Schematic of the
field contributions
− 
z

(
r
,
)/
2
++++++++++
− 
z

(
r
,
)/
2

z

(
r
,
)/
2
−−−−−−−−−

z

(
r
,
)/
2
Thus the total electric fields are:
E
1,
total
(
r
,
)
=
(
r
,
)
n
1
/
2
−
(
r
,
)
n
2
/
2
=
0 above the dipole layer
E
2,
total
(
r
,
)=−
(
r
,
)
n
1
/
2
+
(
r
,
)
n
2
/
2
=
0 below the dipole layer
giving
n
1
[
E
1,
total
−
E
2,
total
]=
0
Between the two layers for finite
the electric field is constant, directed downward and equal
to,
E
3,
total
(
r
,
(
r
,
)
n
1
/
2
−
(
r
,
)
n
2
/
2
=−
(
r
,
)
n
1
/
.
The total potential above the dipole layer (where

z
2

=
+ 
z
1

)is
1,
total
(
r
,
)
=
+
(
r
,
) +
−
(
r
,
)=−
z
1

(
r
,
)/
2
+ 
z
2

(
r
,
)/
2
=
(
r
,
)/
2
Below the dipole layer (where

z
1

=
+ 
z
2

)
.
2,
total
(
r
,
)
=

z
2

(
r
,
)/
2
− 
z
1

(
r
,
)/
2
(
r
,
)/
2
,
and for finite
between the two charge layers where

z
2

=
− 
z
1

the total potential is
3,
total
(
r
,
z
1

(
r
,
)/
2
+ 
z
2

(
r
,
)/
2
=