Physics II chapter 24 Notes

# Physics II chapter - Chapter 24 Capacitance and Dielectrics In this chapter the storage of electrical energy capacitors response of matter to

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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 V6.02 BQ/RS F’10 46 symbol for a capacitor in a circuit diagram: 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 - Q +Q potential difference ab V between the two conductors is always proportional to the charge Q : i.e. / Q C the proportionality constant C is known as the capacitance || V ab ab Q C V always a positive value units: farad (F) = C / V (after Michael Faraday) 1 farad is huge, typically encounter mF, F, nF or pF (milli-, micro-, nano- or pico-Farad: 10 -3 F, 10 -6 F, 10 -9 F, or 10 -12 F) 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

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parallel-plate capacitor A Q V6.02 BQ/RS F’10 47 consider two parallel conducting plates (of any flat shape) of area A separated by distance d and having charges Q and Q Opposites attract charge will reside on inner faces thickness of plates doesn’t matter. if d is very small compared to the dimensions of the faces, these act like two infinite sheets of uniform charge / QA  and /  is constant and parallel to E A . E is uniform between plates as shown with magnitude This E can be found by considering either Gaussian surface shown Consider cylinder B: Encl 0 0 Top Bottom Side ˆˆ /( ) / 0 ( ) ( ) 0 zz Q B Bk E k BE     -OR- Consider cylinder C: Encl 0 0 Top Bottom Side // 0 ( ) ( ) 0 QC C k E k  C E Either gives 00 z Q E A potential difference between the plates (point a on lower, b on upper) capacitance is (parallel-plate capacitor in vacuum) capacitance depends only on area and separation between plates (neglecting “fringe” fields). Large closely-spaced plates will store a lot of charge. Q E A 0 b ab z z z a gap gap Qd V E dl E dz E dz E d A   0 ab Q A C Vd E d Q A d Q Q b B C y a z x
spherical capacitor we saw for spherically symmetric charge Q V6.02 BQ/RS F’10 48 charge on outer shell has no effect on E between shells, so does not affect ab V 0 11 4 ab a b ab Q VV V rr   capacitance is given by if a r and b r differ by a small amount d , acts like a parallel-plate capacitor if b  (isolated sphere of radius a r ): r 0 0 4 4 1/ 0 a a Cr r Example: Find capacitance of a sphere of radius 13 cm 2

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## This note was uploaded on 08/25/2011 for the course PHYSICS II 33-107 taught by Professor B.quinn during the Summer '10 term at Carnegie Mellon.

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Physics II chapter - Chapter 24 Capacitance and Dielectrics In this chapter the storage of electrical energy capacitors response of matter to

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