lecture10 - A Q Recall A Q E = = (between plates) A Qd Ed V...

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Capacitance (Chapter 26) Capacitance (Chapter 26) Capacitance – the property of a conductor or set of conductors and insulators to store electric charge Capacitor – an electronic component that has the ability to store charge Definition Calculating Capacitance Dielectrics and Dielectric Constant
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Definition : Capacitance C of two conductors with equal but opposite charges Q C V = V = potential difference created when charge +Q is on one conductor, and –Q is on the other. Unit : (F) farad volt coulomb 1 = Typically ranges from 1 μ F = 10 -6 F and 1pF = 10 -12 F 1 F is a LOT of stored charge !!!
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1) Find the electric field as a function of r using Gauss’s Law. 2) Choose a path along a field line: the potential change with each small change dr in distance is dV = - E(r)dr 3) Integrate from start to end of field line to find the potential difference. 4) C=Q/ V Finding C for Symmetrical Charges
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Example 1: Parallel Plates Example 1: Parallel Plates area A, separation d d +Q -Q Surface charge densities:
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Unformatted text preview: A Q Recall A Q E = = (between plates) A Qd Ed V = = (uniform ) E d A V Q C = = Hence, C depends only on the geometry of the plates Quiz: Quiz: d +Q-Q As the plates are moved apart, which of the following will i) increase? ii) decrease? iii) stay the same? A) Electric field between the plates B) Electric potential difference between the plates C) Capacitance of the plates Example 2: Concentric Spheres Example 2: Concentric Spheres R 1 R 2 1 2 1 1 1 4- -= R R C Derive: +Q-Q Examples: Examples: 1) 2 sheets of foil, 25 cm x 40 cm, 1 mm apart (in air.) 2) The earth and the ionosphere (height: 100 km) as a pair of concentric spheres. Find capacitances of Example 3: Concentric Example 3: Concentric Cylinders Cylinders R R-Q +Q L For L >> R 2 , show: = 1 2 ln 2 R R L C Solution:...
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lecture10 - A Q Recall A Q E = = (between plates) A Qd Ed V...

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