Information Technology Reference
In-Depth Information
G
(
M
,
M
v
)
| =−
(
r
MM
v
)
G
(
M
,
M
v
)
|
S
=
0
.
(1
.
108)
Thus,
grad
V
−
G
(
M
,
M
v
)
di
v
j
(
M
v
)
dV
M
∈
V
j
p
(
M
)
=
(1
.
109)
0
M
∈
V
.
Next we will pass on to the solenoidal part
j
s
.Define
j
s
as
curl
I
(
M
)
M
∈
V
j
s
(
M
)
=
(1
.
110)
0
M
∈
V
,
where
I
can be considered as the magnetization of a magnetic body that is equivalent
to the solenoidal current of the density
j
s
distributed within the domain
V.
Note that
(1.110) does not provide the unique determination of
j
s
. Evidently
j
s
can be also
taken as
curl
I
(
M
)
j
s
(
M
)
=
M
∈
V
,
(1
.
111)
where
I
(
M
)
=
I
(
M
)
+
grad
(
M
)
and
is arbitrary scalar function. But we eliminate such an arbitrariness by impos-
ing the requirement that
di
v
I
=
0
.
So, we write
curl
I
(
M
)
=
j
s
(
M
)
di
v
I
(
M
)
=
0
M
∈
V
,
(1
.
112)
whence, with due regard for (1.104),
=−
=−
.
.
I
(
M
)
curl
j
s
(
M
)
curl
j
(
M
)
(1
113)
Now, using the Green function introduced by (1.108), we find
G
(
M
,
M
v
)
curl
j
(
M
v
)
dV
M
∈
V
I
(
M
)
=
(1
.
114)
V
∈
.
0
M
V
Here the
curl
may be taken out of the integral. Since
di
v
I
=
0, we express
I
as
I
=
curl
P
, where
P
is a vector field. Then (1.113) assumes the form
P
=−
j
,
whence
G
(
M
,
M
v
)
j
(
M
v
)
dV
M
∈
V
=
(1
.
115)
P
(
M
)
V
0
M
∈
V
.
