1. Charge and Polarization
Wednesday, February 14, 2007
Charge and Polarization

2. Announcements Tonight’s assignment:
Electrostatics #1
Post-test from thermodynamics exam to be turned in tomorrow

3. Demonstration #1
Demonstrate how you can pick up the tissue without touching it in any way with your body.
What is occurring on the atomic level that lets you do this?

4. The atom
The atom has positive charge in the nucleus, located in the protons. The positive charge cannot move from the atom unless there is a nuclear reaction.
The atom has negative charge in the electron cloud on the outside of the atom. Electrons can move from atom to atom without all that much difficulty.

5. Question
You charge the balloon by rubbing it on hair or on a sweater, and the balloon becomes negative. How can it pick up a neutral tissue?

6. This is an electroscope
Pole
The electroscope is made from a metal or other conductor, and may be contained within a flask.
The vanes are free to move.
Vanes

7. Demonstration #2
Rub the black rod with the fur. Bring the rod toward the pole of the electroscope. What happens to the vanes?
Come up with an atomic-level explanation for your observations.

8. Demonstration #3
Rub the glass rod with the silk. Bring the rod toward the pole of the electroscope. What happens to the vanes?
Come up with an atomic-level explanation for your observations.

9. Demonstration #4
What happens when your touch the electroscope with the glass rod?

10. Charge
Charge comes in two forms, which Ben Franklin designated as positive (+) and negative(–).
Charge is quantized.
The smallest possible stable charge, which we designate as e, is the magnitude of the charge on 1 electron or 1 proton.
We say a proton has charge of e, and an electron has a charge of –e.
e is referred to as the “elementary” charge.
e =  Coulombs.
The coulomb is the SI unit of charge.

11. Sample Problem
A certain static discharge delivers -0.5 Coulombs of electrical charge. How many electrons are in this discharge?

12. Sample Problem
How much positive charge resides in two moles of hydrogen gas (H2)?
How much negative charge?
How much net charge?

13. Sample Problem
The total charge of a system composed of 1800 particles, all of which are protons or electrons, is 31x10-18 C.
How many protons are in the system?
How many electrons are in the system?

14. Coulomb’s Law and Electrical Force
Thursday, February 15, 2007
Coulomb’s Law and Electrical Force

15. Announcements Tonight’s assignment:
Electrostatics #2
Post-test from thermodynamics exam due; please turn it in.
Questions on Electrostatics #1?
Clicker Quiz

16. Electric Force Charges exert forces on each other.
Like charges (two positives, or two negatives) repel each other, resulting in a repulsive force.
Opposite charges (a positive and a negative) attract each other, resulting in an attractive force.

17. Coulomb’s Law – form 1
Coulomb’s law tells us how the magnitude of the force between two particles varies with their charge and with the distance between them.
k = 8.99  109 N m2 / C2
q1, q2 are charges (C)
r is distance between the charges (m)
F is force (N)
Coulomb’s law applies directly only to spherically symmetric charges.

18. Coulomb’s Law – form 2
Sometimes you see Coulomb’s Law written in a slightly different form
eo = 8.85  C2/ N m2
q1, q2 are charges (C)
r is distance between the charges (m)
F is force (N)
This version is theoretically derived and less practical that form 1

19. Spherically Symmetric Forces
Newton’s Law of Gravity
Coulomb’s Law

20. Sample Problem
A point charge of positive 12.0 μC experiences an attractive force of 51 mN when it is placed 15 cm from another point charge. What is the other charge?

21. Sample Problem qA = 1.50 nC A B qB = -0.50 nC 1.3 m
Calculate the mass of ball B, which is suspended in midair. A
qA = 1.50 nC
1.3 m B
qB = nC

22. Superposition Electrical force, like all forces, is a vector quantity.
If a charge is subjected to forces from more than one other charge, vector addition must be performed.
Vector addition to find the resultant vector is sometimes called superposition.

