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Phys 133 – Chapter 301 Chapter 28 Electric Potential

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Phys Chapter 292 Looking ahead New force (Chapter 25) New potential energy (Chapter 28)

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Phys Chapter 293 Electric Potential Energy (U elec ) Potential energy ~ Gravitational ~ Uniform electric field ~ Point charge

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Phys Chapter 294 Gravitational potential (energy) Defined Then defined For the gravitational force In general

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Phys Chapter 295 Uniform field: Electric potential energy where

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Phys Chapter 296 s Uniform field: Electric potential energy s Direction of lower potential energy depends on type of charge Lower potential energy Positive chargeNegative charge

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Phys Chapter 297 Do Workbook 29.6

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Phys Chapter 298 A proton is released from rest at the positive plate of a parallel plate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. What will be the speed if the experiment is repeated with double the amount of charge on the capacitor plates? (Ans: 7.07x10 4 m/s) Problem 29.3

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Phys Chapter 299 Electrical Potential Energy of Two Point Charges where

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Phys Chapter 2910 Question b) Two point charges (+/- Q) have their separation increased. Does the electric potential energy of the system (A) increase, (B) decrease or (C) remain the same? a) Two point charges (both +Q) have their separation increased. Does the electric potential energy of the system (A) increase, (B) decrease or (C) remain the same?

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Phys Chapter 2911 Question ans Like charges Opposite charges

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Phys Chapter 2912 Do Workbook 29.3

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Phys Chapter 2913 An electron (q=-e) is sent from very far away towards a charged sphere (Q=-0.25 nC). It gets to a distance of 1.10 mm from the center of the sphere before turning around. What is the initial speed of the electron? (Ans: 2.68x10 7 m/s) What was the speed of the same electron with same initial conditions when it was 2.20 mm away? e=1.6x C, m e =9.1x kg, K=9x10 9 Nm 2 /C 2 Problem

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Phys Chapter 2914 Problem ans

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Phys Chapter 2915 Electric Potential (V elec ) Potential ~ Gravitational ~ Uniform electric field ~ Point charge

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Phys Chapter 2916 Electric Potential (V elec ) Potential only depends on source charges Charge creates potential define Look at Gravitational Uniform electric field Point charge

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Phys Chapter 2917 Gravitational Potential environment object Environment only

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Phys Chapter 2918 Electric potential capacitor s 0 (from before) environment object Environment only

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Phys Chapter 2919 Capacitor: potential representations

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Phys Chapter 2920 Draw V(x) for the two equipotential surfaces Draw U(x) for a proton in these potentials Draw U(x) for an electron in these potentials

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Phys Chapter 2921 Workbook 29.18b extension A proton is at x=0, moving to the right with 5x J of kinetic energy. What is its kinetic energy at point a? What if it were an electron?

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Phys Chapter 2922 Workbook 29.18b extension ans proton electron Not enough energy to reach a

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Phys Chapter 2923 a)In the figure which capacitor plate, left or right, is the positive plate? b)What is the electric potential energy of a proton at the midpoint of the capacitor? c)What is the electric field strength inside the capacitor? Problem Modified In general d)What is the electric field strength inside the capacitor in terms of and o ? e)What is the electric field strength inside the capacitor in terms of ∆V and d (the distance between the plates?

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Phys Chapter 2924 Only potential difference matters

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Phys Chapter 2925 Electric potential two point charges (from before)

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Phys Chapter 2926 Point particle: potential representations

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Phys Chapter 2927 Do Workbook 29.21

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Phys Chapter 2928 Electric Potential: multiple charges No vectors

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Phys Chapter 2929 Do Workbook 29.25

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Phys Chapter 2930 a) Find an expression for the electric potential V(x,y) for a dipole with point charges +/- Q at y= +/- a. Problem b) Use the result for the dipole to find the electric potential at x=2 m, y=7 m when a=2 m, and Q=2 nC. c) What is the potential energy of a proton placed there?

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Phys Chapter 2931 Problem ans r+r+ y-a xx y+a r-r-

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Phys Chapter 2932 Problem plot

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Phys Chapter 2933 Problem ans c) What is the potential energy of a proton placed there? b) Use the result for the dipole to find the electric potential at x=7 m, y=2 m when a=2 m, and Q=2 nC.

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Phys Chapter 2934 Potential of continuous charge distribution where Then let solve

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Phys Chapter 2935 The figure shows a thin rod of length L and charge Q. Find an expression for the electric potential a distance x away from the center of the rod on the axis of the rod. Problem 29.69

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Phys Chapter 2936 Problem x y P (d,0) riri i th xixi d Find potential at P due to i th bit of charge Sum up contribution from each charge at P

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