1. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric charge Forces between charged objects The field model and the electric field Forces and torques on charged objects in electric fields Chapter 20 Electric Forces and Fields Topics: Sample question: In electrophoresis, what force causes DNA fragments to migrate through the gel? How can an investigator adjust the migration rate? Slide 20-1

2. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Coulomb’s Law Slide 20-15

3. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Force of Gravity Slide 6-35

4. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. All charges in the diagrams below are equal magnitude. In each case, a small positive charge is placed at the blank dot. In which cases is the force on this charge: to the right? to the left? zero? Conceptual Example Problem Slide 20-28

5. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. All charges in the diagrams below are of equal magnitude. In each case, a small, positive charge is placed at the black dot. In which case is the force on the small, positive charge the largest? Slide 20-25 Checking Understanding

6. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Coulomb Force Problems 1.Sum of Electric Forces from Point Charges 2.Levitation 3.Static Equilibrium 4.Comparing Electric Forces and Gravitational Forces

7. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Coulomb’s Law and Three Charges Two charged particles, with charges q 1 = +q and q 2 = +4q, are located at a distance d = 2 cm apart on the x axis. Where can a 3 rd charge be placed so that this 3 rd charge has F e net = 0 N, i.e the 3 rd charge is in equilibrium. Hint: Draw a diagram of the electric forces on the 3 rd charge in various positions. What are the conditions of equilibrium?

8. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Coulomb’s Law and Three Charges Two charged particles, with charges q 1 = +q and q 2 = +4q, are located at a distance d = 2 cm apart on the x axis. Where should a third charged particle, with charge q 3 = +q, is placed so that F e net = 0 (equilibrium). For equilibrium, there are 3 conditions Charges must be on x-axis F e,1=>3 = F e,2=>3 The two forces must point in opposite directions

9. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Charge & Forces 1. Draw individual and net forces acting on object B for the four situations below. 2. Calculate the magnitude and direction of the net force on object B. Be sure to state your assumptions Slide 20-3

10. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Strategic Problem Solving Strategy (SPS) When solving problems, it is important to show how you reasoned from the information given in the problem and key physics ideas to your final answer. The correct final answer with units is only worth 1-3 points. The remainder of the points (70-90% of credit) are awarded for the quality of your solution. You are expected to include the following to receive full credit: Prepare Identify the Physics: State explicitly which physics’ principle(s) apply to the problem situation and that you will use to solve the problem Drawing a Picture: Draw at least one picture to visualize the physics of the problem and define your variables and constants. For motion problems this could be a motion diagram, motion graph, or pictorial diagram Collecting Necessary Information: State all the information given in the problem with correct units. Include preliminary calculations such as unit conversions Assume/Observe: State assumptions or observations that would be useful Solve Start with key equation(s) in symbol form Solve for the unknown quantity in symbols before numeric calculations Then substitute numbers with units and calculate the numeric answer Assess Check to see if your answer is reasonable Does it answer the question that was asked Does it have the right units?

11. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Solving Problems - Prepare (also identify key physics)

12. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Solving Problems (continued)

13. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Two hanging cans Slide 20-3 You and a friend are doing the laundry when you unload the dryer and your friend wants to get some idea of the amount of charge that causes static cling. You immediately take two empty soda cans, which each have a mass of 120 grams, from the recycling bin. You tie the cans to the two ends of a string (one to each end) and hang the center of the string over a nail sticking out of the wall. Each can now hangs straight down 30 cm from the nail. You take your flannel shirt from the dryer and touch it to the cans, which are touching each other. The cans move apart until they hang stationary at an angle of 10º from the vertical. Assuming that there are equal amounts of charge on each can, you now calculate the amount of charge transferred from your shirt.

14. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A model of the mechanism for electrostatic interactions A model for electric interactions, suggested by Michael Faraday, involves some sort of electric disturbance in the region surrounding a charged object. Physicists call this electric disturbance an electric field.

15. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Gravitational field due to a single object with mass We find a mathematical description of the "strength" of Earth's gravitational field at a particular location that is independent of the test mass:

16. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric field due to a single point-like charged object We use a similar approach of test charges to construct a physical quantity for the "strength" of the electric field:

17. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric field due to a single point-like charged object

18. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric field due to a single point-like charged object We can interpret this field as follows: The E field vector at any location points away from the object creating the field if Q is positive, and toward the object creating the field if Q is negative.

19. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Observational experiment Go through Force and Force / q test Movie Link

20. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Observational experiment (movie link)

21. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Superposition principle When multiple charged objects are present, each object makes its own contribution to the E field.

22. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Using the superposition principle

23. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Electric Field Slide 20-34

24. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Electric Field of a Point Charge Slide 20-35

25. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nature of Electric Field E-field Applet 1 http://physics.weber.edu/schroeder/software/EField/ http://physics.weber.edu/schroeder/software/EField/ Back-up applet:https://phet.colorado.edu/en/simulation/charges-and- fieldshttps://phet.colorado.edu/en/simulation/charges-and- fields What observations can we make about E-fields? Source Charges and Test Charges? Superposition of E-fields?

26. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Field Warm-up 1.Check your predicted vectors with the applet at the locations marked with an “x”. 2.Compare your predictions and resolve discrepancies. 3.Draw the positive charge off the bottom of screen – check predictions. 4.Note the magnitude and direction of the top, middle vector

27. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nature of Electric Field Test charge is a small positive charge to sample the E-Field Charge of test charge is small compared to source charges (source charges are the charges that generate the field) E-field vectors E-field is the force per charge E-field vectors points away from + charges E-field vectors point towards - charges E-field for point charges gets weaker as distance from source point charges increases For a point charge E = F e / q = [k Q q / r 2 ] / q = k Q / r 2

28. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Find the Electric Field Given the following forces that a positive test charge feels if placed at these three points, find the E-field vectors at these points.

29. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Find the Electric Field Given the following forces that a positive test charge feels if placed at these three points, find the E-field vectors at these points. How would the Force vectors and E-field vectors change at point 3 for the following changes: Replace the positive test charge (+q) with a negative test charge (-q) Replace the positive test charge (+q) with a test charge twice as large (+2q)

30. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Positive charges create an electric field in the space around them. In which case is the field at the black dot the smallest? Checking Understanding Slide 20-36

31. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. All charges in the diagram below are of equal magnitude. In each of the four cases below, two charges lie along a line, and we consider the electric field due to these two charges at a point along this line represented by the black dot. In which of the cases below is the net field to the right? Slide 20-36 Checking Understanding

32. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. All charges in the diagram below are of equal magnitude. In each of the four cases below, two charges lie along a line, and we consider the electric field due to these two charges at a point along this line represented by the black dot. In which case is the magnitude of the field at the black dot the largest? Slide 20-41 Checking Understanding

33. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Are the Fields Real??? Are either or both of these a possible electric field? Explain the reasoning behind your answer (Focus on the vectors, not the source charges)

34. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nature of Electric Field Vectors Test charge is a small positive charge to sample the E-Field Charge of test charge is small compared to source charges (source charges are the charges that generate the E-field) E-field vectors E-field is the force per charge E-field vectors points away from + charges E-field vectors point towards - charges E-field for point charges gets weaker as distance from source point charges increases E-fields add as vectors, at a point in space E net,x = E 1x + E 2x + … For a point charge E = F e / |q| = [k |Q| |q t | / r 2 ] / |q t | = k |Q| / r 2 Electric Force

35. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E-field lines

36. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E field lines E field lines point away from an area of positive charge and point toward an area of negative charge. Closer to the charged objects, the lines are closer together; the number of lines per unit area (the density of lines) is larger where the E field is stronger.

37. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Tip

38. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E field lines

39. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

40. Conceptual Exercise 15.2 Draw E field lines for a large, uniformly charged plate of glass.

41. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Lab Prep: Work, Potential Energy, Conservative Forces, Conservation of Energy, and Electric Potential 1.Dot Product 2.Work 3.Potential Energy 4.Conservation of Energy, Bar Charts, Potential Energy and Work 5.Electric Energy 6.Conservation of Energy

42. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric potential energy: A qualitative analysis A positively charged cannonball is held near another fixed positively charged object in the barrel of the cannon. Some type of energy must decrease if gravitational and kinetic energies increase in this process.

43. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric potential energy: A qualitative analysis Consider two oppositely charged blocks, one of which can slide without friction. When the negatively charged block is released and moves nearer the nut, the kinetic energy of the system increases.

44. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric potential energy: A quantitative analysis Use the generalized work- energy principle to analyze a situation where only the electric potential energy changes when work is done.

45. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric potential energy

46. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

47. Example Two oppositely charged objects (with positive charge +q and negative charge –q) are separated by distance r i. Will the electric potential energy of the system decrease or increase if you pull the objects farther apart? Explain.

48. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric potential energy of multiple charge systems Each pair of charged objects has an associated electric potential energy, and the total electric potential energy of the system is the sum of the energies of all pairs. For three charged objects, the total electric potential energy is:

49. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Skills for analyzing processes involving electric force and electric potential energy In conjunction with your problem-solving strategy: Decide whether you can consider the charged objects to be point-like. If you are using the work-energy principle, construct an energy bar chart. Decide where the zeros for potential energies are.

50. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Equipotential surfaces and E field

51. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Lab Prep: Work, Potential Energy, Conservative Forces, Conservation of Energy, and Electric Potential 7.Using Work by the electric force to find equipotential surfaces 8.In equilibrium, no work is done by the electric force to move a charge around on a conductor, the charge has the same the same electric potential everywhere on a conductor => therefore, the surface of a conductor is an equipotential surface.

52. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The V field Can we describe electric fields using the concepts of work and energy? To do so, we need to describe the electric field not as a force-related E field, but as an energy-related field.

53. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric potential due to a single charged object

54. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

55. The superposition principle and the V field due to multiple charges where Q 1, Q 2, Q 3, … are the source charges (including their signs) creating the field and r 1, r 2, r 3, … are the distances between the source charges and the location where we are determining the V field. So Electric Potentials (V) add just like Electric Potential Energies