1. Lesson 17 Electric Fields and Potential
Eleanor Roosevelt High School
Chin-Sung Lin

2. Electric Fields

3. Gravitational & Electric Forces
What are the formulas for the following physics laws?
Law of Universal Gravitation
Coulomb’s Law

4. Gravitational & Electric Forces
Law of Universal Gravitation
Coulomb’s Law
Fg = G
m1 m2 r2
Fe = k
q1 q2 r2

5. Gravitational Field
What’s the definition of gravitational field?

6. Gravitational Field Fg g = m Gravitational Field: Force per unit mass
Fg: gravitational force (N)
m: mass (kg)
g: gravitational field strength (N/kg, or m/s2)

7. Electric Field Fe E = q Electric Field: Force per unit charge
Fe: electric force (N)
q: charge (C)
E: electric field strength (N/C)

8. Gravitational & Electric Fields
Gravitational Field
Electric Field
g = Fg m
E = Fe q

9. Electric Field
Source Charge
Test Charge +Q +q r Fe Fe q
E =

10. Electric Field
Source Charge
Test Charge +q –Q Fe r Fe q
E =

11. Electric Field Fe E = q Electric field is a vector
A vector includes ___________ and ____________
Source Charge
Test Charge +q +Q Fe r Fe q
E = +q –Q Fe r

12. Electric Field Fe E = q Electric field is a vector
A vector includes direction and magnitude
Source Charge
Test Charge +q +Q Fe r Fe q
E = +q –Q Fe r

13. Electric Field
Can you apply Coulomb’s law to this formula and then simplify it? Fe
E =
= ??? q
Source Charge
Test Charge +Q +q r Fe

14. Electric Field E = Fe q = k q Q r2 q = k Q r2
Electric Field: Force per unit charge
E = Fe q = k
q Q
r2 q
= k Q r2
Fe: electric force (N)
q: test charge (C)
Q: source charge (C)
E: electric field strength (N/C)
r: distance between charges (m)
k: electrostatic constant (N m2/C2)

15. Electric Field Example
What is the magnitude of the electric field strength when an electron experiences a 5.0N force?

16. Electric Field Example
What is the magnitude of the electric field strength when an electron experiences a 5.0N force?
E = Fe / q E = 5 N / (1.6 x C) = 3.13 x 1019 N/C

17. Electric Field Example
What are the magnitude and direction of the electric field 1.5 m away from a positive charge of 2.1*10-9 C?

18. Electric Field Example
What are the magnitude and direction of the electric field 1.5 m away from a positive charge of 2.1*10-9 C?
E = k Q / r2 E = (8.99 x 109 N m2/C2) (2.1 x 10-9 C) / (1.5 m)2 = 8.4 N/C Direction: away from the positive charge

19. Electric Field Exercise
There is a negative charged particle of 0.32 C in the free space. (a) What are the magnitude and direction of the electric field 2.0 m away from the particle? (b) What are the magnitude and direction of the electric force when an electron is placed m away from this particle? [3 minutes]
– 0.32 C
e –
2.0 m

20. Electric Field Exercise
There is a negative charged particle of 0.32 C in the free space. (a) What are the magnitude and direction of the electric field 2.0 m away from the particle?
E = k Q / r2 E = (8.99 x 109 N m2/C2) (0.32 C) / (2.0 m)2 = 7.2 x 108 N/C Direction: toward the negative charge

21. Electric Field Exercise
There is a negative charged particle of 0.32 C in the free space. (b) What are the magnitude and direction of the electric force when an electron is placed 2.0 m away from this particle?
E = Fe / q Fe = q E Fe = (1.6 x C) (7.2 x 108 N/C) = 1.15 x N

22. Aim: Electric Field DoNow: (4 minutes)
Write down the definition of Electric Field in words
Write down the formulas of Electric Field in two different forms
Define every symbol in the formula and identify their units
Identify the relationships between Electric Field and other variables

23. Aim: Electric Field

24. Electric Field Fe Q E = = k q r2 Electric Field: Force per unit charge
Fe: electric force (N)
q: test charge (C)
Q: source charge (C)
E: electric field strength (N/C)
r: distance between charges (m)
k: electrostatic constant (N m2/C2)

25. Electric Field 1 1 E ~ Fe E ~ Q E ~ E ~ q r2
Electric Field: Force per unit charge
E ~ 1 r2 1 q
E ~
E ~ Fe
E ~ Q
Fe: electric force (N)
q: test charge (C)
Q: source charge (C)
E: electric field strength (N/C)
r: distance between charges (m)
k: electrostatic constant (N m2/C2)

26. Electric Field
If you shift the test charge around, where can you find the electric field with the same magnitude?
Source Charge
Test Charge +Q +q Fe Fe q
E =

27. Electric Field
Source Charge +q +Q Fe
Test Charge E

28. Electric Field
What will happen if you move the test charges away from the source charge?
Source Charge
Test Charge +q +Q Fe E

