1Bweek7 - Physics 1B Walter Gekelman Capacitors and...

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1 Physics 1B Class Notes© Week 7 Walter Gekelman Capacitors and Capacitance Consider the potential on axis of a ring of charge (1) V = 1 4 πε 0 Q x 2 + a 2 . X is the distance from the center For a line of charge with charge density (chg/length) λ , and length 2a, the potential at a point x above the center is (2) V = 1 4 0 Q 2 a ln a 2 + x 2 + a a 2 + x 2 a and the potential of a single charge located at the origin as a function of the distance r away from it is (3) V = 1 4 0 Q r The potential between the plates of a parallel plate capacitor (plate area A, seperation between plates d is (4) V = d ε 0 Q A . These all have the form (5) Q = CV where Q is the charge on either plate. Note the quantity C depends only upon the geometry of the object. It is called the capacitance and in mks its unit is the Farad (named in honor of Michael Faraday) For example the parallel plate capacitor
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2 For a cylindrical capacitor Find the E field from Gauss’s law and then show that : When the charge on a capacitor is increased then the electric field within it increases and it consequently stores more energy. The energy stored, W is: As Q=CV this can be re-written: W = 1 Q 2 2 C = 1 2 C 2 V 2 C = CV 2 2 Capacitors in Series: Consider 2 capacitors in series with a battery across them.
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This note was uploaded on 11/12/2010 for the course PHYSICS 1B 318007241 taught by Professor Corbin during the Spring '10 term at UCLA.

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1Bweek7 - Physics 1B Walter Gekelman Capacitors and...

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