CONDUCTOR

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LECTURE 15

• CONDUCTOR FREE SPACE BOUNDARY CONDITIONS

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Introduction








free space
conductor
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Short Wave Radio
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OBJECTIVES

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

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GRAPHICAL ILLUSTRATION
E1n
E1t
E1
Medium 1
Medium 2
E2
E2n
E2t
E1
E2
Normal component
E1t E1n
E2n E2t
Tangential component
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NORMAL 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
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TANGENTIAL 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
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CONDUCTOR 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
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GRAPHICAL ILLUSTRATION
Conductor
Free space



Unit vector normal to the surface





rs
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SUMMARIZED 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.

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EXAMPLE 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.

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EXAMPLE 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
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THANK YOU

• QUESTIONS AND ANSWERS