obtained in the foregoing problem, find the electric field strength
E in the cylinder and the polarization P of the dielectric whose per-
mittivity is equal to 8.
3.3. Electric Capacitance. Energy of an Electric Field
- Capacitance of a parallel-plate capacitor:
C = 88 0 S/d. (3.3a) - Interaction energy of a system of point charges:
(^1) 2 qicpi• (3.3b)
- Total electric energy of a system with continuous charge distribution:
1
= cpp dV (3.3c) - Total electric energy of two charged bodies 1. and 2:
W = WI+ W2+ Wi2, (3.3d)
where WI and W 2 are the self-energies of the bodies, and W12 is the interaction
energy, - Energy of a charged capacitor:
W qV^ q^2 CV^2
" = 2 = 2C — 2
(3.3e)- Volume density of electric field energy:
ED 880 E 2
2 (3.3f)
3.101. Find the capacitance of an isolated ball-shaped conductor
of radius Ri surrounded by an adjacent concentric layer of dielectric
with permittivity s and outside radius R 2.
3.102. Two parallel-plate air capacitors, each of capacitance C,
were connected in series to a battery with emf 6. Then one of the
capacitors was filled up with uniform dielectric with permittivity a.
How many times did the electric field strength in that capacitor
decrease? What amount of charge flows through the battery?
3.103. The space between the plates of a parallel-plate capacitor
is filled consecutively with two dielectric layers 1 and 2 having
the thicknesses d 1 and d 2 and the permittivities 8 1 and 8 2 respectively.
The area of each plate is equal to S. Find:
(a) the capacitance of the capacitor;
(b) the density a' of the bound charges on the boundary plane if
the voltage across the capacitor equals V and the electric field is
directed from layer (^1) to layer 2.
3.104. The gap between the plates of a parallel-plate capacitor
is filled with isotropic dielectric whose permittivity 8 varies linearly
from el to 6 2 (8 2 > 8 1 ) in the direction perpendicular to the plates.
The area of each plate equals S, the separation between the plates
is equal to d. Find:
(a) the capacitance of the capacitor;
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