Edward C. Jordan Memorial Offering of the First Course under the Indo-US Inter-University Collaborative Initiative in Higher Education and Research: Electromagnetics for Electrical and Computer Engineering by Nannapaneni Narayana Rao Edward C. Jordan Professor of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, Illinois, USA Amrita Viswa Vidya Peetham, Coimbatore July 10 – August 11, 2006

the Continuity Equation 3.2 Gauss’ Laws and the Continuity Equation

GAUSS’ LAW FOR THE ELECTRIC FIELD

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

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

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:

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

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

LAW OF CONSERVATION OF CHARGE Continuity Equation

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)