Monday, January 5, 2009

1. Monday, January 5, 2009 Spherical Distribution Laws

2. Announcements USAYPT participants�I need paperwork and fees by tomorrow at the latest! New notes packet�we�re starting E&M!

3. When we say that an object is �charged�, what do we really mean? If a particle bears an electrical charge, we can generally assume it has an excess of electrons (negative charge) or an excess of protons (positive charge). Fine point: usually, only electrons move, so positive charge (an excess of protons) is really an absence of electrons.

4. Fundamentals of Electrical Charge Charge on electron: -e Charge on proton: +e e = 1.602 ? 10-19 Coulombs , C Any charge q is a multiple of the number of extra electrons or missing electrons such that q = ne

5. Let�s talk about spherical distribution. What do you think we mean by a �spherical distribution law�? Give an examples.

6. Let�s talk about spherical distribution. Write the formula for the surface area of a sphere.

7. Spherical distribution law for gravity

8. Spherical distribution law for electrical force k = 8.99 ? 109 Nm2/C2 q1 and q2 are spherical or point charges in Coulombs. r is the separation between the centers of the charges

9. How are electrical and gravitational forces similar? They both follow spherical distribution laws. The forces diminish as the surface area of a sphere.

10. How are electrical and gravitational forces different? Electrical forces can be attractive or repulsive, while gravitational forces are only attractive. Gravitational forces are much weaker than electrical forces.

11. For Two Charges The electrostatic force is repulsive if the charges are of the same sign and attractive if the charges are of unlike sign. The force exerted on charge A by charge B is always equal and opposite of the force exerted by charge B on charge A (Newton�s 3rd Law)

12. For More Than Two Charges Determine the force on a charge due to each of the other charges in the vicinity. Do a vector addition.

14. Tuesday, January 6, 2009 Gravitational and Electric Fields

15. Announcements USAYPT participants�I need paperwork and fees today.

17. What is meant by a force field? A force field creates a force when an object is placed in it. It is a property of empty space. An electric field creates an electric force on a charge placed in it. The electric field is created by a charge distribution. A gravitational field creates a gravitational force on a mass placed in it. The gravitational field is created by a mass distribution.

18. Draw the gravitational field around the earth. Gravitational Field

19. How can you calculate the gravitational force on a small mass in a gravitational field? Gravitational Field

20. What is an equation that can be used for gravitational field calculations? Gravitational Field

21. What is the value of the gravitational field at the surface of the earth? Gravitational Field

22. And now�the Electric Field Boot up computer. Go to my folder on the N: drive Go to Period 2, Projects, Volume 2 When you are at the right place, look up.

23. The Electric Field Draw the electric field around a positive charge.

24. The Electric Field Draw the electric field around a negative charge.

25. The Electric Field How can you calculate the electric force on a small charge in an electric field from the magnitude of the electric field?

26. The Electric Field What is an equation that can be used for electric field calculations? What is the limitation of the equation shown above?

27. Summary of the Electric Field This equation can be used to calculate the electric field a distance r away from a the center of a spherically symmetric charge distribution of qo Coulombs. Another charge q entering the electric field created by qo will experience a force F, which can be calculated by the equation F = qE.

28. Summary of Electric Field Direction The direction of the electric field at a point in space is the direction that a small positive charge at rest (a �test charge�) wishes to move if it is placed at that location. Thus, the electric field points away from positive charges and toward negative charges. If more than one charges is generating the field, vector addition must be done to add the fields produced by each of the charges to get the resulting field. This is called �superposition� of the individual fields.

29. Wednesday, January 7, 2008 Charge distributions

30. Announcements Saturday practice for USAYPT from 10:00 to 2:00 PM. Who can come? Get out homework Ch23: 7,8,9 for self correction.

34. Sample problem: Determine where the electric field is zero if a 2.0 mC charge is located at the origin and a -3.0 mC charge is located at x = 1.0 meter.

35. Limitations of Coulomb�s Law Coulomb�s Law equations for Force and Field can only be used directly for point charges or spherically symmetric charges. For more complicated �continuous charge distributions� we need to break up the charge distribution into little bitty pieces and use Coulomb�s Law and superposition together to determine the electric field at a given location in space near the charge distribution.

36. Linear Charge Distribution When charge resides on a long thin object such as a wire or a ring, we call that a linear charge distribution. It is sometimes convenient for us to define a linear charge density, ?, which is charge per unit length. ? = Q/L = dQ/dL

37. Surface Charge Distribution

38. General Procedure - continued You need to integrate over a spatial variable (not charge!). Appropriate choices are linear distance, arc length, or angle (x,y,s,q,f) Find a common variable that r and/or dq both depend on. See if symmetry (and trig) can be used to simplify the problem by elimination of off-axis components of E. Find the appropriate limits to the integral. Don�t skip set-up steps. The physics is in the setup!

39. Volume Charge Distribution

40. General Procedure for Electric Field Calculations Each little infinitesimally small charge dq in a charge distribution containing Q total Coulombs creates its own tiny electric field dE at a point P in space a distance r from dq. I can add all these little infinitesimal fields dE together to get the field at point P. What does this sound like to you?

41. Thursday, January 8, 2008 More on Charge Distributions

42. Announcements Get out HW Ch 23: 13,14,15 to grade.

45. Sample Problem Determine the electric field magnitude and direction a distance y away from an extremely long, straight wire of charge density l.

46. Sample Problem Determine the electric field magnitude and direction a distance x away from a ring of radius R bearing charge Q.

47. Friday, January 9, 2009 Motion of Charged Particle in E-field

50. Sample Problem: Determine the electric field magnitude and direction at point P in the figure shown. The semicircular ring bears charge -2.0mC and has a radius of 0.50 m.

