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. Newton’s Laws of Motion Newton ’ s Zeroeth Law of Motion Objects are dumb. They do not know the past and they are not good predictors of the future. They only know what forces act on them right now. Newton ’ s First Law of Motion Every object continues in a state of rest or a state of motion with a constant speed in a straight line unless acted on by an unbalanced net force. Newton ’ s 2nd Law of Motion When a force, F, acts on an object with a mass, m, it produces an acceleration, a, equal to the force divided by the mass. Newton ’ s Third Law of Motion To every action there is an equal and opposite reaction. Or, when one object exerts a force on a second object, the second exerts an equal and opposite force on first. a = F net m

3. 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

4. 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

5. 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

6. 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

7. 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)

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

9. 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.

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

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

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

13. Are E-field lines trajectories? E-field Applet 2 http://webphysics.davidson.edu/physlet_resources/bu_semester2 /menu_semester2.html E-field and trajectory => gravitational example with thrown eraser E-Field Applets Field lines and field vectors Electric Field from a point Charge Electric Field from two charges (like and unlike – dipole) Plate of Charge (different Applet - falstad.com/vector2defalstad.com/vector2de Motion of a Test Charge What observations can we make about E-field lines?

14. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E-field Strength and Symmetry Examples from Gravity Spherical Earth Flat Earth Field Strength Field converges => Magnitude of Field increases Field diverges => Magnitude of Field decreases Field uniform => ??? E-field Symmetry Point Charge => Spherical Symmetry Line of Charge => Cylindrical Symmetry Plate of Charge => ???

15. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Consider an infinite sheet of charge What kind of symmetry would we expect? What will the field look like? Is the field (A) converging, (B) diverging, or (C) neither -- (D) can’t tell What can we say about E-field strength? A charged sheet can be considered to be like an infinite sheet when we look at points a distance d away where d << L, where L is the length of a side of the sheet

16. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Consider an infinite sheet of charge Epsilon nought, is electric permitivity of free space Electric permitivity is a measure of how well electric field can pass through space or material

17. 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: Q left = +Q Q right = -Q Case 2: Q left = 2Q Q right = Q A B C

18. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Conceptual Exercise 15.2 Draw E field lines for a very large, uniformly charged plate of glass.

19. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dipole and Uniform Electric Fields Slide 20-45

20. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Field Lines Slide 20-50

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

22. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A set of electric field lines is directed as below. At which of the noted points is the magnitude of the field the greatest? Slide 20-46 Checking Understanding

23. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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.Increase the magnitude of the charge on both plates B.Decrease the magnitude of the charge on both plates C.Increase the distance between the plates D.Decrease the distance between the plates E.Increase the area of the plates (while keeping the magnitude of the charges the same) Checking Understanding

24. 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.Increase the magnitude of the charge on both plates B.Decrease the magnitude of the charge on both plates C.Increase the distance between the plates D.Decrease the distance between the plates E.Increase the area of the plates (while keeping the magnitude of the charges the same)

25. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Nature of Electric Field Lines E-Field lines start on + charges and end on -- charges Larger charges will have more field lines going out/coming in Density of Field lines is a measure of field strength – the higher the density the stronger the field The E-field vector at a point in space is tangent to the field line at that point. If there is no field line, extrapolate

26. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Conductors and Electric Fields Slide 20-55

27. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Forces and Torques on Charges in Electric Fields Slide 20-56

28. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 20-5

29. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Determining the E field produced by given source charges

30. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 1.Determine the magnitude and the direction of the electric field at point A. E-field Superposition Example In your physical diagram, make sure you label your r’s as well as your angles

31. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 1.Determine the magnitude and the direction of the electric field at point A. 2.Determine the individual forces and the net force on charge B for each of the following cases. Slide 20-66 E-field Superposition Examples

32. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example Problem 1 Two small metal spheres attached to insulating stands reside on a table a distance d apart. The left sphere has positive charge +q and the right sphere has negative charge −q. Determine the magnitude and direction for the E field at a distance d above the center of the line connecting the spheres.

33. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Problem-solving strategy: Incorporating the E field into Newton's second law In the ”Prepare" step, be sure to determine the E field produced by the environment. Is it produced by point-like charges (making it non-uniform) or by large charged plates (making it uniform)?

34. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example Problem 2 Inside an inkjet printer, a tiny ball of black ink of mass 1.1 x 10 −11 kg with charge −6.7 x 10 −12 C moves horizontally at a speed of 40 m/s. The ink ball enters an upward-pointing uniform E field of magnitude 1.0 x 10 4 N/C produced by a negatively charged plate above and a positively charged plate below. The plates deflect the ink ball so that it lands at a particular spot on a piece of paper. Determine the deflection of the ink ball after it travels 0.010 m in the E field.

35. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. What to do to do well in this class A.Focus on key physics concepts May seem like basics but will help you solve even complex problems Focus on principle rather than recipes Need to have a functional understanding of key concepts Express key equations as sentences Know where they come from and what they mean Know how and when to apply them Know which equations are general and which are special cases Must know when not to apply special cases Look at a problem after a good physics diagram and maybe a good physical diagram and know what key physics concepts apply in that problem Memorize key concepts so you can look at a problem, say that’s Newton 2, and know the associated equation in a snap Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

36. What to do to do well in this class A.Focus on key physics concepts How to do this When you look at problems, mentally group problems by the physics rather than the physical situation After each class or at least each week, create a notesheet to organize a structure of the new key concepts for each chapter and note how they fit in with previous key concepts Use the note sheet to do homework problems (a) do as many homework problems as you can just using this sheet. (b) then go to your notes and the textbook for your missing pieces Use flash cards to memorize key concepts - include the concept description, relevant equations, diagrams, and what types of problems benefit from using that concept Pay close attention to examples done in class and note the physics and assume/observes in each example and how these are used Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

37. Chapter 21 Key Equations (Physics 151) Key Energy Equations from Physics 151 Types of Energy Conservation of Energy Equation (key concept) Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

38. Chapter 21 Key Ideas (Physics 151) Conservation of Energy Energy Bar Charts (Visualization for Conservation of Energy) Displays Conservation of Energy Equation in graphical form Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

39. Energy Bar Graph Sample

40. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Equations (Physics 151) Key Energy Equations from Physics 151 Definition of Work Where Work done by a conservative force (F g, F s, & F e ) Also work done by conservative force is path independent Conservation of Energy Equation Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

41. 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.

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

43. 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.

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

45. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Finding the electric potential energy when the V field is known If we know the electric potential at a specific location, we can rearrange the definition of the V field to determine the electric potential energy:

46. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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  V= 0 V is an equipotential line (The electric force does zero work on a test charge that moves on an equipotential line and  Pe e = Delta U e = 0 J) For a point charge For very large charged plates, must use Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

47. Electric Potential Energy Example Problem The electric field between two charged plates is uniform with a strength of 4 N/C. Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. a. Draw several electric field lines in the region between the plates. b. Determine the change in electrical potential energy in moving a positive 4 microCoulomb charge from A to B. c. Find Delta V between A and B.

48. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Define Capacitance Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitance is a measure of how much charge can be stored in a capacitor for a given amount of voltage Determine the capacitance of a parallel plate capacitor (most common type of capacitor)

49. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Capacitance of a Parallel-Plate Capacitor Slide 21-31

50. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitance and Capacitors The charge ±Q on each electrode is proportional to the potential difference ΔV C between the electrodes: Slide 21-29

51. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dielectrics and Capacitors The molecules in a dielectric become oriented in a way that reduces the electric field from external source charges in the dielectric. This means that the electric field within the dielectric is less than it would be in air, allowing more charge to be stored for the same potential.

52. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Choosing the System Slide 10-16

53. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dot Product Slide 4-19 Dot product or scalar product is a way of multiplying two vectors to get a scalar result Dot products can be calculated either independent of a coordinate system where is the angle between the two vectors Note that in this vector form the sign of the dot product only depends on the angle Component form of Dot Product

54. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Ideas (Physics 151) Dot Product Method for multiplying two vectors to get a scalar Definition of Work Work is how forces add energy to or take away energy from a system. It is the effect of a force applied over a displacement. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

55. Dot Product: Example 1 Dot product or scalar product is a way of multiplying two vectors to get a scalar result Dot products can be calculated either independent of a coordinate system where is the angle between the two vectors Vector A has a magnitude of 4 units Vector B has a magnitude of 3 units Angle between them = 60 degrees

56. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy Bar Chart Example 1

57. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy Bar Chart Example II

58. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy Bar Chart Example III