23. y (m) 2.0 1.0 -3 mC 2 mC 4 mC 1.0 2.0 x (m) Sample Problem
What is the force on the 4 mC charge?
y (m)
2.0
1.0
-3 mC
2 mC
4 mC
1.0
2.0
x (m)

24. y (m) 2.0 -3 mC 1.0 2 mC 4 mC 1.0 2.0 x (m) Sample Problem
What is the force on the 4 mC charge?
y (m)
2.0
-3 mC
1.0
2 mC
4 mC
1.0
2.0
x (m)

25. Friday, February 16, 2007
The Electric Field

26. Announcements Tonight’s assignment: Turn in Electrostatics #1
Write name and assignment number on paper.
Questions on Electrostatics #2?
Clicker Quiz

27. The Electric Field
The presence of + or – charge modifies empty space. This enables the electrical force to act on charged particles without actually touching them.
We say that an “electric field” is created in the space around a charged particle or a configuration of charges.
If a charged particle is placed in an electric field created by other charges, it will experience a force as a result of the field.
Sometimes we know about the electric field without knowing much about the charge configuration that created it.
We can easily calculate the electric force from the electric field.

28. Why use fields?
Forces exist only when two or more particles are present.
Fields exist even if no force is present.
The field of one particle only can be calculated.

29. Field around + charge
The arrows in a field are not vectors, they are “lines of force”.
The lines of force indicate the direction of the force on a positive charge placed in the field.
Negative charges experience a force in the opposite direction.

30. Field around - charge

31. Field between charged plates

32. Field Vectors from Field Lines
The electric field at a given point is not the field line itself, but can be determined from the field line.
The electric field vectors is always tangent to the line of force at that point.
Vectors of any kind are never curvy!

33. Field Vectors from Field Lines

34. Force from Electric Field
The force on a charged particle placed in an electric field is easily calculated.
F = E q
F: Force (N)
E: Electric Field (N/C)
q: Charge (C)

35. Sample Problem
The electric field in a given region is 4000 N/C pointed toward the north. What is the force exerted on a 400 μg styrofoam bead bearing 600 excess electrons when placed in the field?

36. Sample Problem
A 400 μg styrofoam bead has 600 excess electrons on its surface. What is the magnitude and direction of the electric field that will suspend the bead in midair?

37. Sample Problem
A proton traveling at 440 m/s in the +x direction enters an an electric field of magnitude 5400 N/C directed in the +y direction. Find the acceleration.

38. For Spherical Electric Fields
The Electric Field surrounding a point charge or a spherical charge can be calculated by:
E = k q / r2
E: Electric Field (N/C)
k: 8.99 x 109 N m2/C2
q: Charge (C)
r: distance from center of charge q (m)
Remember that k = 1/4peo

39. Monday, February 19, 2007
Superposition

40. Announcements Pass forward Electrostatics #2
If you were at NAIMUM, pass forward Post-test from Thermo examination
Tonight’s Assignment: Electrostatics #4
Are there any questions on Electrostatics #3
Clicker Quiz

41. Principle of Superposition
When more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges.
Again, as with force vectors, this is referred to as superposition.

42. Remember…
Electric field lines are NOT VECTORS, but may be used to derive the direction of electric field vectors at given points.
The resulting vector gives the direction of the electric force on a positive charge placed in the field.

43. Sample Problem
A particle bearing -5.0 μC is placed at -2.0 cm, and a particle bearing 5.0 μC is placed at 2.0 cm. What is the field at the origin?

44. Sample Problem
A particle bearing 10.0 mC is placed at the origin, and a particle bearing 5.0 mC is placed at 1.0 m. Where is the field zero?

45. Sample Problem What is the charge on the bead? It’s mass is 32 mg.
E = 5000 N/C
40o

46. Electric Field Plotter Laboratory
Tuesday, February 20, 2007
Electric Field Plotter Laboratory

47. Announcements Questions on Electrostatics HW #4?
Hints will be uploaded today for #4 and #5.
Pass up Electrostatics HW #3.
Lunch Bunch tomorrow:
Bring an instrument or your voice.
Turn in Waves #1 tomorrow during your regular class.

