4 6 Boundary Conditions Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edw[.]
Trang 1Introduction 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
Trang 2Boundary Conditions
Trang 3Why boundary conditions?
Medium
Inc.
wave Ref.
wave
Trang 4regardless of where the contours, surfaces, and volumes are Example:
C2
C1
C3
Trang 5Example of derivation of boundary conditions
d
dt
E l B S
abcda
d
dt
Medium 1
Medium 2
a
c d
b
n
a
s
a
Trang 61 2 0
t t
E E
or,
0 0 0 0
ab
E ab E cd
1 2 0
a × E E
Trang 7Summary of boundary conditions
a × E E
a × H H J
a D D
1 2 0 or 1 2 0
Trang 8Perfect 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,
or 0
a ×E = 0
or
n S Ht JS
a × H = J
or
n S D n S
a D
0 or 0
a B
Trang 9 E
E
n
a
S
n
a
Trang 10Dielectric-Dielectric Interface
0, 0
a × E E
a × H H
Trang 11Medium 1, e0
Medium 2, 3e0
E t1
E t2
E n1
E n2
D n1
D n2
n
a
Medium 1, m0
Medium 2, 2m0
H t1
B n1
B n2
H t2
H n1
H n2 n
a
Trang 12D4.11 At a point on a perfect conductor surface,
(a) and pointing away from
the surface Find D D0 x 2 y S 2 0z is positive
0
0
2 2
2 2
n
D D
D a
2
D
D
Trang 13and pointing toward the
surface D0 is positive
0 0.6 x 0.8 y
D
(b)
a
D
2
0 0
D D
D
D
Trang 141 is entirely normal.
E
2 1 2 e0 1
D D E
(a)
n z
At 0, 0, , a
2
0
e
y
z
(0, 0, a)
r < a
(0, a, 0)
r > a
0, ,
Trang 15(c)
1 is entirely tangential
E
n y
2 1 E0 z
1 2
0
Solve 0
n n
a × E E
At 0, , ,
2 2