PHY2049: Chapter 251ÎCoulomb’s law and Gauss’ lawE field Force FPotential V Energy UÎApplications: Capacitance (Ch. 25)Electric circuits (Ch. 26)Review and Overview(differentiate)(differentiate)(integrate)(integrate)---- F=qE ------- U=qV ---Coulomb’s lawGauss’law(equivalent)Current I=dq/dtPHY2049: Chapter 252Ch. 25 SubjectsÎCapacitor and Capacitance: definitions and units ÎCapacitance: calculationÎCapacitors in parallel and seriesÎEnergy stored in electric fieldÎDielectrics (insulators)PHY2049: Chapter 253CapacitorsCapacitorsCapacitors on a computer motherboardPHY2049: Chapter 254Î Capacitor Two conductors, electrically isolated from each other Particularly when the pair is used as a device in an electronic circuit to store charge and for other purposesÎ Capacitance C is a constant that characterizes given pair of conductors in given configuration (Can be generalize to a single conductor. Read Section 25-3.) For given (applied) V, capacitor with larger C stores more q For given q, smaller V appears in capacitor with larger CÎ UnitsF (farad) 1 F = 1 C/V (C: coulomb, not capacitance) Note: ε0=8.854x10-12C2/N m2=(same value) F/mDefinitions and UnitsCVq=PHY2049: Chapter 255Let us postpone the question for the moment.Why do we consider only +q and –q forming a pair? Why not +q and –Q?PHY2049: Chapter 256Capacitance calculation 1: parallel platesAqεE01=00εqEAdS=+=⋅∫AEGauss’ lawSolve for EPotential difference (Do not worry about sign.+ is always high.)AqdεEddV01==⋅−=∫+−sEdAεVqC0==Capacitance [capacitance]=ε0x [length]F = F/m x mPHY2049: Chapter 257Capacitance calculation 2: coaxial cylindersrLqπεE021=∫∫+−=⋅−=bardrLqπεdV021sEGauss’ lawSolve for E◊ [capacitance]=ε0[length]◊ Depends only weakly on radii◊ Inner conductor cannot be approximated to be line with no thickness. Then C=∞.Ignore ends, approximating cylinder to be infinitely longPotential difference (Do not worry about sign.+ is always high.)00)2(εqrLπEdS=+=⋅∫AE=−abab ln ln ln()abLπεVqCln20==CapacitanceRadii a and
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