Biomedical Engineering Reference
In-Depth Information
Substituting into IE,
⎛
⎜
1
⎞
⎟
+ ʹ
⎛
⎜
1
⎞
⎟
+ ʹ
⎛
⎜
1
⎞
⎟
2
2
2
IE
= ʹ
x
y
+
r E
z
−
r E
(2.11)
41
x
41
x
2
2
2
n
n
n
0
0
0
The standard primed IE′ is
ʹ
ʹ
2
ʹ
ʹ
2
ʹ
ʹ
2
x
n
y
n
z
n
IEʹ =
+
+
(2.12)
2
2
2
x
y
z
Equating IE = IE′ and assuming
1
n r E
x
yields
2
0
41
n
ʹ =
n
0
(2.13)
s
⎛
⎜
⎞
⎟
r n
2
41 0
n
ʹ =
n
−
E
1
y
x
0
2
ʹ
−
ʹ
y
z
y
z
y
ʹ =
+
y
=
2
2
2
2
r
⎛
⎜
⎞
⎟
41
n
ʹ =
n
+
n E
2
1
x
x
0
0
2
ʹ
+
ʹ =
−
y
z
y
z
z
+
= =
z
2
2
2
2
ʹ
2
ʹ
2
y
z
2
y
=
+
− ʹ ʹ
y z
2
2
ʹ
2
ʹ
2
y
z
z
ʹ =
+
+ ʹ ʹ
y z
2
2
ʹ
2
ʹ
2
y
z
yz
=
−
2
2
This index change is
Δ
n n
= ʹ − ʹ =
0
n
n
(2.14)
i
i
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