Answer energy is stored in the electric field itself

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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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This note was uploaded on 07/31/2011 for the course PHY 2049 taught by Professor Any during the Summer '08 term at University of Florida.

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