48. The electric field and voltage
The electric field points in the direction of largest negative voltage change.
If the black lead of a voltmeter is placed at a fixed point, and the red lead is moved around at constant distance from the black lead until the largest negative reading is obtained on the voltmeter, this can be used to map the electric field at that point in space.
Using the voltmeter, you can map field lines from a + electrode to a – electrode. E
-0.23

49. Electric Field Plotter Lab
Wire one painted silver electrode to the + DC outlet and the other painted silver electrode to the – DC outlet of your power supply. Your teacher will show you how to do this. Set the power supply to around 10 Volts DC.
Touch the black lead to one electrode and the red lead to the other electrode to make sure you are getting a good, steady voltage reading of around 8 to 10 Volts
Mark + by the positive electrode and – by the negative electrode.
Starting at the +electrode, map a field line by placing the black lead down on the paper and carefully rotating the red lead (at constant distance from the black lead) until the display reads a maximum negative voltage. Carefully mark the field vector at that location with a pencil.
Place the black lead at the arrowhead you just drew, and map a new field vector.
Continue marking field vectors until you arrive at the negative electrode.
You must mark several good field lines during the class period.

50. Wednesday, February 21, 2007
Shielding, excess charges on conductors, charging by induction, finish Electric Field lab.

51. Guest Speaker: Nick Antonas
Thursday, February 22, 2007
Guest Speaker: Nick Antonas

52. Electric Potential and Potential Energy
Friday, February 23, 2007
Electric Potential and Potential Energy

53. Announcements Pass forward Electrostatics #5
Tonight’s HW: Electrostatics #7 (there was no new HW assigned yesterday)
Sign up for AP exams next week!

54. Electric Potential Energy
Electrical potential energy is the energy contained in a configuration of charges. Like all potential energies, when it goes up the configuration is less stable; when it goes down, the configuration is more stable.
Electrical potential energy increases when charges are brought into less favorable configurations (ex:, like-sign charges getting closer together, or unlike-sign charges farther apart).
Electrical potential energy decreases when charges are brought into more favorable configurations.
The unit is the Joule.

55. Electric Potential
Electric potential is hard to understand, but easy to measure.
We commonly call it “voltage”, and its unit is the Volt.
Electric potential is easily related to both the electric potential energy, and to the electric field.

56. Electrical Potential and Potential Energy
The change in potential energy is directly related to the change in voltage.
U = qV
U: change in electrical potential energy (J)
q: charge moved (C)
V: potential difference (V)
All charges will spontaneously go to lower potential energies if they are allowed to move.

57. Electrical Potential and Potential Energy
Since all charges try to decrease potential energy, and DU = qDV, this means that spontaneous movement of charges result in negative DU.
Positive charges like to DECREASE their potential (DV < 0)
Negative charges like to INCREASE their potential. (DV > 0)

58. Sample Problem
A 3.0 μC charge is moved through a potential difference of 640 V. What is its potential energy change?

59. Electrical Potential in Uniform Electric Fields
The electric potential is related in a simple way to a uniform electric field.
V = -Ed
V: change in electrical potential (V)
E: Constant electric field strength (N/m or V/m)
d: distance moved (m) d E DV

60. Sample Problem
An electric field is parallel to the x-axis. What is its magnitude and direction if the potential difference between x =1.0 m and x = 2.5 m is found to be +900 V?

61. Sample Problem y(m) C 1.0 A B 1.0 2.0 x(m)
What is the voltmeter reading between A and B? Between A and C? Assume that the electric field has a magnitude of 400 N/m.
y(m) C
1.0 A B
1.0
2.0
x(m)

62. Sample Problem y(m) C 1.0 A B 1.0 2.0 x(m)
How much work would be done BY THE ELECTRIC FIELD in moving a 2 mC charge from A to C? From A to B? from B to C?. How much work would be done my an external force in each case?
y(m) C
1.0 A B
1.0
2.0
x(m)

63. Energy Conservation in Electric Fields
Monday, February 26, 2007
Energy Conservation in Electric Fields

64. Announcements
Electrostatics HW #7 assigned Friday, due tomorrow. Any questions so far?
HW #8 due Wednesday.
Pass #5 forward, if you haven’t already.
Lunch today is last chance to correct exams. Next exam is Monday, March 5. The grade for this one goes on the 4th 9 weeks period.

