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Chap23_PHY2049 - Chapter 23 Electric Potential Electric...

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Chapter 23 – Electric Potential - Electric Potential Energy - Electric Potential and its Calculation - Equipotential surfaces - Potential Gradient
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0. Review The work done raising a basketball against gravity depends only on the potential energy, how high the ball goes. It does not depend on other motions. A point charge moving in a field exhibits similar behavior. = = b a b a b a dl F l d F W ϕ cos arrowrightnosp arrowrightnosp Work: - If the force is conservative: Potential energy Work-Energy: b b a a U K U K + = + U U U U U W a b b a b a Δ - = - - = - = ) (
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Electric Potential Energy in a Uniform Field: - When a charged particle moves in an electric field, the field exerts a force that can do work on the particle. The work can be expressed in terms of electric potential energy. - Electric potential energy depends only on the position of the charged particle in the electric field. 1. Electric Potential Energy Ed q d F W b a 0 = = Electric field due to a static charge distribution generates a conservative force: y E q U U W b a = Δ - = 0
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- Test charge moving from height y a to y b : ) ( ) ( 0 b a a b b a y y E q U U U W - = - - = Δ - =
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Independently of whether the test charge is (+) or (-): - U increases if q 0 moves in direction opposite to electric force. - U decreases if q 0 moves in same direction as F = q 0 E.
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Electric Potential Energy of Two Point Charges: A test charge (q 0 ) will move directly away from a like charge q. - = = = b a r r r r r b a r r qq dr r qq dr F W b a b a 1 1 4 4 1 0 0 2 0 0 πε πε The work done on q 0 by electric field does not depend on path taken, but only on distances r a and r b (initial and end points). = = b a b a r r r r b a dl r qq dl F W ϕ πε ϕ cos 4 1 cos 2 0 0 dr = dl cos φ If q 0 moves from a to b, and then returns to a by a different path, W (round trip) = 0
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- Potential energy when charge q 0 is at distance r from q: r qq U U r r qq W b a b a 0 0 0 0 4 1 1 4 πε πε = Δ - = - = Graphically, U between
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