3.141. Each plate of a parallel-plate air capacitor has an area
S.
What amount of work has to be performed to slowly increase the
distance between the plates from x
1
to x
2
if
(a) the capacitance of the capacitor, which is equal to
q,
or (b) the
voltage across the capacitor, which is equal to
V, is
kept constant
in the process?
3.142. Inside a parallel-plate capacitor there is a plate parallel
to the outer plates, whose thickness is equal to = 0.60 of the gap
width. When the plate is absent the capacitor capacitance equals
c
= 20 nF. First, the capacitor was connected in parallel to a cons-
tant voltage source producing
V =
200 V, then it was disconnected
from it, after which the plate was slowly removed from the gap.
Find the work performed during the removal, if the plate is
(a) made of metal; (b) made of glass.
3.143. A parallel-plate capacitor was lowered into water in a hor-
izontal position, with water filling up the gap between the plates
d = 1.0
mm wide. Then a constant voltage V = 500 V was applied
to the capacitor. Find the water pressure increment in the
gap.
3.144. A parallel-plate capacitor is located horizontally so that
one of its plates is submerged into liquid while the other is over its
surface (Fig. 3.33). The permittivity of the liquid is equal to a,
its density is equal to p. To what height will the level of the liquid
in the capacitor rise after its plates get a charge of surface density o
-
?
Fig. 3.33
Fig. 3.34.
3.145. A cylindrical layer of dielectric with permittivity a is
inserted into a cylindrical capacitor to fill up all the space between
the electrodes. The mean radius of the electrodes equals
R,
the gap
between them is equal to
d,
with
d << R.
The constant voltage V
is applied across the electrodes of the capacitor. Find the magnitude
of the electric force pulling the dielectric into the capacitor.
3.146. A capacitor consists of two stationary plates shaped as
a semi-circle of radius
R
and a movable plate made of dielectric
with permittivity a and capable of rotating about an axis
0
between
the stationary plates (Fig. 3.34). The thickness of the movable plate
is equal to
d
which is practically the separation between the station-
ary plates. A potential difference
V
is applied to the capacitor.
Find the magnitude of the moment of forces relative to the axis
0
acting on the movable plate in the position shown in the
figure.
