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. 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.

3. 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.

4. 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

5. 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. Note: E-field lines represent the force a test object would feel at that point; however, test objects do not necessarily move along field lines.

6. 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

7. 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

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

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

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

11. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A dipole is held motionless in a uniform electric field. For the situation below, when the dipole is released, which of the following describes the subsequent motion? A. The dipole moves to the right. B. The dipole moves to the left. C. The dipole rotates clockwise. D. The dipole rotates counterclockwise. E. The dipole remains motionless. Checking Understanding

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

13. 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

14. 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

15. 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.

16. 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)?

17. 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.

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

19. 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

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

21. 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.

22. Chapter 21 Key Equations (Physics 151) Key Energy Equations from Physics 151 Definition of Work Where Work- Energy Theorem (only valid when particle model applies) 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.

23. Energy Bar Graph Sample

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

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

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

27. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Review of Work Definition of Work: where 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 Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

28. 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.

29. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Potential Energy Slide 21-9

30. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Potential Energy Slide 21-9 Case A - Book starts & stops at rest Case C - Charge at rest at A and B

31. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Equations (2) Key Energy Equations from Physics 152 Electric Potential Energy for 2 point charges (zero potential energy when charges an infinite distance apart)  Potential Energy for a uniform infinite plate 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 =>  V Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

32. Graphing the electric potential energy versus distance Because of the 1/r dependence, the electric potential energy approaches positive infinity when the separation approaches zero, and it becomes less positive and approaches zero as like charges are moved far apart.

33. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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? Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

34. Changes in Electric Potential Energy -  PE e For each situation below, identify which arrangement (final or initial) has more electrical potential energy within the system of charges and their field. Slide 21-16 Initial (A) Final (B)Greatest  PE e (a) (b) (c) (d)Hydrogen Atom

35. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Changes in Electric Potential Energy – Delta PE e For each situation below, identify which arrangement (final or initial) has more electrical potential energy within the system of charges and their field. Slide 21-16 Initial (A) Final (B)Greatest  PE e (e) (f) (g)

36. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Changes in Electric Potential Energy – Delta PE e Is the change ∆PE e 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 Slide 21-11

37. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Potential Model Worksheet 2: Energy and Potential in Uniform Fields Rank the change in gravitational potential energy for the following lettered objects in the Earth ’ s gravitational field. Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. a.. most  _______ _________ ________ ________ _______ _______ ________ b. Explain your ranking, stating why each is greater than, less than, or equal to its neighbors. c. Where is the energy stored? What gains or loses energy as the masses move from one place to another?

38. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 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. Determine the change in electrical potential energy in moving a negative 12 microCoulomb charge from A to B.

39. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Gravitational Potential Energy: Example Problem 2 A spacecraft is launched away from earth Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. a. Draw several gravitational field lines in the region around Earth. b. Determine the change in gravitational potential energy when the spacecraft moves from A to B, where A is 10 million miles from Earth and B is 30 million miles from Earth.

40. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Potential Energy: Example Problem 3 A small charge moves farther from a positive source charge. Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. a. Draw several electric field lines in the region around the source charge. b. Determine the change in electrical potential energy in moving a positive 4 nC charge from A to B, where A is 3 cm from the source charge and B is 10 cm away. c. Determine the change in electrical potential energy in moving a negative 4 nC charge from A to B.

41. 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.

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

43. 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:

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

45. 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

46. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Quantitative Example Suppose that the heart's dipole charges −Q and +Q are separated by distance d. Write an expression for the V field due to both charges at point A, a distance d to the right of the +Q charge. 1. Simplify and diagram. 2. Represent mathematically.

47. 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:

48. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Potential difference – Delta V The value of the electric potential depends on the choice of zero level, so we often use the difference in electric potential between two points.

49. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Particles in a potential difference A positively charged object accelerates from regions of higher electric potential toward regions of lower potential (like an object falling to lower elevation in Earth's gravitational field). A negatively charged particle tends to do the opposite, accelerating from regions of lower potential toward regions of higher potential.