S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Engineering Electromagnetics Fall 2004 Shreekanth Mandayam ECE Department Rowan University Lecture 3b September 22, 2004

S. Mandayam/ EEMAG-1/ECE Dept./Rowan UniversityPlan Electrostatics Recall: Discrete (Point) Charges Spherical Coordinate System Continuous Charge Distributions Line Charge Cylindrical Coordinate System Plane Charge Volume Charge Poisson’s/Laplace’s Equations Analytical solutions for a parallel plate capacitor Electrostatic boundary conditions Numerical solution of Laplace’s Equation Finite difference approximation Electric Field Potential

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University EEMAG-1: Topics Today

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Recall: Battle Plan

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Spherical Coordinate System x P(r, ,  ) r   y z O DEMO: chargedist

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Cylindrical Coordinate System x P( , , z)   y z O z DEMO: chargedist

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Recall: Battle Plan

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Poisson’s & Laplace’s Equations

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Analytical Solution: 1-D Case x = 0 x = d V s = 10V charge-free region

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Boundary Conditions Why do we need boundary conditions? Equations describing e-mag fields are differential equations Solution + Constant

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Electrostatic BCs Two types of BCs Basic Equations

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University The Dielectric-Dielectric Boundary E1E1 E2E2 E 2n E 2t E 1t E 1n   ww hh D1D1 D2D2 D 2n D 2t D 1t D 1n   ss hh

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Numerical Solution: 2-D Laplacian Field x y h h

S. Mandayam/ EEMAG-1/ECE Dept./Rowan UniversitySummary