Title: CONDUCTOR
1LECTURE 15
- CONDUCTOR FREE SPACE BOUNDARY CONDITIONS
2Introduction
free space
conductor
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3Short Wave Radio
4OBJECTIVES
- To relate mathematically fields that propagates
between various materials. - To derive boundary conditions at the interface.
5GRAPHICAL ILLUSTRATION
E1n
E1t
E1
Medium 1
Medium 2
E2
E2n
E2t
E1
E2
Normal component
E1t E1n
E2n E2t
Tangential component
6NORMAL COMPONENTS
E1n
E2n
E1n
S
1
Maxwells equation (Gausss law)
rs
1
0
h
2
2
3
Assume h ? 0
E2n
Boundary condition for normal components
7TANGENTIAL COMPONENTS
E1t
1
2
1
Maxwells equation (Conservation of energy)
h
2
4
3
l
E2t
0
0
Assume again h ? 0
Boundary condition for tangential components
8CONDUCTOR FREE SPACE BOUNDARY CONDITION
1
Conductor
Free space
2
e0
e0
Boundary condition for normal components
0
Boundary conditions for conductor
free space/dielectric
Boundary condition for tangential components
0
9GRAPHICAL ILLUSTRATION
Conductor
Free space
Unit vector normal to the surface
rs
10SUMMARIZED THE PRINCIPLES WHICH APPLY TO
CONDUCTORS IN ELECTROSTATIC FIELDS
- 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.
11EXAMPLE 15.1
- Let potential field V 100(x2 - y2) and point P(
2, -1, 3) lies on a conductor-free space
boundary. - Determine the profile of the conductor.
- Determine the electric field intensity at point
P. - Determine the surface charge at point P.
12EXAMPLE 15.2
- A potential field is given as V (100e-5x sin 3y
cos 4z) 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, 233 V/m, 0, 2.06 nC/m2
13THANK YOU