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

ELECTRICITY AND MAGNETISM 311
442. Since the dielectric is polarized, the intensity will increase at points A
and C and decrease at point B.
2nQ
443. E=-A-=50.2 CGSE.
t,
444. The capacitances and, therefore, the charges of the balls immersed in
kerosene increase e, times:
q~=e,ql' and q;=s,q.
The force of interaction of the charges in the dielectric, on the contrary,
diminishes e, times.
Hence,
q q e q q e,~2rllr!
F =_1_1_=.L...!....!.. ~. 0 0088 d
8,R2 R2 R2(rl +r2)2 . yne
The force of interaction increases e, times, while if the balls were disconnected
from the battery it would decrease e, times.
445. As a result of motion of the plates, the charge on the capacitor will
be increased by
AQ=QI- Q,=!A (..!..._..!...)
431 d. d 1
tlA ( 1 1 )
The battery will perform the work W = '~Q = 4n d. - d
1
The electrostatic energy of the capacitor will be increased by
AW,=Wes-Wet =6~1_'~1=';~ (~I- ~J
The mechanical work WI was performed when the plates were moved closer
.to each other. On the basis of the law of conservation of energy, W = W1+AWe.
Therefore,
W 1=W-AW
=,IA (..!..._..!...)
e 8n d, d 1
At the expense of the work of the battery, the electrostatic energy of the
capacitor increased and the mechanical work W1 was done.
448. Let us consider for the sake of simplicity a dielectric in the form of
a homogeneous very elongated parallelepiped (Fig. 426).
Let us resolve the field Eo in which the piece of dielectric (for example,
8 rod) is placed into components directed along the rod and perpendicular
to it. These components will cause bound charges to appear on surfaces AB,
CD, Be and AD. The field of the bound charges between surfaces AD, BC,
and AB. DC weakens the components' of the field Eo inside the dielectric,
the component perpendicular to the rod being weakened more since the bound
. charges on surfaces AD and Be are close to each other and their field is
similar to the homogeneous field of a plane capacitor, while the charges on
the surfaces of the small area are moved far apart. For this reason the full
field inside the dielectric will not coincide in direction with the field Eo.
The dipoles appearing will therefore be oriented not along Eo, but along a
certain direction OP forming the angle p with Eo. (This refers to both ordi­
~ary and dipole molecules.) From an electrical standpoint, a polarized dielectnc
can be regarded as a large dipole forming the angle ~ with the field Ea.