Chapter_24 - 37 Chapter 24 Capacitance and Dielectrics In...

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Unformatted text preview: 37 Chapter 24: Capacitance and Dielectrics In this chapter… ¡ the storage of electrical energy Æ capacitors ¡ response of matter to electric fields Æ dielectrics Capacitors and Capacitance (24-1) ¡ capacitor : a set of conductors (usually two) arranged to store charge (and hence, electrical energy) when potential difference is applied • we say that a charge Q is stored in a capacitor when a charge Q + resides on one of the conductors and Q − resides on the other conductor • symbol for a capacitor in a circuit diagram: ¡ potential difference ab V between the two conductors is always proportional to the charge Q : the proportionality constant C is known as the capacitance • always a positive value • units: 1 farad (F) = 1 C / V (after Michael Faraday) ¢ 1 farad is huge, typically encounter μ F or pF (micro- or pico-Farad) • the capacitance is a measure of the ability of a capacitor to store energy • capacitance depends only on the shapes and sizes of the conductors and the nature of the insulating material between them ¡ parallel-plate capacitor • consider two parallel conducting plates (of any flat shape) of area A separated by distance d and having charges Q and –Q • if d is very small compared to the dimensions of the faces, these act like two infinite sheets of uniform charge / Q A σ = and / Q A σ − = − • E G is uniform between plates as shown with magnitude ab Q C V = E G A d Q Q − Q E A σ ε ε = = 38 • potential difference between the plates (point a on upper, b on lower) • capacitance is (parallel-plate capacitor in vacuum) • capacitance depends only on area and separation between plates (neglecting “fringe” fields) ¡ spherical capacitor • we saw for spherically symmetric charge Q • charge on outer shell has no effect on E G between shells, so does not affect ab V • capacitance is given by • if a r and b r differ by a small amount d , acts like a parallel-plate capacitor ¡ cylindrical capacitor (coaxial cable) • for cylindrically symmetric charge distribution λ • if length is L , then / Q L λ = and b b ab a a Qd V E d l E d l E d A ε = ⋅ = = = ∫ ∫ G G ab Q A C V d ε = = 1 1 4 ab a b a b Q V V V r r πε ⎛ ⎞ = − = − ⎜ ⎟ ⎝ ⎠ 4 4 1 1 a b...
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This note was uploaded on 07/14/2008 for the course PHYS 33107 taught by Professor Morningstar during the Spring '08 term at Carnegie Mellon.

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Chapter_24 - 37 Chapter 24 Capacitance and Dielectrics In...

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