Chapter 23 lecture for ctools - Electric Potential Energy...

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Electric Potential Energy and Electric Potential
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Recall from Mechanics…… We often had 2 ways to solve for an object’s motion: 1. Force equation: 1. Energy equation: (conservation of energy) 2 2 dt r d m a m F = = external W K U E = + = ) ( Work done by a force in a displacement from initial position i to final f: l d F W f i f i = (Work in Joules)
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E F 0 = = l d F W E roundtrip is a conservative force if: (i.e. The work done is independent of path taken from i to f)
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The electrostatic force is Conservative f i W E F 0 = = l d F W E roundtrip is a conservative force if: i.e. Is independent of path taken from i to f ) ( ) ( r U r F E - = Then, the following are true: 1. There exists a scalar potential energy function U(r) with 2. U f + K f = U i + K i if no external work is done (conservation of energy) 3. For a slow displacement from rest to rest (K=0): ΔU= U f – U i = W ext,i→f = -W E,i→f (Change in U is the negative of the work done by the conservative force) z k y j x i + + = ˆ ˆ ˆ
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Question 1 In a uniform electric field a charged particle is slowly displaced from point a to point b (from rest to rest). Which statements are true? E a b A. For a + charge F ext does + work and F E does – work B. For a – charge F ext does - work and F E does + work C. U for a + charge is higher at point a D. U for a – charge is higher at point a 1. None of them 2. A and B 3. C only 4. A, B, and D 5. All of them
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U for a point charge q 0 near point charge q f 0 0 2 0 r take e, convenienc for ) 1 1 ( r r kqq dr q r kq l d E q l d F
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