S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Engineering Electromagnetics 1 0909.301.01 Fall 2004 Shreekanth Mandayam ECE Department Rowan University.

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S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Engineering Electromagnetics Fall 2004 Shreekanth Mandayam ECE Department Rowan University Lecture 7a October 19, 2004

S. Mandayam/ EEMAG-1/ECE Dept./Rowan UniversityPlan Magnetostatics Direct Currents A “Leaky” Capacitor Analogy b/w direct currents and electrostatic field Matlab PDE Toolbox Conductive Media DC mode Fields for symmetric current distributions Line current Coax cable Solenoid Magnetic Force

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

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Direct (Steady) Currents

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Governing Equations Direct current problems and E-static problems are analogous!

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University A “Leaky” Capacitor d VsVs z x I Permitivity,  Conductivity,  I I VsVs C G

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

Matlab PDE Toolbox Conductive Media DC Mode

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Governing Equations dl IsIs  ds Recall: Field due to a line current

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

S. Mandayam/ EEMAG-1/ECE Dept./Rowan UniversitySolenoid z x y c a n turns

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Poisson’s Equation Vector Poisson’s Equation Scalar Laplacian

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

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 Magnetostatic Field Let DEMO: motionbstat x y At time zero At time t R

S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Matlab PDE Toolbox Magnetostatics Mode

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