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Lecture 10 - Electric potential

Lecture 10 - Electric potential - Electric potential energy...

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1 Lecture 10 Electric Potential Energy and Electric Potential Electric potential energy Electric forces are conservative (Coulomb’s law is mathematically identical to Newton’s gravitational force, which is conservative). So we can write the work done by them as a change in potential energy. B A to B B A A W F dl U U U     Electric potential energy of two point charges A test charge q moves from point A to point B near another charge Q . The work done by the electric force is: q B A to B A W F dl B A e e qQ qQ k k r r     B A r e r qQ k r B A 2 r r e dr r qQ k B r A r B Q A ( ) constant e qQ U r k r Electric potential energy function for two point charges   B A U U Example: Electric potential energy. Three charges q = 3.0 nC are initially fixed at the corners of an equilateral triangle of side a = 1.0 cm. One of them is released. Find its kinetic energy when it has doubled the distance to each of the other two charges. q q q a q = 3.0 nC a = 1.0 cm q q q 2 a 2 2 9 2 9 f 2 Nm (3.0 10 C) 2 2(9 10 ) 8.1 J 2 C 2(0.01 m) q K k a i i f f K U K U 2 2 f 0 2 2 2 q q k K k a a
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2 ACT: Stored energy What is the electric energy stored in a system of three charges q = 3.0 nC that form an equilateral triangle of side a = 1.0 cm? (with U infinity = 0) = How much energy did I put in the system when I built it? = How much work was done to built it? q q q a q = 3.0 nC a = 1.0 cm The stored energy is: A. Positive. B. Negative. C. Zero. We have to push the charges to arrange them like this Add energy Or: Unless charges are somehow fixed, they will move to a situation with less energy ( U infinity = 0).    i f ( ) U U U Work to bring the first charge from infinity: q = 3.0 nC a = 1.0 cm ext,2 i f W U U Work to bring the second charge from infinity: N (3 0 10 C) 2 0 q k a   ext,1 by E field,1 W W 0 0 0 2 2 ext,3 i f 0 q q W U U k k a a Work to bring the third charge from infinity: total stored 0 8.1 16.2 24.3 J (> 0, as expected) W U 2 9 2 9 2 Nm (3.0 (9 10 ) 8.1 J C 0.01 m
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