Electrostatics covers the properties of electric charges, electrostatic force, and electric fields. Key points include: - There are two types of electric charges: positive and negative. Like charges repel and unlike charges attract. - Charge is quantized and conserved. It exists in integer multiples of the fundamental unit, e. - Coulomb's law describes the electrostatic force between two point charges. The force is proportional to the product of the charges and inversely proportional to the square of the distance between them. - Electric fields are vector fields that exist around charged objects. The electric field strength is defined as the force per unit charge. Field lines are used to represent electric fields graphically.

1. Electrostatics
Topic covered - Property of charges , Electrostatic Force and
Electric Field

2. Electric Charges
1. Two kinds of charges: Positive and Negative
2. Like charges repel, unlike charges attract
3. Charge is conserved
4. Charge is quantized
LINK

3. The total charge in a closed system remains constant.
Charges are transferred.
The total charge in a closed system remains constant.
⮚ Neutral objects have equal amounts of positive and negative charge.
⮚ Only electrons are transferred in solids.
⮚ Single charges may not be created nor destroyed.
⮚ Pairs of opposite charges may be created or destroyed.
Examples: Charge separation by friction
Chemical equations
Beta Decay
Pair production / pair annihilation
Law of Conservation of Charge

4. SI Unit for Charge
● Coulomb [C] is the SI unit for charge.
● Coulomb is a derived unit based on the fundamental unit for
current, Ampere.
● Coulomb is a humongous amount of charge.

5. Natural unit for charge
On the atomic level, the unit of charge is the
elementary charge, e.
● +e is the charge of a proton
● -e is the charge of an electron
● +2e is the charge of an alpha particle

6. Natural unit for charge
On the sub-atomic level, fractional charges
exist.
Quarks have + (1/3) e
or + (2/3) e

7. Charge is Quantized
In 1909 Robert Millikan confirmed that electric charge always
occurs in integral multiples of the fundamental unit of charge, e.
q is the standard symbol for charge (units - Coulombs)
Money is quantized, the
smallest unit of US
currency is the penny!
Total
Charg
e Number of
fundamental
charges
Elementary
Charge
1.6 x 10-19 C

8. Particle Mass Charge
electron 9.11 x 10 -31 kg -1.6 x 10 -19 C -1e
proton 1.672 x 10 -27 kg +1.6 x 10 -19 C +1e
neutron 1.674 x 10 -27 kg 0
Fundamental particle properties

9. An object has a net charge of +3 Coulombs
1. How many more protons than electrons are on the object?
2. Can you determine the total number of protons on the
object?

10. Object
# of Excess
Protons/Electrons
Quantity of Charge (Q)
in Coulombs (C)
A
1 x 106 excess
electrons
- 1.6 x 10-13 C
B 2 x 108 excess protons + 3.2 x 10-11C
C
2 x 1010 excess
electrons
- 3.2 x 10-9 C
Ex: Find the total charge on the object in each case

11. Conductors and Insulators
Good conductors
have many “free”
electrons
EX: Metals
Insulators have few
“free” electrons
Ex: Rubber, wood

12. Insulators and Conductors
Electrical Conductibility
Insulators Conductors
No movement of
charges within the
object
Free movement
of charges
Semi-conductors
Limited number
of free carriers
Wood, plastics,
glass
Silicon,
Germanium
Metals (Cu, Ag,
Al)
Grounding: The “Earth” is considered an infinite sink of charges

13. Ground (Earthing)
● Grounding: The “Earth” is considered an infinite source or
sink for excess charge.
● Grounding prevents charge from building up on the chassis
of appliances.
● Mutual grounding provides a common reference point.

14. Coulomb’s Law
In 1785 Charles Coulomb established a law of electric force
between two stationary charged particles.
1. Force inversely proportional to square of distance
2. Force along the line joining the particles
3. Force proportional to the product of the charges
4. Force attractive between opposite sign charges.
5. Force repulsive between charges of the same sign
k = Coulomb constant
= 8.99 x 109 N⋅m2/C2

15. Direction of the Coulomb Force
1. Force can be attractive or repulsive
2. Equal in magnitude
3. Opposite in direction

16. Ex: If q1 =-3uC, q2 = +4uC, and d = 2 m,
find the electric force between the charges.
+
-
q1
q2d
F12
F21

17. Coulomb Force is
proportional to 1/r2
Hyperbolic relationship between force and distance
link

18. Analogy to Gravitational Force
Coulomb
Force
Gravitational
Force
The gravitational force can only be attractive.
Example: Compare the
gravitational force in the hydrogen
atom to the Coulomb (electric)
force. Which is stronger?

