1. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Engineering Electromagnetics 1 0909.301.01 Fall 2004 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/fall04/eemag1/ Lecture 7a October 19, 2004

2. 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

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

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

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

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

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

8. Matlab PDE Toolbox Conductive Media DC Mode

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

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

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

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

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

14. Lorentz Force Law Force [N] Charge [C] Electric Field [V m -1 ] Velocity [m s -1 ] Magnetic Flux Density [T]

15. 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

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

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