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PHY2061
R. D. Field
Department of Physics
chp38_5.doc
University of Florida
Finding the Missing Term (
integral method
)
We are looking for a
new term in
Ampere’s Law
of the form,
r
r
Bd
l
I
d
dt
C
E
⋅=
+
∫
1
0
µδ
Φ
,
where
δ
is an unknown constant
and
IJ
d
A
E
d
A
S
E
S
=⋅
=
⋅
∫∫
rr
r
r
Φ
,
where
S
is any surface bounded by
the curve
C
1
.
Case I (
use surface S
1
):
If we use the surface
S
1
which is bounded by the curve
C
1
then
r
r
r
r
r
l
I
d
J
E
t
dA
I
C
E
S
+
=
+
⋅
=
1
00
1
0
µ
δ
∂
Φ
,
since
E = 0 through the surface S
1
.
Case II (
use surface S
2
):
If we use the surface
S
2
which is bounded by the curve
C
1
then
r
r
r
r
r
l
I
d
J
E
t
I
C
E
S
+
=
+
=
1
1
0
ε
Φ
,
since
J = 0 through the surface S
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 Spring '08
 FRY
 Physics

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