29. Electric Field
Source Charge +q +Q Fe
Test Charge E

30. Electric Field
Source Charge +q +Q Fe
Test Charge E Fe E Fe

31. Electric Field
Source Charge +q +Q Fe
Test Charge E

32. Electric Field Representation
Vector representation - +

33. Electric Field Representation
Line-of-Force representation - +

34. Electric Field Representation
How do you decide the strength of electric field? - +

35. Electric Field Representation
When the field lines are denser, the field is stronger - +

36. Electric Field Representation
Where can you find the the strongest electric field? E C A D B

37. Electric Field: Point Charge
Line-of-Force representation - +

38. Electric Field: Pair of Charges
Line-of-Force representation

39. Electric Field: Pair of Charges
Sketch the electric field for like charges? + +

40. Electric Field: Pair of Charges
Line-of-Force representation + +

41. Electric Field: Pair of Charges
Line-of-Force representation

42. Electric Field: Parallel Plates
Line-of-Force representation

43. Electric Field: Parallel Plates
Anything special for the electric field between the parallel plates charged with opposite charges?

44. Electric Field: Parallel Plates
The electric field between the parallel plates is uniform except at both ends

45. Electric Field Example
A charged droplet of mass 5.87 x kg is hovering motionless between two parallel plates. The parallel plates have a electric field of 1.2 x N/C and are 2.00 mm apart. (a) What is the charge on the particle? (b) By how many electrons is the particle deficient?

46. Electric Field Example
A charged droplet of mass 5.87 x kg is hovering motionless between two parallel plates. The parallel plates have a electric field of 1.2 x N/C and are 2.00 mm apart. (a) What is the charge on the particle?
E = Fe / q Fe = E q Fg = m g Fe = Fg E q = m g (1.2 x 107 N/C) q = (5.87 x kg) (9.81 m/s2) q = 4.80 x C

47. Electric Field Example
A charged droplet of mass 5.87 x kg is hovering motionless between two parallel plates. The parallel plates have a electric field of 1.2 x N/C and are 2.00 mm apart. (b) By how many electrons is the particle deficient?
e - = 1.6 x C number of e - = 4.80 x C / 1.6 x C = 3000 e –

48. Electric Field Exercise
A charged droplet of mass 5.87 x kg is hovering motionless between two parallel plates. The parallel plates have a electric field of 9.6 x N/C and are 2.00 mm apart. What is the charge on the particle?

49. Electric Field Exercise
A charged droplet of mass 5.87 x kg is hovering motionless between two parallel plates. The parallel plates have a electric field of 9.6 x N/C and are 2.00 mm apart. What is the charge on the particle?
E = Fe / q Fe = E q Fg = m g Fe = Fg E q = m g (9.6 x 106 N/C) q = (5.87 x kg) (9.81 m/s2) q = 6.0 x C

50. Electric Field Exercise
A positively charged ball with mass 20 g is hanging between two charged parallel plates from the ceiling through an insulating wire with length 0.1 m. The electric field strength of the charged parallel plates is 4.2 x 109 N/C. When the ball is in balance, the wire and the vertical line form an angle of 60o. What is the charge of the ball?

51. Electric Fields

52. Electric Fields

53. Electric Fields

54. Electric Fields

55. Electric Fields

56. Electric Fields and Shielding
Electric Shielding

57. Electric Fields and Shielding
Cancellation of electric force
The electric forces of area A and area B on P completely cancel out A B P

58. Electric Potential

59. Aim: Electric Potential
DoNow: (3 minutes)
Write down the formulas of Electric Field
Draw the electric field surrounding a pair of opposite charge
Draw the electric field surrounding a pair of charged parallel plates

60. Aim: Electric Potential

61. Electric Field Fe Q E = = k q r2 Electric Field: Force per unit charge
Fe: electric force (N)
q: test charge (C)
Q: source charge (C)
E: electric field strength (N/C)
r: distance between charges (m)
k: electrostatic constant (N m2/C2)

62. Electric Field: Pair of Charges
Line-of-Force representation

63. Electric Field: Parallel Plates
Line-of-Force representation

64. Gravitational Potential Energy (GPE)

65. Gravitational Potential Energy (GPE)
What happens in the picture?
What types of energy have been converted?

66. Gravitational Potential Energy (GPE)
What happens in the picture?
What types of energy have been converted?
If we want to pull the weight up back to its original position, what should we do?

67. Gravitational Potential Energy (GPE)
What happens in the picture?
What types of energy have been converted?
If we want to pull the weight up back to its original position, what should we do?
How much work do we need?

68. Electric Potential Energy (EPE)
What are they in common? + -

69. Electric Potential Energy (EPE)+ -
What happens in the picture?
What types of energy have been converted?
If we want to pull the weight up back to its original position, what should we do?
How much work do we need?

70. Electric Potential Energy (EPE)
What are they different? + -

71. Electric Potential Energy
What did the monkey do in order to bring a positively charged ball toward a positively charged object?

