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it could also be a readable quantity (as discussed in [
21
]). Hereinafter, when
we refer to dot charge we will implicitly refer to the aggregated charges of the
corresponding dots.
S II-B - Charge-Field Models.
As long as the aggregated charges of the
molecule under different bias conditions (point charge based driver, switching
field or clock signal) are obtained by means of simulations, it is possible to
compute the electric field generated by the charge distribution of the mole-
cule at any specific working point through mathematical equations developed
in MatLab/Octave. Particularly, a single charge +
q
1
is considered to be placed
at (
x
0
,y
0
,z
0
), and the electric field
E
(
x, y, z
) can be evaluated by means of a
positive test charge +
q
t
positioned in (
x, y, z
). The distance
r
1
between
q
1
and
q
t
and its modulus
r
1
are defined as
r
1
=
2
(
x − x
0
)
2
+(
y − y
0
)
2
+(
z − z
0
)
2
(1)
r
1
=
r
1
· r
(2)
where
r
is the unit vector of the axis that includes the space point of
q
1
and
q
t
.
Following the Gauss law, the Coulomb force
F
1
experimented by the test charge
can be evaluated as
F
1
=
1
4
ʳʾ
0
q
1
·
q
t
r
1
· r.
(3)
Then, the electric field generated by
q
1
and measured by the test charge is
computed as
−
E
1
=
F
1
q
t
1
4
ʳʾ
0
q
1
r
1
· r.
=
(4)
Considering a system of N point charges, the different forces related to the
multiple charge distribution of the whole system affect the test charge. This
effect could be summarized by defining a total force calculated by
N
−−→
F
tot
=
1
4
ʳʾ
0
q
i
·
q
t
r
2
i
· r
i
(5)
i
=1
and so the equation for the total electric field becomes
E
tot
(
x, y, z
)=
−−→
N
F
tot
q
t
1
4
ʳʾ
0
q
i
r
2
i
=
· r
i
.
(6)
i
=1
Finally, considering a generic test charge placed at a generic point of the space
(
x, y, z
), the three components (
E
x
,
E
y
and
E
z
) of the electric field generated
by a system of point charges are given by
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