S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Engineering Electromagnetics Fall 2004 Shreekanth Mandayam ECE Department Rowan University Lecture 4a September 28, 2004

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

S. Mandayam/ EEMAG-1/ECE Dept./Rowan UniversityPlan Electrostatics Numerical solution of Laplace’s Equation Finite difference approximation A little more on electrostatic potential Capacitance Parallel plate capacitor: A closer look Fringing fields in a “real” capacitor RF Electronics - Microstrip Lines Coaxial cable Lorentz Force Law Motion of a charge in an electrostatic field

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 UniversityCapacitance Capacitance Good! Capacitance Bad!

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Parallel-Plate Capacitor d VsVs z x

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University A “Real” Capacitor

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University RF Electronics 10 GHz Satellite Receiver Downconverter

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Microstrip Lines rr w d conductor Ground plane (conductor) insulator “Cross-talk”

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Microstrip & Strip Line Configurations rr  r1  r2 rr rr microstrip buried microstrip striplines

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Coaxial Cable z x y a  b VsVs

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Lorentz Force Law Force [N] Charge [C] Electric Field [V m -1 ] Velocity [m s -1 ] Magnetic Flux Density [T]

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Motion of a Charge in a Uniform Electrostatic Field x z At time zero At time t At time zero At time t Let DEMO: motionestat

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