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 1b September 8, 2004

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

3. S. Mandayam/ EEMAG-1/ECE Dept./Rowan UniversityPlan Review of scalars and vectors Time- and space-varying Scalar and vector fields Time harmonic fields Phasors Complex vectors Review of Vector Analysis Dot and Cross products Gradient of a scalar field Divergence of a vector field Curl of a vector field

4. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Scalars & Vectors DEMO: spactimscal DEMO: spactimvec Fields http://engineering.rowan.edu/~shreek/fall04/eemag1/tutorial.html

5. S. Mandayam/ EEMAG-1/ECE Dept./Rowan UniversityFields Field: A space (and time) varying quantity Static field: space varying only Time varying field: space and time varying Scalar field: Magnitude varies in space (and time) Vector field: Magnitude & direction varies in space (and time) Moving Fields…... Electromagnetic waves

6. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Time Harmonic Fields Fields that vary periodically (sinusoidally) with time Time Harmonic Scalar Fields Phasor Transform P Real, time harmonic scalar Complex Number (Phasor)

7. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Time Harmonic Vector Fields Phasor Transform P Real, time harmonic vector Complex Vector

8. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Vector Analysis: Review Magnitude of a vector Position (or Radius) Vector Unit Vector in any direction

9. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Dot Product DEMO: vecalgebra Physical meaning?

10. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Cross Product DEMO: vecalgebra Physical meaning?

11. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Gradient of a Scalar Field DEMO: grad Physical meaning?

12. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Divergence of a Vector Field DEMO: div Physical meaning?

13. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Curl of a Vector Field DEMO: curl Physical meaning?

14. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Recall: Fields Field: A space (and time) varying quantity Static field: space varying only Time varying field: space and time varying Scalar field: Magnitude varies in space (and time) Vector field: Magnitude & direction varies in space (and time) Moving Fields…... Electromagnetic waves

15. S. Mandayam/ EEMAG-1/ECE Dept./Rowan University Electromagnetic Fields

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