chapter 4 - PHYS 133- WINTER 2008 WEEK 4, CHAPTER 29 29.2....

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PHYS 133- WINTER 2008 WEEK 4, CHAPTER 29 29.2. Model: The mechanical energy of the electron is conserved. A parallel plate capacitor has a uniform electric field. Visualize: The figure shows the before-and-after pictorial representation. The electron has an initial speed v i = 0 m/s and a final speed v f after traveling a distance d = 1.0 mm. Solve: The electron loses potential energy and gains kinetic energy as it moves toward the positive plate. The potential energy U is defined as U = U 0 + qEx , where x is the distance from the negative plate and U 0 is the potential energy at the negative plate (at x = 0 m). Thus, the change in the potential energy of the electron is Δ U e = U f – U i = ( U 0 + qEd ) – ( U 0 + 0 J) = qEd The change in the kinetic energy of the electron is ! K = K f " K i = 1 2 mv f 2 " 1 2 mv i 2 = 1 2 mv f 2 Now, the law of conservation of mechanical energy gives Δ K + Δ U = 0 J. This means 1 2 mv f 2 + qEd = 0 J ! v f = " 2 qEd m = " 2 ( ) " 1.60 # 10 " 19 C ( ) 20,000 N / C ( ) 1.0 # 10 " 3 m ( ) 9.11 # 10 " 31 kg = 2.65 # 10 6 m /s Assess: Note that Δ U e = qEd is the change in the potential energy of the electron. It is negative because q = e for the electron. Thus, the potential energy becomes more negative as d increases, that is, the potential energy of the electron decreases with an increase in d (or x ). 29.6. Model: The charges are point charges. Visualize: Please refer to Figure Ex29.6. Solve: For a system of point charges, the potential energy is the sum of the potential energies due to all pairs of charges: U elec = Kq i q j r ij i,j ! = U 12 + U 13 + U 23 = K q 1 q 2 r 12 + K q 1 q 3 r 13 + K q 2 q 3 r 23 = 9.0 " 10 9 N m 2 / C 2 ( ) 2 nC ( ) # 1.0 nC ( ) 0.03 m + 2 nC ( ) # 1.0 nC ( ) 0.03 m + # 1 nC ( ) # 1.0 nC ( ) 0.03 m $ % & ( ) = # 0.60 " 10 # 6 J # 0.60 " 10 # 6 J + 0.30 " 10 # 6 J = # 0.90 " 10 # 6 J Assess: Note that U 12 = U 21 , U 13 = U 31 , and U 23 = U 32 .
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chapter 4 - PHYS 133- WINTER 2008 WEEK 4, CHAPTER 29 29.2....

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