72. Electric Potential Energy
What did the monkey do in order to bring a positively charged ball toward a positively charged object?
When the ball was released, what happened to the ball? Why?

73. Gravitational Potential Energy
The work performed in taking a mass from height A to height B does not depend on the path B A

74. Electric Potential Energy
The work performed in taking a charge from A to B does not depend on the path B A

75. Gravitational Potential Energyx2
What happens when we double the mass?

76. Gravitational Potential Energyx2
When mass is doubled, the gravitational potential energy is also doubled
PE2 = (2m)gh = 2(mgh) = 2PE1

77. Electric Potential Energy+ - x2
What did we double here?

78. Electric Potential Energy+ - x2
We doubled the charge.
What happens when we double the charge?

79. Electric Potential Energy+ - x2
When charge is doubled, the electric potential energy is also doubled

80. Electric Potential Energy
Potential Energy – Capability to Do Work
W or EPE
W: electric (potential) energy
aka work (J)
W is a scalar (not a vector)

81. Electric Potential Energy
Potential Energy – Capability to Do Work
W or EPE
W: electric (potential) energy
aka work (J)
W ~ q

82. Electric Potential W V = q Electric potential energy per unit charge
W: electric (potential) energy, aka work (J)
V: electric potential, aka potential difference,
aka voltage (V, Volts)
q: charge (C)

83. Electric Potential W = qV
Electric potential (V) is based on a zero reference point
Only the potential difference matters
Electric potential (Voltage, V) is the work (W) required to bring a unit charge (1 C) from the zero reference point
V is a scalar (not a vector)

84. Electric Potential Example
How much work is required to move 3.0 C of positive charge from the negative terminal of a 12- volt battery to the positive terminal?

85. Electric Potential Example
How much work is required to move 3.0 C of positive charge from the negative terminal of a 12- volt battery to the positive terminal?
V = W / q W = q V W = (3.0 C) (12.0 V) = 36.0 J

86. Electric Potential Example
If an electron loses 1.4 x J of energy in traveling from the cathode to the screen of a computer monitor, across what potential difference must it travel?

87. Electric Potential Example
If an electron loses 1.4 x J of energy in traveling from the cathode to the screen of a computer monitor, across what potential difference must it travel?
V = W / q W = q V V = (1.4 x J) / (1.6 x C) = 8750 V

88. Electric Potential Example
Can you make up a question using the definition of electric potential?

89. Electric Potential Example

90. Electric Potential: Parallel Plates
What is special about the electric field between the charged parallel plates?

91. Electric Potential: Parallel Plates
Electric Field (E): is uniform due to uniform density of the electric field lines E E E

92. Electric Potential: Parallel Plates
If we place test charge at different locations between the charged parallel plates, compare the forces experienced by these test charges E E E

93. Electric Potential: Parallel Plates
Electric Force (Fe): experienced by a test charge is constant due to Fe = qE E E E Fe Fe Fe

94. Electric Potential: Parallel Plates
Compare the work required to move test charges from the negative plate to the positive plate Fe Fe Fe E E E d

95. Electric Potential: Parallel Plates
Electric potential energy / work (W): required to move a test charge from negative plate to positive plate is constant due to W = Fe d E Fe d Fe Fe

96. Electric Potential: Parallel Plates
Given the following formulas, can you derive the formula for Electric potential (V) and Electric field (E)?
W = Fe d
Fe = q E
V = W q

97. Electric Potential: Parallel Plates
Electric potential (V):
W = Fe d and Fe = q E
W = q E d W
q E d
V = =
= E d q q V
V = E d or
E = d

98. Electric Potential: Parallel Plates
Electric potential (V): relative to the negative plate is proportional to the distance to it due to V = E d E d V

99. Equipotential Lines: Parallel Plates
Equipotential Lines: on an equipotential line, voltages are all the same
Equipotential lines are perpendicular to field lines V2 V2 V2 E E E d2 V1 V1 V1 d1

100. Equipotential Lines: Point Charge
Equipotential Lines for a point charge:

101. Equipotential Lines: Point Charge
Equipotential Lines for a charge pair

102. Electric Field and PotentialFe V
E = = d q
E: electric field (N/C or V/m)
V: electric potential / potential difference /
voltage (V, Volts)
d: distance between parallel plates (m)
q: charge (C)

103. Electric Potential Example
A charged droplet of mass 5.87x kg is hovering motionless between two parallel plates. The parallel plates have a potential difference of V and are 2.00 mm apart. What is the charge on the particle?

104. Electric Potential Example
A charged droplet of mass 5.87x kg is hovering motionless between two parallel plates. The parallel plates have a potential difference of V and are 2.00 mm apart. What is the charge on the particle?
E = Fe / q Fe = E q Fg = m g Fe = Fg E q = m g E = V / d V q / d = m g (24000 V) q / ((0.002 m) = (5.87 x kg) (9.81 m/s2) q = 4.80 x C

105. The End