!
Model No. ES-9080
Basic Electrostatics System
27
Analysis:
The calculations needed to determine the dielectric constant are long,
but straight forward:
Before inserting the dielectric...
Let
be the charge on the capacitor plates, and
be the capacitance
of the plates, without the dielectric.
Let
be the charge on
C
E
, the internal capacitance of the
electrometer.
Let
be the initial reading of the electrometer.
The total charge in this initial system is given by
After inserting the dielectric …
Let
be the new charge on the capacitor plates; the capacitance is
now
.
Let
be the new charge on
, the internal capacitance of the
electrometer. Since there is no dielectric in
, its value is still the
same.
Let
be the new reading of the electrometer.
The total charge in the system after inserting the dielectric is given by
Now, the total amount of charge in the system was never changed, so
and
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before
after
Figure 3.6: Circuit diagrams with and without the dielectric
q
p
C
p
q
E
V
i
q
P
q
E
+
C
P
C
E
+
V
i
=
q
c
p
C
c
p
q
c
E
C
E
C
E
V
i
q
c
p
q
c
E
C
c
p
C
E
+
=
V
f
+
q
p
q
E
+
q
c
p
q
c
E
+
=
C
p
C
E
+
V
i
C
c
p
C
c
E
+
V
f
=