LECTURE 15 CONDUCTOR FREE SPACE BOUNDARY CONDITIONS Introduction

LECTURE # 15 CONDUCTOR – FREE SPACE BOUNDARY CONDITIONS

Introduction + + + + free space conductor - - - -

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OBJECTIVES n n To relate mathematically fields that propagates between various materials. To derive boundary conditions at the interface.

GRAPHICAL ILLUSTRATION E 1 n E 1 t E 1 Medium # 2 E 2 n E 2 t E 1 t + E 1 n E 2 Normal component Tangential component E 2 n + E 2 t

NORMAL COMPONENTS E 1 n 1 E 1 n S E 2 n Maxwell’s equation (Gauss’s law) rs #1 + + + #2 2 + h 0 3 E 2 n Assume h → 0 Boundary condition for normal components

TANGENTIAL COMPONENTS E 1 t #1 1 E 1 t 2 h #2 4 Maxwell’s equation (Conservation of energy) 3 ℓ E 2 t 0 Assume again h → 0 Boundary condition for tangential components E 2 t 0

CONDUCTOR – FREE SPACE BOUNDARY CONDITION #1 Free space e 0 #2 Conductor e 0 Boundary condition for normal components 0 Boundary condition for tangential components 0 Boundary conditions for conductor – free space/dielectric

GRAPHICAL ILLUSTRATION Conductor Free space + + + Unit vector normal to the surface + + + rs

SUMMARIZED THE PRINCIPLES WHICH APPLY TO CONDUCTORS IN ELECTROSTATIC FIELDS n n n The static electric field intensity inside a conductor is zero. The static electric field at the surface of a conductor is everywhere directed normal to that surface. The conductor surface is an equipotential surface.

EXAMPLE 15. 1 n Let potential field V = 100(x 2 - y 2) and point P( 2, -1, 3) lies on a conductor-free space boundary. q q q Determine the profile of the conductor. Determine the electric field intensity at point P. Determine the surface charge at point P.

EXAMPLE 15. 2 n A potential field is given as V = (100 e-5 x sin 3 y cos 4 z) V. Let point P(0. 1, p/12, p/24) be located at a conductor-free space boundary. At point P, find the magnitude of: (i) V; (ii) E; (iii) En; (iv) Et; (v) rs. Answer: 37. 1 V, 233 V/m, 0, 2. 06 n. C/m 2

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