1. Ch. 21 The Electric Field I: Discrete Charge Distributions

2. Ch. 21 Overview  Properties of Charge  Conductors and Insulators  Forces between Charges  Comparison of the Electrostatic and Gravitational Forces  The Electric Field  Electric Dipoles in Electric Fields

3. Which of the following are fundamental properties of matter? (CT) 1. Mass 2. Charge 3. Spin 4. 1 and 2 5. 1,2, and 3 12345

4. Charge  If you rub a piece of amber with fur the amber will attract bits of paper  Greek term for amber – Elektronos from which we derive electron  If two amber rods are brought together, they will repel

5. If charges can attract or repel each other then what do they exert on each other? (GR)

6. What does it suggest about charges that the force between them can be both attractive and repulsive? (GR) How is this different than the force between masses? (Gravity) (GR)

7. If a piece of fur is rubbed against an amber rod, the amber rod becomes negatively charged. What is the sign of the charge of the fur? (TPS) 1. Negative 2. Positive 3. It is uncharged 4. Cannot be determined 12345

8. If a piece of fur is rubbed against an amber rod, the amber rod becomes negatively charged. What is the sign of the charge of the fur? (CT) 1. Negative 2. Positive 3. It is uncharged 4. Cannot be determined 12345

9. Properties of Charge  Charges exert forces on each other  Forces can be repulsive or attractive  Two Types of Charge called +/- due to Franklin  Like charges repel, opposite charges attract  Charge is conserved  Charge is quantized

10. Quantization of Charge  Basic unit of charge is the charge of an electron  e = -1.602 x 10 -19 C  The charge of a proton is opposite the charge of the electron p = 1.602 x 10 -19 C = |e| p = 1.602 x 10 -19 C = |e|  SI (derived) unit of charge is the coulomb, C

11. Quantization of Charge (cont.)  The charge, q, on any object can be expressed as q = Ne where N is some integer  Fundamental SI units 1 C = 1 As (ampere second)

12. Ex: How many electrons are there in -1 C of charge?

13. Solution: q = Ne Solve for N N = q/e N = -1 C/ -1.602 x 10 -19 C N = 6.2 x 10 18 electrons

14. A student makes the following statement. When I rub a piece of glass with silk, the glass obtains 17.5 charges and silk has -11.3. What if anything is wrong with the students statement? (TPS) 1. The statement contains no errors 2. The statement violates charge conservation 3. The statement violates charge quantization 4. 2 and 3 5. Cannot be determined 12345

15. A student makes the following statement. When I rub a piece of glass with silk, the glass obtains 17.5 charges and silk has -11.3. What if anything is wrong with the students statement? (TPS) 1. The statement contains no errors 2. The statement violates charge conservation 3. The statement violates charge quantization 4. 2 and 3 5. Cannot be determined 12345

16. Insulators and Conductors What is the difference between an insulator and a conductor? (BRST)

17. Insulators and Conductors  In an Insulator all of the electrons are strongly localized around an individual atom  In a Conductor about one electron per atom is shared by the metal as a whole. This electron is called a free electron

18. Two uncharged metal spheres are in contact. A negatively charge amber rod is brought near one of the spheres. Draw a sketch showing the charge distribution on the spheres.

19. + -

20. The electroscope  Simple Device Used to indicate charge  Two metal foil leaves are suspended from the bottom of a conducting rod

21. Electroscope Demonstration  What happens when a charged insulating rod is brought near the electroscope?  What happens when a charge insulating rod is rubbed against the electroscope?  What happens when you bring your hand near the electroscope?  What happens when you touch the charged electroscope?

22. A piece of PVC pipe is rubbed with a piece of fur and then brought near an empty aluminum can lying on its side. What will happen to the can? (TPS) 1. Nothing 2. It will be repelled from the can 3. It will be attracted to the can 4. It cannot be determined 12345

23. A piece of PVC pipe is rubbed with a piece of fur and then brought near an empty aluminum can lying on its side. What will happen to the can? 1. Nothing 2. It will be repelled from the can 3. It will be attracted to the can 4. It cannot be determined 12345

24. Insulators vs. Conductors  An uncharged plastic rod is placed on the bulb of an electroscope. A charged plastic rod is brought near the other plastic rod but away form the electroscope. What will happen?  A piece of metal is placed on the bulb of an electroscope. A charge plastic rod is brought near the other plastic rod but away form the electroscope. What will happen?

25. A plastic rod is charged and brought near a few small pieces of paper. What will happen to the paper? 1. Nothing since the paper is an insulator 2. The paper will be attracted to the rod 3. The paper will be repelled by the rod 4. Cannot be determined 12345

26. How is it possible that the insulating paper can be attracted to the rod?

27. Induced Polarization  Bringing a charge near an insulator can cause a slight rearrangement of the electrons around the nucleus of the atom  The insulator can then be slightly attracted to charge  Ex. Rub a balloon on your head and stick it to the wall

28. Coulomb’s Law  Like charges repel  Opposite charges attract  Force depends inversely on the square of the distance between the charges

29. Charles Coulomb  Determined form of force between charges using a torsional balance

30. Coulomb’s Law q2q2 r q1q1

31.  k e = 8.99 x 10 9 N m 2 /C 2  ε 0 = 8.85 x 10 -12 C 2 /Nm 2 (Ch. 19)

