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Unformatted text preview: 2/1/2012 1 Lecture 8-1 Potential Energy of a Multiple-Charge Configuration (Review) (b) (a) 1 2 / kq q d 1 3 1 3 2 2 2 q q q q q k k k d d q d + + 2 d i j ij i j i j i j q q U U k r r < < = =- a a 1 1 1 2 2 1 , 2 i j j ij i i i i j i j i j i i i j i j n j i i i i j i i j q q q U U k q k qV r r r r q U qV whereV k r r < < = = = = =-- = =- a a a a a a For n charges, Lecture 8-2 Again, Electrostatic Potential Energy The electrostatic potential energy of a system ( relative to ) is the (external) work needed to bring the charges from an infinite separation to their final positions. r 12 r 13 r 23 q 1 q 2 q 3 1 2 1 3 2 3 12 13 23 kq q kq q kq q U W r r r = = + + ( 29 2 3 3 1 1 2 1 2 3 12 13 23 12 13 23 1 1 2 2 3 3 1 2 1 2 kq kq kq kq kq kq q q q r r r r r r qV q V q V = + + + + + = + + Generally for n charges: 1 1 , 2 j i j n i i i j i i q V k r U qV r = = =- a a The factor 1/2 comes from compensating for double- counting potential energy of each pair of charges. Lecture 8-3 Electrostatic Potential Energy of Conductors bring dq in from q+dq, v +d v v kq U W dq dq R = = = Spherical conductor q, v R Total work to build charge from 0 up to Q: 2 1 2 2 Q kq kQ U U dq QV R R kQ V R = = = = = q v dq U Q V kq v R = Lecture 8-4 Capacitors Typically made of two conductors and, when charged, each holds equal and opposite charges . A capacitor is a device that is capable of storing electric charges and thus electric potential energy . => charging Its purpose is to release them later in a controlled way. => discharging Capacitors are used in vast majority of electrical and electronic devices. Capacitors come in a variety of sizes and shapes. The world's first integrated circuit included one capacitor 2/1/2012 2 Lecture 8-5 Lecture 8-6 Capacitance Capacitor plates hold charge Q The two conductors hold charge +Q and Q , respectively....
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