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

4.6 Boundary Conditions

Why boundary conditions? Medium 1 Medium 2 Inc. wave Trans. wave Ref. wave

Maxwell’s equations in integral form must be satisfied regardless of where the contours, surfaces, and volumes are. Example: C3 C1 C2 Medium 1 Medium 2

Example of derivation of boundary conditions Medium 1 Medium 2

or,

Summary of boundary conditions

Perfect Conductor Surface (No time-varying fields inside a perfect conductor. Also no static electric field; may be a static magnetic field.) Assuming both E and H to be zero inside, on the surface,

Dielectric-Dielectric Interface

Example: D4.11 At a point on a perfect conductor surface, and pointing away from the surface. Find . D0 is positive. (a)

and pointing toward the surface. D0 is positive. (b)

Example: (a)

(b) (c)