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Phys 0175 - Lecture 14

# Phys 0175 - Lecture 14 - Lecture 14(Feb 6 2009 Chapter 25...

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Lecture 14 (Feb. 6, 2009): Chapter 25: Capacitance (conclusion) Energy stored in a capacitor Electric field energy Capacitor with a dielectric material Atomic view of dielectric material Applying Gauss’ Law to dielectric material Illustrative examples

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Energy storage in capacitors: 2 0 0 1 2 f q W f q q dq V dW V dq C C q W dW q dq C C = = = = = = The electric potential energy stored in a capacitor is equal to the amount of work that has to be done to charge it: If we take U=0 for an uncharged capacitor, then 2 2 1 1 2 2 2 q U W CV qV C = = = =
Electric-Field Energy: We can think of the electric energy in a capacitor as being stored in the electric field that exists in the region between the plates. If a parallel plate capacitor has plate area A and plate spacing d, then the volume between the plates where the electric field exists is A*d. Hence the energy density is u = U/Ad = ½CV 2 /Ad Since C = ε 0 A/d for a parallel plate capacitor and V = Ed, we get u = ½ε 0 E 2 provided the space between the plates is a vacuum.

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Dielectric materials: Nonconducting materials that are placed between the conducting plates of most capacitors
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Phys 0175 - Lecture 14 - Lecture 14(Feb 6 2009 Chapter 25...

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