1. Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by
Nannapaneni Narayana Rao
Edward C. Jordan Professor of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
Distinguished Amrita Professor of Engineering
Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India

2. 1.6
The Magnetic Field

3. The Magnetic Field
acts to exert force on charge when it is in motion.
B = Magnetic flux density vector
Alternatively, since charge in motion constitutes current, magnetic field exerts forces on current elements.

4. Units of B:
Sources: Currents;
Time-varying electric field

5. Ampère’s Law of Force

6. Magnetic field due to a current element (Biot-Savart Law)
B circular to the axis of the current element

7. Ex.

9. Current Distributions
Filamentary Current
I (A)
(b) Surface Current
Surface current density, JS (A/m)

10. (c) Volume Current
Density, J (A/m2)

11. P1.44 a1 a a2
P(r, f, z)

13. For infinitely long wire,

14. Magnetic Field Due to an Infinite Plane Sheet of Uniform Surface Current Density
This can be found by dividing the sheet into infinitely long strips parallel to the current density and using superposition, as in the case of finding the electric field due to an infinite plane sheet of uniform surface charge density. Instead of going through this procedure, let us use analogy. To do this, we first note the following:

15. Point Charge Current Element

16. (b) Line Charge Line Current
rL0

17. (c) Sheet Charge Sheet Current
Then,
(c) Sheet Charge Sheet Current
rS0