16'4 Dielectrics, Energy

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16.4 Dielectrics, Energy

• Dielectric constant-effect on capacitance
• Energy stored in a capacitor

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Dielectric constant,?
Parallel plate capacitors, carrying charge q
Vacuum
q
?Vo
-q
material with dielectric constant, ?
q
?V
Potential due to charge q decreased by ?
-q
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Dielectric constants
Material dielectric constant, ? Vacuum 1.000000
Air 1.00059 Polyethylene 2.3 Paper 3.4 Pyrex
5.6 Water 80
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q
-q
Electric field is decreased Permittivity is
increased Compared to vacuum
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Effect on the capacitance
Capacitance is increased by ? compared to vacuum
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A parallel plate capacitor consists of metal
sheets(A 0.25m2) separated by a teflon sheet
(?2.1) with a thickness of 0.005 mm. (a) find
the capacitance. (b) Find the maximum voltage.
The maximum electric field across Teflon is
60x106 V/m.(dielectric strength)
(a)
d0.005m
?2.1
A0.25m2
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A parallel plate capacitor consists of metal
sheets(A 0.25m2) separated by a teflon sheet
(?2.1) with a thickness of 0.005 mm. (a) find
the capacitance. (b) Find the maximum voltage.
The maximum electric field across Teflon is
60x106 V/m.(dielectric strength)
(b)
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Molecular basis for dielectric constant

Dipolar molecules. e.g. water
are oriented in an E field
E
-
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Oriented molecules decrease the net charge near
the plates
The E field in the Capacitor is reduced
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Dielectric Screening High dielectric constant of
water allows ions to dissociate
Na
Cl-
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Biological membranes nerve function
A biological membrane has a specific capacitance
of 1.0 µF/cm2. If thickness of the dielectric
portion of the membrane is 2.0 nm. Find the
dielectric constant of the membrane.
Compare to ?2.5 for silicone oil
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Energy stored in a capacitor.
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Energy to charge a capacitor
q
?V
?q
-q
Work done to transfer charge ?q across potential
?V ?W ?q ?V
After charge transfer the potential increases by
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Total work to charge the capacitor is the area
under the ?V vs q plot
?V
?q
q
Energy stored
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A parallel plate capacitor consists of metal
sheets(A 0.25m2) separated by a teflon sheet
(?2.1) with a thickness of 0.005 mm. Find the
maximum energy that can be stored.
C9.2x10-7F
?Vmax300V
C
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Capacitors