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1-31-08Lec08

# 1-31-08Lec08 - Lecture 8-1 Again Electrostatic Potential...

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Lecture 8 Lecture 8 - 1 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 = = + + ( ) 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 n i i i U qV = = The factor 1/2 comes from compensating for double- counting potential energy of each pair of charges.

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Lecture 8 Lecture 8 - 2 Electrostatic Potential Energy of Conductors bring dq in from q+dq, v +d v v kq U W dq dq R Δ =Δ = = Spherical conductor q, v R Total work to build charge from 0 up to Q: 2 0 1 2 2 Q kq kQ U U dq QV R R = Δ = = = ∫ ∫ q v dq U Δ Q V kq v r =
Lecture 8 Lecture 8 - 3 Capacitors • 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. +Q - Q Q Δ Q Q Δ Typically made of two conductors and, when charged, each holds equal and opposite charges .

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Lecture 8 Lecture 8 - 4 Capacitance • Capacitor plates hold charge Q The two conductors
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1-31-08Lec08 - Lecture 8-1 Again Electrostatic Potential...

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