51. Motion of Charged Particles in Electric Fields If the electric field is constant, acceleration will be constant, and kinematic equations can be employed. The motion is not unlike projectile motion.

52. Sample problem What is the speed and position of an electron released from rest in this electric field after 3.0 ns?

53. Sample problem What is the velocity and position of this electron 3.0 ns after it enters the field?

54. Static Electricity Experiment #1 Blow up the balloon and charge it by rubbing it against your hair. Can you deflect a flowing stream of water with the charged balloon? Is the water charged? If not, why is it being deflected? See if your group can come up with a plausible answer.

55. Static Electricity Experiment #2 Cut 2 20-cm strips of transparent tape (mass of each 65 mg). Fold about 1 cm tape over at one end of each strip to create a handle. Press both pieces of tape side-by-side on your lab table and rub your finger back and forth across the strips. Quickly pull the strips off the lab table. Hold the handles together and the strips will repel each other, forming an inverted �V�. Estimate the charge on each strip. Assume the charges act as though they are at the center of mass of the strip. Hint: Begin by drawing a Free Body Diagram!

56. Monday, January 12, 2009 Electric Flux

57. Announcements Get out homework (page 7 in packet)

58. Flux Flux means �flow�. Consider three rectangular wire loops in a vector field. Which one has maximum flux (or flow) of the field lines through it?

59. To Increase Flux Increase the field Increase the area of the loop Make sure the hoop is appropriately angled

60. The Area Vector The �area vector� is defined as a vector perpendicular to a surface with magnitude equal to the scalar area of the surface. Consider the angle between v and A.

61. Flux Equation The flux is proportional to field vector magnitude, area vector magnitude, and the cosine of the angle between them.

62. Flux Equation

63. Flux Equation for Electric Field

64. Area Vectors For a Closed Shape This rectangular prism has six surfaces. Each surface has an area vector that points outward from center of the prism, and is normal to the surface.

65. Another Example This cylinder is a bit more complicated. The top and bottom have areas that can easily be calculated, and the corresponding vectors point outward. On the sides, we must define and infinite number of infinitesimally small areas, each of which defines a little vector (dA) that points outward.

66. The Calculation of Flux Over a Closed Surface in a Vector Field At each point on the closed surface, we must take the dot product with the vector field to get the flux for that small area. Then we add all these dot products up together to get the flux for the entire surface. This leads to some interesting observations. If there is a �source� of the vector field in the closed shape, the flux over its surface is positive. If there is a �sink� of the vector field in the closed shape, the flux over its surface is negative. If there is neither a source or sink of the vector field in the closed shape, the flux over its surface is zero.

67. What do we mean by �source� and �sink� of an electric field? The source is where the field starts, and the sink is where the field terminates. In an electric field, the source is the positive charge, and the sink is the negative charge. Therefore, If a closed shape encloses a positive charge, the flux is positive. If a closed shape encloses a negative charge, the flux is negative. If the closed shape encloses no net charge, the flux is zero.

68. Mathematical Representation For a general vector field, v: For an electric field, E:

69. Sample Problem: Calculate the electric flux through a spherical surface of radius 2.0 m containing a point charge of 3mC at its center.

70. Problem 24.1: Draw an electric dipole, and sketch three Gaussian surfaces for which one has positive electric flux, one has negative electric flux, and one has zero electric flux.

71. Problem 24.2: A vertical field of 2.4 x 104 N/C exists above Earth�s surface when thunderstorm is brewing. What is flux through car of approximate rectangular size of 5.0 m by 3.0 m if it is traveling on a road with a 10o slope.

72. Problem 24.6: A uniform field of ai + bj intersects a surface of area A. What is the flux through the area if the surface lies in (a) the xy plane? (b) the xz plane (c) the xy plane?

73. Problem 24.9: A cone with base radius R and height h is located on a horizontal table. A horizontal uniform field E penetrates the cone. Determine the electric flux that enters the left-hand side of the cone.

74. Tuesday, January 13, 2009 Gauss�s Law of Electricity

75. Announcements Get out homework Problems 23: 46,47,52

79. Gauss� Law of Electricity q: net charge (C) enclosed inside a given Gaussian surface. This is a sum of all + and - charges ?o: electrical permittivity of free space 8.85 ? 10-12F/m 8.85 ? 10-12C2/Nm2 ?E: electrical flux over the Gaussian surface

80. Other forms of Gauss�s Law

81. Gaussian Surface A Gaussian surface is simply any closed shape in space, which can be of any arbitrary shape. All Gaussian surfaces give the same answer in Gauss�s Law if they enclose the same net charge! So, to make the math easier, Gaussian surfaces are typically chosen for convenience and high symmetry with regard the electric field.

82. What�s Gauss�s Law Good For? Gauss�s Law can be used to determine how much charge is enclosed in a surface. More commonly, Gauss�s Law is used to determine the electric field at a point in space.

83. Sample Problem

84. Non-constant Fields Do some investigating of the properties of electric fields at: http://www.falstad.com/mathphysics.html

85. January 14, 2009 Application of Gauss�s Law

86. Announcements Get out HW problems 24: 3,5,7,8 Exciting movie

90. Sample Problem: Derive the electric field a distance y away from a long charged wire bearing a linear charge distribution l. (NOT IN PACKET)

91. Sample Problem: Derive the electric field outside a charged non-conducting cylinder with an even charge distribution.

92. Sample Problem: Derive the electric field INSIDE a charged non-conducting cylinder with an even charge distribution.

93. January 15, 200 8 Electric Force Lab

94. Announcements Problems 24: 13,14,15 Movie!