Transcript 25-5 Dielectrics If the charge is held constant, insertion of a dielectric

Lecture PowerPoints
Physics for Scientists and
Engineers, 3rd edition
Fishbane
Gasiorowicz
Thornton
© 2005 Pearson Prentice Hall
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Chapter 25
Capacitors and Dielectrics
Main Points of Chapter 25
• Definition of capacitance
• Calculation of capacitance
• Energy in capacitors and in electric
fields
• Equivalent capacitance for series
and parallel connections
• Dielectrics
• Microscopic description of
dielectrics
25-1 Capacitance
• Simplest capacitor – two equal
and oppositely charged
conductors
Parallel-plate
capacitor:
25-1 Capacitance
Coaxial cable:
Spherical capacitor:
25-1 Capacitance
Conductors of arbitrary
shape and size:
Isolated conductor:
Q: Where’s the other plate?
A: At infinity, effectively.
25-1 Capacitance
• Potential difference between the conductors
depends on the charge on them
•VαQ
• Definition of capacitance:
• C = Q/V
• Depends only on geometry and materials
25-1 Capacitance
Capacitance of a parallel-plate capacitor
• Field is uniform in middle of
capacitor
• Capacitance (ignoring edge
effects):
(25-4)
25-2 Energy in Capacitors
• Each bit of charge added
increases the electric field;
subsequent charges take
more work
• Total work to charge
capacitor to Q:
(25-7)
25-2 Energy in Capacitors
Potential energy of a charged
capacitor:
(25-8)
All three
expressions are
equivalent!
(25-9)
(25-10)
25-3 Energy in Electric Fields
Using the known electric field
inside a parallel-plate capacitor:
(25-11)
Then dividing by the capacitor’s volume
Ad, we find the energy density:
(25-12)
25-3 Energy in Electric Fields
(25-12)
This is a general expression
for the local energy density in free space,
for a constant or variable electric field—not
just for a parallel-plate capacitor.
25-4 Capacitors in Parallel and in Series
Finding the equivalent capacitance:
Parallel connection
(25-14)
25-4 Capacitors in Parallel and in Series
Finding the equivalent capacitance:
Series connection
(25-14)
Just remember—the equivalent capacitance is Ceq, not 1/Ceq!
25-5 Dielectrics
• Dielectric = insulator
• Molecules act as dipoles,
permanent or induced
• This effectively reduces the
electric field
25-5 Dielectrics
Dielectric also increases
capacitance:
Some dielectric constants:
(25-18)
25-5 Dielectrics
If the charge is held constant, insertion of a
dielectric causes the voltage to decrease:
25-5 Dielectrics
If the voltage is held constant, insertion of
a dielectric causes the charge to increase:
25-5 Dielectrics
Addition of dielectric to capacitor modifies
capacitance equation – use ε instead of ε0:
(25-23)
Dielectric strength – maximum electric field
that a material can sustain before breaking
down (becoming conductive as electrons
are ripped off atoms by intense field)
25-6 The Microscopic
Description of Dielectrics
For polar molecules (having a
permanent dipole moment), an
external field tends to rotate them
25-6 The Microscopic
Description of Dielectrics
For nonpolar molecules, an external
field tends to polarize them
25-6 The Microscopic
Description of Dielectrics
In either case, the induced electric
field reduces the overall field:
25-6 The Microscopic
Description of Dielectrics
Gauss’ Law
If the dielectric is uniform (same
 throughout):
(25-28)
If not:
(25-29)
Summary of Chapter 25
• Capacitor is two equal and oppositely
charged conductors
• Capacitance depends only on geometry
and dielectrics
• Electric fields carry energy
• Capacitors in parallel add; capacitors in
series add reciprocals
• Dielectrics reduce electric field,
increasing capacitance