65. Conservation of Energy Review
In a conservative system, energy changes from one form of mechanical energy to another.
When only the conservative electrostatic force is involved, a charged particle released from rest in an electric field will move so as to lose potential energy and gain an equivalent amount of kinetic energy.
The change in electrical potential energy can be calculated by
DUE = qDV.

66. Sample Problem
If a proton is accelerated through a potential difference of 2,000 V, what is its change in potential energy?
How fast will this proton be moving if it started at rest?

67. Sample Problem
A proton at rest is released in a uniform electric field. How fast is it moving after it travels through a potential difference of V? How far has it moved?

68. Bonus Demo Lab
Charge two Mylar or Plastic beads by touching a charged rubber rod. Describe what happens, using what you know about electrostatics.
Calculate the number of excess electrons on each bead.

69. Bonus Demo Lab
Charge two Mylar or Plastic beads by touching a charged rubber rod. Describe what happens, using what you know about electrostatics.
Calculate the number of excess electrons on each bead.

70. Bonus Demo Lab
Charge two Mylar or Plastic beads by touching a charged rubber rod. Describe what happens, using what you know about electrostatics.
Calculate the number of excess electrons on each bead.

71. Potential and Potential Energy of Configurations of Point Charges
Tuesday, February 27, 2007
Potential and Potential Energy of Configurations of Point Charges

72. Announcements
Electrostatics HW #7 assigned Friday, due today. Pass it forward.
HW #8 due tomorrow. HW #9 assigned tonight.
SIGN UP FOR AP EXAMINATIONS – PREREGISTRATION IN GUIDANCE.

73. Electric Potential Energy for Spherical Charges
Electric potential energy is a scalar, like all forms of energy.
U = kq1q2/r
U: electrical potential energy (J)
k: 8.99  109 N m2 / C2
q1, q2 : charges (C)
r: distance between centers (m)
This formula only works for spherical charges or point charges.

74. Sample Problem y (m) 2.0 1.0 2 mC 4 mC x (m) 1.0 2.0
What is the potential energy of the configuration shown below?
y (m)
2.0
1.0
2 mC
4 mC
x (m)
1.0
2.0

75. Sample Problem y (m) 2.0 -3 mC 1.0 2 mC 4 mC x (m) 1.0 2.0
How much work was done in assembling the charge configuration shown below?
y (m)
2.0
-3 mC
1.0
2 mC
4 mC
x (m)
1.0
2.0

76. Electric Potential (spherical)
For a spherical or point charge, the electric potential can be calculated by the following formula
V = kq/r
V: potential (V)
k: 8.99 x 109 N m2/C2
q: charge (C)
r: distance from the charge (m)
Remember, k = 1/(4peo)

77. Sample Problem y (m) 2.0 -3 mC 1.0 2 mC 4 mC x (m) 1.0 2.0
What is the electric potential at (2,2)?
y (m)
2.0
-3 mC
1.0
2 mC
4 mC
x (m)
1.0
2.0

78. Equipotential surfaces
high
highest
medium
low
lowest
positive
negative

79. Equipotential surfaces
High potential
Low potential

80. Question
What can you say about the intersection between field lines and equipotential surfaces?

81. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Sample Problem
Draw field lines for the charge configuration below. The field is 600 V/m, and the plates are 2 m apart. Label each plate with its proper potential, and draw and label 3 equipotential surfaces between the plates. You may ignore edge effects.

82. Sample Problem
Draw a negative point charge of -Q and its associated electric field. Draw 4 equipotential surfaces such that DV is the same between the surfaces, and draw them at the correct relative locations. What do you observe about the spacing between the equipotential surfaces?

83. Fill in the following table for spherical charges
Force
Potential Energy
Field
Potential

84. What is magnitude and direction of electric field
What is magnitude and direction of electric field? b) What is shortest distance one can go to undergo a change of 5.00 V?

85. Wednesday, February 28, 2007
Review

86. Announcements Pass forward Electrostatics #8.
Tomorrow I will collect Electrostatics #9, and Friday Electrostatics #10.The free response problems in packet are due Friday at beginning of class.
HW Quiz Friday near end of class.