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Unformatted text preview: CV 2
2C
So capacitors store and release energy as they acquire
and release charge
This energy is available to drive circuits
PHY2049: Chapter 25 16 Where is the Energy Stored?
Answer: Energy is stored in the electric field itself!!
Example: Find energy density of two plate capacitor
E field is constant ε 0 ( A / d ) ( Ed )
U
CV
=
=
= 1 ε0E 2
u=
2
2 Ad
Ad 2 Ad
2 2 Energy density depends only on E field!
A general result, independent of geometry
Can be shown more generally by Maxwell’s equations u = 1 ε0E 2
2
PHY2049: Chapter 25 17 Example: Spherical Charged Conductor
Capacitance: C = ε 0 4π R Q2
Q2
=
Total energy of spherical conductor: U =
2C 8πε 0 R
Calculate directly: integrate energy density over volume u= 1 ε E2
20 U =∫ U = ∫ u dV
R dV = 4π r 2dr 2 ⎛Q⎞
Q2
ε0 ⎜
4π r 2dr =
2
⎜ 4πε r 2 ⎟
⎟
8πε 0 R
0
⎝
⎠ ∞1 R ∞ PHY2049: Chapter 25 Checks! 18 Dielectric Materials and Capacitors
Insulating material that can be polarized in E field
Induced
charges +++++++++++++++++++++++++
 κ Dielectric
material +++++++++++++++++++++++++
 Induced charges at dielectric surface partially cancel E field
E → E / κ κ > 1 is “dielectric constant”
V → V / κ (since V = Ed)
C → κC
(since C = Q / V) “Good” dielectric requires more than high κ value
Good insulator
High breakdown voltage
Low cost (no charge leakage)
(no arcing...
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 Summer '08
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 Physics, Capacitance, Charge, Electric Fields

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