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George Cross Electromagnetism Electric Field Lecture27 (2)

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Electric field, field of multiple charges, field of continuous charge, parallel plate capacitor, motion of charge in electric field, motion of dipole in field

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George Cross Electromagnetism Electric Field Lecture27 (2)

1. 1. General Physics Physics 120 Chapter 27: THE ELECTRIC FIELD Antelope Valley College Math & Sciences Dept George Cross
2. 2. TODAYS LECTURE • THE ELECTRIC FIELD – Electric Field Models – The Electric Field of Multiple Point Charges – The Electric Field of a Continuous Charge Distribution – The Electric Fields of Rings, Disks, Planes, and Spheres – The Parallel-Plate Capacitor – Motion of a Charged Particle in an Electric Field – Motion of a Dipole in an Electric Field
3. 3. CHAPTER 27 QUIZ 1. Which statement/s is/are not true? • The electric field obeys the principle of superposition. • The tangent to an electric field line at a point gives the direction of the field at that point. • The density of electric field lines is directly proportional to the strength of the field. • Negative charges are sources of electric field lines and positive charges are sinks of electric field lines. • Electric fields are what you find in PlayStation football and soccer games.
4. 4. CHAPTER 27 QUIZ 2. An electric dipole in a uniform electric field experiences • Happiness and excitement • only a net external force. • only a torque. • both a net external force and a torque. • neither a net external force nor a torque. • answer depends on the strength of the field
5. 5. 3. Choose the correct statement/s concerning electric field lines: a.) field lines may cross b). field lines are close together where the field is large c). field lines point away from negative charge d). a point charge released from rest moves along a field line e). field lines are made with white chalk f). none of these are correct
6. 6. 4. What device provides a practical way to produce a uniform electric field? a). A Cathodic Ray Tube b). An Infinite line of charge c). An infinite sheet of charge d). A parallel plate capacitor e). X-Box f). A battery
7. 7. 5. Which of these charge distributions did not have its electric field calculated in detail in Chapter 27? a. A line of charge. . b. A ring of charge. . c. A plane of charge d. A parallel-plate capacitor e. They were all calculated
8. 8. CHAPTER 27 QUIZ 1. Which statement/s is/are not true? • The electric field obeys the principle of superposition. • The tangent to an electric field line at a point gives the direction of the field at that point. • The density of electric field lines is directly proportional to the strength of the field. • Negative charges are sources of electric field lines and positive charges are sinks of electric field lines. • Electric fields are what you find in PlayStation football and soccer games.
9. 9. CHAPTER 27 QUIZ 2. An electric dipole in a uniform electric field experiences • Happiness and excitement • only a net external force. • only a torque. • both a net external force and a torque. • neither a net external force nor a torque. • answer depends on the strength of the field
10. 10. 3. Choose the correct statement/s concerning electric field lines: a.) field lines may cross b). field lines are close together where the field is large c). field lines point away from negative charge d). a point charge released from rest moves along a field line e). field lines are made with white chalk f). none of these are correct
11. 11. 4. What device provides a practical way to produce a uniform electric field? a). A Cathodic Ray Tube b). An Infinite line of charge c). An infinite sheet of charge d). A parallel plate capacitor e). X-Box f). A battery
12. 12. 5. Which of these charge distributions did not have its electric field calculated in detail in Chapter 27? a. A line of charge. . b. A ring of charge. . c. A plane of charge d. A parallel-plate capacitor e. They were all calculated
13. 13. Electric Field Models We can understand much of electrostatic and electrodynamic physics using 4 simple field models
14. 14. Electric Field of a Point Charge For multiple charges: Fon q = F1on q + F2on q + F3on q + … Enet = Fon q/q = F1onq/q + F2on q/q + F3on q/q + … Enet = ΣEi (Principle of Superposition)
15. 15. Simple Example of Superposition Principle
16. 16. Limiting Cases & Typical Field Strengths • • • Near an object, electric field depends on object shape and charge distribution Far away from the object, it appears to be a point charge These are limiting cases. We will use limiting cases to help us understand and simplify our discussion during class
17. 17. Example of strong electric field: ionizes the gas inside the field
