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. the Continuity Equation
3.2
Gauss’ Laws and
the Continuity Equation

3. GAUSS’ LAW FOR THE ELECTRIC FIELD

5. Divergence of D = r
Ex. Given that
Find D everywhere.

6. Noting that r = r (x) and hence D = D(x), we set

7. Thus,
which also means that D has only an x-component. Proceeding further, we have
where C is the constant of integration. Evaluating the integral graphically, we have the following:

8. r r0
From symmetry considerations, the fields on the two sides of the charge distribution must be equal in magnitude and opposite in direction. Hence,
C = – r0a

10. GAUSS’ LAW FOR THE MAGNETIC FIELD r
From analogy
Solenoidal property of magnetic field lines. Provides test for physical realizability of a given vector field as a magnetic field. r

11. LAW OF CONSERVATION OF CHARGE
Continuity
Equation

12. SUMMARY
(4) is, however, not independent of (1), and (3) can be derived from (2) with the aid of (5).
(1)
(2)
(3)
(4)
(5)