's equation) Solution: Integrate → Apply BCs → E = −∇V Reference: Sadiku, "Elements of Electromagnetics" 7th Ed., Sections 6.1–6.4 #ElectromagneticTheory #Poisson #Laplace #BoundaryValue #Electrostatics #Physics #Engineering #AcEdumy