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Unformatted text preview: 37 Chapter 24: Capacitance and Dielectrics In this chapter the storage of electrical energy capacitors response of matter to electric fields 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 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 = and / Q A = E G is uniform between plates as shown with magnitude ab Q C V = E G A d Q Q Q E A = = 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 if length is L , then / Q L = and b b ab a a Qd V E d l E d l E d A = = = = G G ab Q A C V d = = 1 1 4 ab a b a b Q V V V r r = = 4 4 1 1 a b...
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