32. Two positive charges are separated by a known distance. The distance is then doubled, how does this affect the force? (TPS) 1. The force is unchanged 2. The force is doubled 3. The force is halved 4. The force is quadrupled 5. The force is reduced by ¼ 6. Cannot be determined 12345

33. Two positive charges are separated by a known distance. The distance is then doubled, how does this affect the force? 1. The force is unchanged 2. The force is doubled 3. The force is halved 4. The force is quadrupled 5. The force is reduced by ¼ 6. Cannot be determined 12345

34. Ex. Find the magnitude and direction of the force on charge 1 shown below..25 m q 1 = 2.5 µC q 2 = -3.0 μ C

35. Solution F = kq 1 q 2 /r 2 = 8.99 x 10 9 Nm 2 /C 2 x 2.5 x 10 -6 C x 3.0 x 10 - 6 C/(.25 m) 2 =.27 N The direction is down.

36. How will the force on charge 1 compare to the force on charge 2? (CT) 1. It will be larger 2. It will be the same 3. It will be smaller 4. Cannot be determined without first calculating the answer 12345

37. A student measures the force on each of two charged objects due to the other. She finds the forces to be the same in magnitude and opposite in direction. Which of the following is true about the charges? (CT) 1. The charges must be identical 2. The charges are equal in magnitude and of opposite sign 3. The charges must have the same sign but can have different magnitudes 4. The charges must have opposite signs but can have different magnitudes 5. Cannot be determined 12345

38. In what ways is Coulomb’s Law similar to Newton’s Law of Gravity? What is a significant difference Coulomb’s Law and Newton’s Law of Gravity

39. Comparison of Newton’s Law of Gravity and Coulomb’s Law Inverse Square Law Strength is proportional to product of “source” terms Gravity is always attractive Electrostatic Force can be both attractive and repulsive

40. Ex. Find the ratio of the electrostatic force between two protons and the gravitational force between them if they are separated by.25 m.

41. Solution

42. = 1.24 x 10 36  The electrostatic force is much stronger  Protons are like charges and thus in a nucleus of an atom will repel each other  Gravity is not strong enough to hold the nucleus together  Nucleus is held together by short range force called the “Strong Force”

43. The Electric Field There’s a core question about long range forces such as the electrostatic force or the gravitational force. If two charges are separated by a distance, then how do they “know” there is a force between them.

44. The Electric Field  Newton’s answer for gravity was that they just do – “Action at a distance.”  Michael Faraday borrowed an idea from magnetism and introduced tubes of force

45. Definition of the Electric Field  Consider a small positive charge called a test charge, q 0 brought near a positive charge, Q Qq0q0

46. Which of the following is the correct force vector on the test charge q 0 ? 12345 1. 1. 2. 2. 3. 3. 4. 4. 5. None of the above is correct

47. Suppose the test charge was moved further away from the charge Q, how will the force vector change? 1. It will be larger 2. It will be smaller 3. It will not change 4. Cannot be determined 12345

48. Suppose the test charge was moved closer to the charge Q, how will the force vector change? 1. It will be larger 2. It will be smaller 3. It will not change 4. Cannot be determined 12345

49. Definition of the Electric Field  The test charge will feel a force anywhere it is placed  The “source” charge affects the space around it  The effect on the space around it is the electric field  We test the electric field with the test charge, but the electric field is due to the source charge

50. Definition of the Electric Field

51.  Electric field is force per charge  The electric field is defined so that the test charge is positive  Units – N/C

52. Ex. A force 0f.25 N is exerted to the left on a test charge of magnitude q 0 = 2 μC. a) Sketch the situation. b) What is the magnitude and direction of the electric field at the location of the test charge?

53. Ex. A test charge of magnitude is located in an electric field of magnitude 200 N/C directed to the right. a) Sketch the situation. b) Find the magnitude and direction of the force on the test charge.

54. The Electric Field due to a Point Charge  We can use coulombs law to find the electric field due to a point charge, Q Q q0q0 r

55. The Electric Field due to a Point Charge  Force on the test charge (by definition positive) is given by

56. The Electric Field due to a Point Charge  Electric field is defined as  E = F/q 0  So

57. The Electric Field due to a Point Charge  This result is also usually known as Coulomb’s law

58. If the source charge Q is positive, what is the direction of the electric field at the location of the test charge? (CT) 1. To the right 2. To the left 3. Up 4. Down 5. Cannot be determined 12345

59. If instead the source charge Q is negative, what is the direction of the electric field at the location of the test charge? (CT) 1. To the right 2. To the left 3. Up 4. Down 5. Cannot be determined 12345

60. Ex. A point P is 3.0 cm north of a charged point particle with charge Q = 3.5 pC. a) Sketch the situation. b) Find the magnitude and direction of the electric field at the point P.

61. Superposition  The electric field at a point due to several charges is the sum of the field due to the individual charges  Since the electric field is a vector, vector algebra must be used to find the sum

62. FPE Exercise on Electric Fields

63. Electric Fields in Conductors in Electrostatic equilibrium  A piece of metal is placed in a constant electric field. Sketch a picture of what happens to the charge in the metal  When does the charge separation stop?

64. Electric Fields in Conductors in Electrostatic equilibrium  A conductor in electrostatic equilibrium has an electric field of 0 inside the conductor