Chemistry Reference
In-Depth Information
(
η
,
θ
,
ψ
)
. The electric field formed under a needle-plane electrode system is
given by
V
cos
θ
E
=
F
, with
=
0
,
(3)
F
1
d
sinh
2
η
+
sin
2
θ
sin
θ
ln
cot
θ
/
2
0
assuming
d>R.
Here
R
is the radius of curvature at the tip of needle electrode, and
d
is the distance between the needle tip and the plane electrode.
θ
is approxi-
0
mately expressed as [29]
R
+
.
(4)
θ
=
arcsin
0
R
d
Since the
V/d
represents the electric field formed between the parallel two-
electrode systems, the term
F
1
represents the effect that the parallelly arranged
two-electrode system is replaced by the needle-plane electrode system. Thus we
find that the electric field formed on the plane electrode just under the tip of the
needle electrode (
θ =
π
/
2
and
η
=
) is estimated as
0
V
cos
θ
V
E
=
⋅
0
<
.
(5)
d
ln
cot(
θ
/
2
)
d
0
Figure 8. Electrode arrangement and relationship between prolate coordinates (,,)
η θ ψ
and Carte-
sian coordinates (
x, y, z
).
Search WWH ::
Custom Search