Lecture12 - Physics 132 Introductory Physics Electricity...

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1 February 1, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 1 Physics 132 Introductory Physics: Electricity and Magnetism Winter Quarter 2008 Lecture 12 February 1, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 2 Capacitors and Capacitance A capacitor is a pair of conductors (called plates ) with any shape. Applying a potential difference Δ V between the plates, one plate collects a charge +Q and the other -Q. When talking about capacitors, we usually shorten Δ V to V. V is proportional to Q. We call the proportionality constant the capacitance, C. C = Q V Units: Farad(F) = Coulomb/Volt (don’t confuse the symbol C for capacitance with the unit C for Coulomb) Capacitance depends only on the geometry of the plates (size,shape, spacing, and orientation) and on the material between them. +Q -Q Δ V
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2 February 1, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 3 E Field in a Parallel Plate Capacitor +Q -Q Two plates have area A and are separated by a distance d, holding charge Q. A >> d 2 so the plates are ~infinite (“edge effects” are not important) Use Gauss’ Law to get fields. E is perpendicular to plates. + + + + + - - - - Δ V Φ = q enc ε 0 EA = η A 0 E = 0 = Q = 0 Top Gaussian surface: All charge on inner surfaces of the plates. Bottom Gaussian surface gives E field between plates: February 1, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 4 Capacitance of a Parallel Plate Capacitor = 0 V = E d x 0 = + = 0 dx = 0 Qd 0 C = = 0 = 0 = 0 Use the E field to calculate the potential difference. E is uniform between the plates. + + + + + - - - - - Δ V 0 d
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3 February 1, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 5 Charging a Capacitor A battery or power supply acts as a voltage source to produce Δ V across the terminals of C (by moving electrons) Schematic Electrons flow until the voltage across the capacitor is equal to the source voltage V 0 Then Q=CV 0 +Q -Q Δ V February 1, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 6 Steps in Calculating the Capacitance 1) Use Q to calculate E.
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This note was uploaded on 04/18/2008 for the course PHYS 132 taught by Professor Beatty during the Winter '08 term at Ohio State.

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Lecture12 - Physics 132 Introductory Physics Electricity...

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