Physics 2102 Jonathan Dowling Physics 2102 Lecture 11 FRI 06 FEB Capacitance I 25 1 3 QuickTime and a decompressor are needed to see this picture Tutoring Lab Now Open Tuesdays Lab Location 102 Nicholson across the hall from class Lab Hours MTWT 12 00N 5 00PM F 12 N 3 00PM Capacitors and Capacitance Capacitor any two conductors one with charge Q other with charge Q Potential DIFFERENCE between conductors V Q CV Units Farad Q Q Uses storing and where C capacitance releasing electric charge energy Most electronic of capacitance capacitors F Coulomb Volt micro Farads F pico Farads pF 10 12 F New technology Capacitance Capacitance depends only on GEOMETRICAL factors and on the MATERIAL that separates the two conductors e g Area of conductors separation whether the space in between is filled with air plastic etc Q Q We first focus on capacito where gap is filled by AIR ectrolytic 1940 70 ectrolytic new Paper 1940 70 Capacitors Variable air mica Tantalum 1980 on Ceramic 1930 on Mica 1930 We want Parallel Plate Capacitor capacitance C Q V E field between the plates Gauss Law Q E 0 0 A ate E to potential difference V r r d Q Qd dx V E dx A 0 A 0 0 0 Area of each plate A Separation d charge area Q Q A Q d What is the capacitance C Q 0 A C V d C 2 m2 C 2 CC C Units 2 Nm m Nm J V Capacitance and Your iPhone Q 0 A C V d Parallel Plate Capacitor Example A huge parallel plate capacitor consists of two square metal plates of side 50 cm separated by an air gap of 1 mm What is the capacitance C 0A d 8 85 x 10 12 F m 0 25 m2 0 001 m 2 21 x 10 9 F Very Small Lesson difficult to get large values of capacitance without special tricks C 2 m2 C 2 CC C Units 2 F Farad Nm m Nm J V Isolated Parallel Plate Capacitor A parallel plate capacitor of capacitance C is charged using a battery Charge Q potential difference V Battery is then disconnected If the plate separation is INCREASED does Potential Difference V Q a Increase Q is fixed b Remain the same C decreases 0A d c Decrease V Q C V increases Q Parallel Plate Capacitor Battery A parallel plate capacitor of capacitance C is charged using a battery Charge Q potential difference V Plate separation is INCREASED while battery remains connected es the Electric Field Increase Remain the Same Decrease Inside V is fixed by battery C decreases e0A d Q CV Q decreases E Q 0A decreases Q Q Spherical Capacitor hat is the electric field inside he capacitor Gauss Law Q E 2 4 0 r Radius of outer plate b Radius of inner plate a Concentric spherical shells Charge Q on inner shell Relate E to potential difference Q on outer shell between the plates b r r b kQ kQ V E dr 2 dr r r a a a b 1 1 kQ a b Spherical Capacitor What is the capacitance C Q V Q Q 1 1 4 0 a b 4 0 ab b a Radius of outer plate b Radius of inner plate a Concentric spherical shel Charge Q on inner shell Q on outer shell Isolated sphere let b C 4 0 a Cylindrical Capacitor What is the electric field in between the plates Gauss Law QuickTime a decompresso are needed to see Radius of outer plate b Radius of inner plate 0 Length of capacitor a L elate E to potential difference Q on inner rod Q on outer shell etween the plates cylindrical 2 0 L b C Q V Gaussian b surface of ln a radius r a b b Q E 2 rL r r V E dr b Q lnr Q Q ln dr rL 2 0 2 0L a 2 0 L a a Summary Any two charged conductors form a capacitor Capacitance C Q V Simple Capacitors arallel plates C 0 A d pherical C 4 e0 ab b a ylindrical C 2 0 L ln b a
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