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

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)