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Chapter 20 Electric Forces and Fields Topics: • Electric charge • Forces between charged • • objects The field model and the electric field Forces and torques on charged objects in electric fields Sample question: In electrophoresis, what force causes DNA fragments to migrate through the gel? How can an investigator adjust the migration rate? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 20-1 Conductors and Electric Fields Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 20-55 Consider an infinite sheet of charge h Q E= where h = 2e 0 A • Epsilon nought, e 0 = 8.85 ´ 10 -12 C2 N × m2 is electric permitivity of free space • Electric permitivity is a measure of how well electric field can pass through space or materials Discuss charge density Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Consider two infinite sheets of charge What is the E-field at points A, B, and C ? Case 1: A B C Qleft = +Q Qright = -Q Case 2: Qleft = 2Q Qright = Q Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding Two parallel plates have charges of equal magnitude but opposite sign. What change could be made to increase the field strength between the plates? A. B. C. D. E. Increase the magnitude of the charge on both plates Decrease the magnitude of the charge on both plates Increase the distance between the plates Decrease the distance between the plates Increase the area of the plates (while keeping the magnitude of the charges the same) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Answer Two parallel plates have charges of equal magnitude but opposite sign. What change could be made to increase the field strength between the plates? A. B. C. D. E. Increase the magnitude of the charge on both plates Decrease the magnitude of the charge on both plates Increase the distance between the plates Decrease the distance between the plates Increase the area of the plates (while keeping the magnitude of the charges the same) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Equations (Physics 151) Key Ideas on Energy from Physics 151 Dot Product Energy Bar Charts Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Chapter 21 Key Equations (Physics 151) Key Energy Equations from Physics 151 Definition of Work Work W = F i Dr = F Dr cos a Work- Energy Theorem (only valid when particle model applies) Wnet = DKE Work done by a conservative force (Fg, Fs, & Fe) Wg = -DPEg Also work done by conservative force is path independent Conservation of Energy Equation KEi + å PEi + D Esys = KE f + different types Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. å PE f + DEth different types Slide 21-16 Review of Work Definition of Work: Work W = F i Dr = F Dr cos a where a = angle between the vectors • Calculate the work done in moving each ball from y = 0 meters to y = 5 meters • Calculate the work per kg for moving each ball from y = 0 m to 5 m • Calculate the change in gravitational potential energy per kg for moving each ball from = 0 m to 5 m • Calculate the speed each ball would have as it reached the ground if released from 5 meters above the ground Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electric Potential Energy Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-9 Chapter 21 Key Equations (2) Key Energy Equations from Physics 152 q1q2 PEe = k r12 Electric Potential Energy for 2 point charges (zero potential energy when charges an infinite distance apart) Potential Energy for a uniform infinite plate DPEe = -We = - éë Fe × Dr cos a ùû = - ( q E ) Dr cos a For one plate, zero potential energy is at infinity For two plates, zero potential energy is at one plate or inbetween the two plates Electric Potential V and Change in Electric Potential => ΔV PEe V= qtest DPEe We DV = =qtest qtest Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Example: Electric Potential Energy A cart on a track has a large, positive charge and is located between two sheets of charge. Initially at rest at point A, the cart moves from A to C. a. Draw qualitative force diagrams for the cart at positions A, B and C. b. Draw qualitative energy bar charts for the cart when it is at each position A, B and C. List the objects that make up your system: c. How would your force and energy diagrams change (if at all) if the sheet to the right were also positively charged? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Changes in Electric Potential Energy ΔPEe For each situation below, identify which arrangement (final or initial) has more electrical potential energy within the system of charges and their field. Initial (A) Final (B) Greatest ΔPEe (a) (b) (c) (d) Hydrogen Atom Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Changes in Electric Potential Energy ΔPEe For each situation below, identify which arrangement (final or initial) has more electrical potential energy within the system of charges and their field. Initial (A) Final (B) Greatest ΔPEe (e) (f) (g) Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Changes in Electric Potential Energy ΔPEe Is the change ∆PEe of a + charged particle positive, negative, or zero as it moves from i to f? (a) Positive (b) Negative (c) Zero (d) Can’t tell Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-11 Electric Potential Uelec = qV; V = U elec / q Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-10 Chapter 21 Key Equations (3) Key Points about Electric Potential Electric Potential increases as you approach positive source charges and decreases as you approach negative source charges (source charges are the charges generating the electric field) A line where ΔV= 0 V is an equipotential line (The electric force does zero work on a test charge that moves on an equipotential line and ΔPEe= 0 J) For a point charge q 1 q V=K = r 4pe 0 r For very large charged plates, must use DPEe We Fe i Dr qtest E i Dr DV = ==== -E i Dr = - E Dr cos a qtest qtest qtest qtest Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electric Potential and E-Field for Three Important Cases Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-25 Checking Understanding Rank in order, from largest to smallest, the electric potentials at the numbered points. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-14 Example A proton has a speed of 3.5 x 105 m/s at a point where the electrical potential is 600 V. It moves through a point where the electric potential is 1000 V. What is its speed at this second point? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-15