XIX Sympozjum Srodowiskowe PTZE - materialy.pdf

XIX Sympozjum PTZE, Worliny 2009
In the coaxial system of conductors, the charge qi induced in the inner metallic cylinder by the
charge placed between the conductors at the distance r from central ax is (Price):
q i
( r / R)
( r / R)
ln
= q
(3)
ln
0
Integrating (3) through the whole lossy material value, the induced charge value was
obtained:
where ks = rs/R and k0 = r0/R.
2
2 2
( ln(
ks
) −1)
− k0
( ln(
k0
) −1)
2 2
2
( k − k ) ln(
1/
k )
2
ks
Q = Q
, (4)
i
s
0
Substituting (4) to (2), the time dependence of the cumulated charge was obtained:
() t Q(
t = ) exp(
− t / )
c
0
Q = 0 τ , (5)
where τc is the relaxation time constant of the whole system.
The relaxation time constant of the model is greater than the constant of the material:
Conclusions
τ
2 2 2
( ks
− k0
) ln(
k0
)
2
2 2
( ln(
k ) −1)
− k ( ln(
k ) −1)
c = −τ
(6)
2
ks
s
0 0
τ c/τ m
10
1
0 0,1 0,2 0,3 0,4 0,5
k s =r s/R
0,6 0,7 0,8 0,9 1
Figure 2. Dependence of increasing of the relaxation time constant of lossy dielectric partially filling
the metallic container
Presented analysis confirmed that the real value of the time constant of charge decay by
dissipation can be longer that relaxation time constant of the bulk or liquid lossy dielectric
material.
55
k0=0,01
k0=0,02
k0=0,05
k0=0,1
k0=0,2
k0=0,5
k0=0,9