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

96 PROBLEMS
of the vessel is placed into a strong electric field between
the plates of a capacitor owing to which the level of the kerosene
in this part is higher than in the other. A chain of balls
is passed over two pulleys.
The specific weight of the material of the balls is less than
that of the kerosene.
The lifting force acting on the balls will be greater in the
left-hand part than in the right-hand one because more balls
are immersed in the kerosene in the left-hand part. For this
reason the inventor believes that the chain should start rotating
clockwise. Why will there actually be no rotation?
453. The space between the plates of a plane capacitor is
filled with a dielectric whose permittivity is ere One plate is
given a charge +Q and the other -Q. Determine the density
of the bound electric charges that appear on the surface of the
dielectric and the forces that are exerted by the field on the
dielectric.
454. The space between the plates of a plane capacitor is
filled with a dielectric. Each molecule of the dielectric is assumed
to have the form of a "dumb-bell" with a length I whose
ends carry charges +Q and -Q. The number of molecules in
a unit of volume (1 ern") is n.
Let us assume further that all the molecules have turned along
the electric field under its action. Find the intensity E of the
field inside the capacitor filled with the dielectric if before filling
it the intensity of the field was Eo.
455. A dielectric consists of molecules each of which can be
represented as two charges +Q and -Q between which an
"elastic force" acts. The latter term should be understood to mean
that x (the distance between the charges +Q and -Q) can be
found from the equality kx= QE, where E is the intensity
of the field acting on the charges, and k is a proportionality
factor.
Assume that a unit of volume (1 ern") of the dielectric contains
n molecules. Solve Problem 454, assuming that the space
between the plates of the plane capacitor is filled with a dielectric
of this type.
Determine the permittivity of the dielectric.
456. A capacitor is filled with the dielectric whose properties
are described in Problem 455.
Find the energy stored in the dielectric owing to its polarization.
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