Bukhovtsev-et-al-Problems-in-Elementary-Physics

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ELECTRICITY AND MAGNETISM
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(a)
Fig. 159
plate is A and the permittivity of the dielectric is ere Find the
capacitance of the capacitor in both cases.
448. Determine the energy of a plane capacitor having the
space between its plates filled with a dielectric.
449. A plane capacitor is filled with a dielectric whose permittivity
is 8,.. The intensity of the field in the dielectric is E.
What is the intensity of the field in a space made inside the
dielectric and having the form of a long thin cylinder directed
along the field or the form of a parallelepiped one side of
which is much smaller than the other two? The smaller side is
directed along the field.
450. Two rectangular plates with a length I and an area A
are arranged parallel to each other at a distance d. They are
charged to a potential difference U (plane capacitor). A dielectric
with a permittivity e, whose thickness is d and whose width
is equal to that of the plates is drawn into the space between
the latter. The length of the dielectric is greater than 1
(Fig. 160). Find the resulting force F acting on the dielectric
from the side of the field depending on the distance x.
451. Solve Problem 450 if the
capacitor is connected to a battery
whose e.m.f. is U. Disregard the resistance
of the connecting wires.
452. The following design of a perpetuum
mobile has been suggested.
Kerosene is poured into commu- ;!J
nicating vessels (Fig. 161). One part tJ
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95
Fig. 160 Fig. 161