chapter23--PHY131 JAB

# chapter23--PHY131 JAB - Chapter 23 Electric potential...

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1 •Electric potential energy •Electric potential •Calculating electric potential •Equipotential surfaces •Potential gradient Chapter 23: Electric potential

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2 The work by a force F in moving between two points a and b is = b a b a d W l F If the work is done by a conservative force then W a b = - Δ U. §23.1 Electric Potential Energy
3 Electric potential energy (U e ) is energy stored in the electric field. •U e depends only on the location, not upon the path taken to get there (conservative force). •U e = 0 at some reference point •For two point particles take U e = 0 at r = •For the electric force r q kq U e 2 1 =

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4 Example: A proton and an electron, initially separated by a distance r, are brought closer together, how does the potential energy of this system of charges change? Bringing the charges closer together decreases r: . For these two charges r ke U e 2 - = 0 < - = Δ ei ef e U U U This is like a mass falling near the surface of the Earth: positive work is done by the field.
5 When q 1 and q 2 have the same algebraic sign then Δ U e > 0 This means that work must be done by an external agent to bring the charges closer together. Example continued How will the electric potential energy change if both particles have positive (or negative) charge?

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6 What is the potential energy of a system (arrangement) of point charges? To calculate: Begin by placing the first charge at a place in space far from any other charges. No work is required to do this. Next, bring in the remaining charges one at a time until the desired configuration is finished.
7 Example: What is the potential energy of three point charges arranged as a right triangle? 12 r 2 q 1 q 3 q 13 r 23 r 0 = e U 12 2 1 r q kq + 23 3 2 13 3 1 r q kq r q kq + + 12 r 2 q 1 q 3 q 13 r 23 r 0 = e U 12 2 1 r q kq + 23 3 2 13 3 1 r q kq r q kq + + Are these the same?

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8 For an arbitrary number of charges: ∑∑ = > = = n i n i j j ij j i e r q q U 1 1 0 4 1 πε
Electric potential is the electric potential energy per unit charge. test

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chapter23--PHY131 JAB - Chapter 23 Electric potential...

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