12 ISSN 1607-7970. Техн. електродинамікa. 2011. № 5 УДК

621.315
1
2
,
,
1
,
«
»,
.
, 37,
-56, 03056,
2
,
,
.
56,
.
-57, 03680,
(
-
)
,
.
.
,
,
.
,
,
,
.
:
. 8,
. 5.
,
,
,
,
,
-
.
.
[5,7,8]
,
,
-
0
.
,
,
.
-
l
.
,
-
.
,
,
[1 3].
,
-
.
,
-
,
.
,
.
,
,
-
.
.
.
,
.
,
,
r ot E=0,
©
12
.,
[1 3],
div D
,
(1,2)
., 2011
ISSN 1607-7970.
.
a. 2011.
5
E
D
(
)
,
–
.
,
,
D
0=8,85
P
-12
10
E, ke
0 E+P
0 E+
E= 0 (1+ k ) E=
, –
–
0
,
0
E,
(3)
-
–
,
–
.
(1)
-
,
E=-grad
(3)
(4)
.
(4)
(2)
,
,
-div(
0
grad
)= .
(5)
-
.
,
Comsol Multiphysics [8].
,
,
.
Comsol Multiphysics
r,
,
(5)
-
r=0.
T
r
r
z
r
z–
r
(6)
0,
0
z
.
. 1.
-
l
,
l/2
.
[1,3]
,
l
D ndl
n–
.
(7)
0,
.
Comsol Multiphysics
,
.
-
.
,
.
.
.1
.
,
ISSN 1607-7970.
.
. 2011.
5
,
13
,
.
,
,
l
,
l.
,
,
l
-
l.
l
,
-
.,
.
>
.
.
.2
0
(
–
0
)
50
.
,
-
n
0,
n
1,5
15,
,
.
-
V,
[5 7].
[4 7].
,
-
.2
,
V
-
.
V
,
V
[4 7].
.2
V,
1
.
2
.2
0.
,
,
l
,
,
0
l
=1,5
,
15
-
.
0.
=D·n
,
,
.
. 3.
. 3,
. 2.
,
,
1, 2
3
l,
.3
50, 10
.
,
1,
2,
2
. 2.
. 2,
.
l
,
,
-
/ l [1,3].
,
0.
.
14
ISSN 1607-7970.
.
a. 2011.
5
. 4, ,
l/2,
25, 5
-
1
.
.3
,
,
l.
,
l
l<2R,
l,
(
,
l),
-
. 4, .
.4
.
–
.
,
(
,
50
. 5, ,
-
).
.
,
,
.
-
,
,
,
. 5, ,
.
,
,
. 5,
1, 2
,
: V1>V2>V3.
V 1>V 2>V 3,
-
,
3
-
,
,
(
l
5
. 5, , , ).
,
1
,
.
,
-
,
ISSN 1607-7970.
.
.
. 2011.
5
15
-
.,
.
. 1.
,
-
-
,
.
2.
.5
,
-
.
,
,
3.
.
,
,
,
.
1.
.3.
.:
2.
3.
4.
2005. – 930 .
5.
.,
, 2003. – 377 .
.,
.
.,
.,
.
.
.–
.–
/
.,
.
.,
.:
, 1980. – 560 .
, 1964. – 384 .
.–
.:
.
.,
.
". –
.,
//
, 2010. – . 254–257.
:
.
.
,
//
16
. –
4. – C. 3–14.
6.
.
7.
2009. –
,
.
//
2008. –
:
6. – C. 3–9.
8. Comsol Multiphysics 3.5. User’s Guide and introduction.
.
. –
Comsol, Inc. – www.comsol.com
ISSN 1607-7970.
.
a. 2011.
5
621.315
1
2
,
1
,
«
»,
.
, 37,
-56, 03056,
,
2
,
.
, 56,
-57, 03680,
.
(
)
,
.
,
.
-
,
.
,
,
,
–
:
.
,
,
. 8,
,
. 5.
,
,
-
.
The electric field intensification in dielectric space between conducting inclusions
1
2
.Shcherba1, A.D.Podoltsev2
NTUU «Kyiv olytechnic nstitute»,
Politekhnichna, 37, Kyiv-56, 03056, Ukraine,
Institute of lectrodynamics NAS Ukraine,
Peremogy, 56, Kyiv-57, 03680, Ukraine.
The mathematic model for numerical analysis of external low frequency electric field (EF) disturbance in the dielectric
gap between two closely located conducting inclusions, which are placed along the field on a distance less than its
sizes, is developed. It is shown that at decreasing of gap between surfaces such inclusions the field intensity inside this
gap increases according to the law of power function. Also it is revealed that for fixed sizes conducting inclusions,
which located in the line of field, the degree of field intensity in a dielectric gap raises at decreasing of distance between them and with increasing its surfaces curvature. The performed calculations corroborated that at approaching of
cylindrical, spherical and ellipsoidal inclusions the degree of field intensity between the last-named is largest, and between the first-named is lowest. References 8, figures 5.
Key words: electric field, surface charge, dielectric medium, conducting inclusions, intensity, tensed volume.
1. Demirchian K.S., Neiman L.R., Korovkin N.V., Chechurin V.L. Theoretical grounds of electrical engineering.
Vol. 3. – Sankt Peterburg: Piter, 2003. – 377 p. (Rus.)
2.Landau L.D., Lifshits E.M. Electrodynamics of continuum. – Moskva: Nauka, 1980. – 560 p. (Rus.)
3. Nikolskii V.V. Electromagnetic field theory. – Moskva: Vysshaia shkola, 1964. – 384 p. (Rus.)
4. Technique and electrophysics of high voltage / Za redaktsieiu V.O.Brzhezickogo ta V.M.Mikhailova. – Khark v:
Tornado, 2005. – 930 p. (Ukr.)
5. Shidlovskii A.K., Shcherba A.A., Zolotarev V.M., Peretiatko Yu.V. Analysis of electric field microinhomogenety as a factor of threshold electrophysical processes intensity increasing in polymeric insulation of high voltage cables
and self-bearing insulated wires // Tekhnichna elektrodynamika. – 2008. – 4. – P. 3–14. (Rus.)
6. Shcherba M.A. Lows of local tensed volume changing in dielectric with distance changing between conducting microinclusions of different configurations. // Dopov
za materialamy ISTC "Suchasn problemy elektroenergotekhn ky ta avtomatyky". – Kyiv: Pol tekhn ka, 2010. – Pp. 254 – 257. (Rus.)
7. Shcherba A.A., Shcherba M.A. Modeling and analysis of electric field in dielectric medium, disturbed by
conducting microinclusions of different sizes and forms // Tekhnichna elektrodynamika. – 2009. – 6. – C. 3–9.
8. Comsol Multiphysics 3.5. User’s Guide and introduction. Comsol, Inc. – www.comsol.com
28.04.2011
Received 28.04.2011
ISSN 1607-7970.
.
. 2011.
5
17