18. 18. The Electric Field of Multiple Point Charges • Superposition Principle allows us to sum electric fields from all charges • Often easier to break them into components and sum them for each unit vector, i,j,k • See Problem Solving Strategy on p. 820 & example on p. 821
19. 19. Determining Electric Field
20. 20. Determining Electric Field
21. 21. The Electric Field of a Dipole • An electric dipole is two equal but opposite charges separated by a small distance s
22. 22. The Electric Field of a Dipole •An electric dipole is two equal but opposite charges separated by a small distance •May be permanent or induced •Has zero net charge •Has an electric field
23. 23. This is true for any point along the X-axis.
24. 24. Dipole Moment Units of dipole moment are Cm
25. 25. The Electric Field of a Dipole • An electric dipole is two equal but opposite charges separated by a small distance s • Dipole moment p = qs
26. 26. The Electric Field of a Dipole • An electric dipole is two equal but opposite charges separated by a small distance s • Dipole moment p = qs Are we violating Coulombs Law by Having an r3 in the Equation? • Field of a dipole drops off with distance much more quickly than a point charge (Why? It is electrically neutral.) Coulomb’s Law deals with point charges, not dipoles.
27. 27. Field Lines and Field Vectors Another way to visualize an electric field is to draw field lines instead of field vectors like we did in Chapter 26. For a point charge, the field lines were straight in to the center or straight out from the center. For a dipole field lines are curved.
28. 28. Electric Field Lines • Continuous curves drawn tangent to field vectors, therefore, field vector is tangent to field line • Spacing indicates field strength – Closely spaced – strong field – Widely spaced – weak field • Electric field lines never cross • Electric field lines start from positive charges and end on negative charges • Draw arrows along field lines to indicate direction • Just because there is no field line drawn at a specific point doesn’t mean that there is no field there. This is only a way to represent field
29. 29. Using a Test Charge to Determine the Direction of the Force Due to the Dipole Electric Field Field lines follow the direction of the force measured (or equivalently – the electric field vectors).
30. 30. Visualizing the Electric Field of a Dipole Force is parallel to field vectors
31. 31. Using a Test Charge to Determine the Direction of the Force Due to Multiple Charges
32. 32. Electric Field of a Continuous Charge • We will view a collection of atoms making up an extended 3-D object as continuous matter. This discussion will be based upon this view. • Any charged metal object will, since it is a conductor, be uniformly charged over its entire surface – we will consider this to be continuous charge (we will assume it is uniformly charged unless specified otherwise) • Use Q for the total charge on the metal object
33. 33. Linear Charge Density Linear charge density units are C/m
34. 34. Surface Charge Density Surface charge density units are C/m2
35. 35. Finding Electric Field of a Line Charge
36. 36. Finding Electric Field of a Line Charge Check out Problem Solving Strategy on page 826
37. 37. Electric Field of an Infinite Line of Charge • Decreases more slowly than for a point charge (1/r) • This will be approximately true for any r<<L – The field is defined by the closest charges to the point of interest – Outlying points too far away to have much effect • Realistic finite line charges can be approximated using the equation above
38. 38. Electric Field For an Infinite Line of Charge
39. 39. Electric Field For a Ring of Charge
40. 40. Electric Field For a Ring of Charge
41. 41. Electric Field For a Disk of Charge
42. 42. Electric Field For a Plane of Charge
43. 43. Electric Field For a Plane of Charge
44. 44. Electric Field For a Sphere of Charge
45. 45. The Parallel Plate Capacitor
46. 46. The Parallel Plate Capacitor
47. 47. Motion of a Charged Particle in an Electric Field • Established forces on a charge in an electric field • Net force means acceleration (motion) • F = ma = mv2/r = qE • a = qE/m = constant if field is uniform • Motion in a non-uniform field can be very complicated • One simple example of motion in a nonuniform field is orbital motion such as a negatively charged particle around a positive charge
48. 48. Motion of a Charged Particle in an Electric Field
49. 49. Circular Motion of a Charge F = |q|E = mv2/r
50. 50. Motion of a Dipole in an Electric Field
51. 51. A Sample of Permanent Dipoles Align to the Electric Field
52. 52. Motion of a Dipole in an Electric Field
53. 53. Examples of Dipoles in a Non-Uniform Field Dipoles in a non-uniform electric field will experience a net force.
54. 54. Backup Slides