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 7b October 20, 2004

2. S. Mandayam/ EEMAG-1/ECE Dept./Rowan UniversityPlan Magnetostatics Recall: Governing Equations Magnetic Force B-H Curve Quasistatics Governing PDE Skin depth EMI demo Course Review Instructor & Course Evaluation

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

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

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

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

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

8. 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

9. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University The B-H Curve H in A m -1 B in T BrBr HcHc

10. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Electromagnetic Phenomena

11. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Governing PDE

12. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Governing PDE (contd.)

13. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Governing PDE (contd.) Parabolic partial differential equation

14. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Skin Depth Skin depth (standard depth of penetration),  : depth at which the current density is 1/e or 36.8% of surface value Effective depth of penetration: 3  DEMO: skineffect.m houseemiac.m

15. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Skin Depth* (contd.) *D. E. Bray and R. K. Stanley, Nondestructive Evaluation: A Tool in Design, Manufacturing and Service, CRC Press, New York, 1997

16. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Skin Depth* (contd.) *D. E. Bray and R. K. Stanley, Nondestructive Evaluation: A Tool in Design, Manufacturing and Service, CRC Press, New York, 1997

17. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University EEMAG-1: Course Objectives Given a contemporary stastic/quasistatic electromagnetic device/system, the student should be able to – Write down the Maxwell’s equations that describe this device/system Solve these equations for simple geometries using analytical techniques Solve these equations for complex geometries using MATLAB

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

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