19. ⮚ Atomic Radius: 10-10 meters
⮚Nuclear Diameter: 10-15 meters
⮚Mass of electron: me = 9.11 x 10-31 kg
⮚Mass of proton: mp = 1.67 x 10-27 kg
Compare the gravitational
force in the hydrogen atom
to the Coulomb (electric)
force. Which is stronger?
How much stronger?

20. Difference and Similarities between Electricity and Gravity
⮚ Coulomb Law and Law of Gravitation similarities
○ Gravitation is always attractive
○ Electrical force can be attractive or repulsive
○ Electric force dominates the atomic world
○ Gravitational forces dominates the macroscopic scale: people, planets,
galaxies
○ Electric forces are stronger !!!

21. A metal sphere is charged by losing 5.18 x 1013 electrons
while a second sphere is charged by losing 15.54 x 1013
electrons. The two spheres are 25 cm apart. Determine
the force between the two spheres.

22. Two uniformly charged spheres are firmly fastened to and
electrically insulated from a table. The charge on sphere 2 is three
times the charge on sphere 1. Which diagram correctly shows the
magnitude and direction of the electrostatic forces:

23. Alternate Form of Coulomb’s law
Coulomb’s constant k is often written in terms of the
permittivity of free space e0
Coulomb’s Law can then be written
as:

24. Superposition
PrincipleWhen more than two charges are present, the resultant
force on any one of them is equal to the vector sum of the
forces exerted by each of the individual charges.

25. Solution:
⮚ Note the direction of forces
⮚ Resolve F32 and F31 into their x and y components
⮚ Add the x and y components of F32 and F31 to find x and y
components of F3
⮚ Find the magnitude and direction of F3
450F32
F31
450
Three point charges located at corners of triangle as shown. Find
The resultant force on q3
q1 = q3 = 5 μC
q2 = -2 μC
a = .1 m

26. Two 2 gram balloons are suspended by strings that are 60 cm long. The
two balloons establish equilibrium with an angle between the two strings
of 250. Determine the charge on each balloon. Assume the same amount
of charge is on each.

27. Methods of Charging
1. Friction - Transfer of electrons between neutral objects.
1. Induction - A neutral object becomes charges without
ever contacting the charged object.
1. Conduction - A charged body comes in contact with
another body and charge is transferred between them.

28. 1. Friction - When two neutral objects are rubbed together.
One gives up its negative charges to the other. One becomes
positively charged while the other becomes equally negative.
Hair gives up
electrons to the
balloon.

29. Frictional charging is a result of transfer of electrons
Some materials are greedy and steal electrons, they have a high
electroconductivity, while others are willing to give them up.

30. 2. Induction - When an object is charged by the influence of
a charged object near, but not in contact with it. The word
induction means to influence without contact.
1. Positively charged object brought near,
does not touch the electroscope.
2. Ground’s attached and electrons are
drawn up.
3. Ground is removed trapping electrons
on the electroscope.
4. Electroscope ends up oppositely
charged to the object brought near.

31. Electrons attracted by the positive
object toward the top of the
electroscope. The foil leaves at the
bottom have a positive charge so
they repel each other.
Electrons pushed by negative
object toward the bottom of the
electroscope. The foil leaves at
the bottom have a negative
charge so they repel each other.
Temporary polarization by
induction

32. Electrostatic Induction occurs only in conductors.
Ground - Is an infinite source or sink for electrons.

33. Induction

34. Induction

35. Polarization and Induction

36. ● A negatively charged rubber rod is brought near an
uncharged sphere
● The charges in the sphere are redistributed.
● After the sphere is grounded they leave the sphere
● The positive charge on the sphere is evenly distributed
● Charging by induction requires no contact with the
object inducing the charge
Induction

37. 3. Conduction – Charging by contact
When charging something by contact:
1. A charged objects must touch and transfer some electrons.
2. The objects become charged alike.
3. The original charged object becomes less charged.

38. Conduction
● A charged object (the rod) is placed in
contact with another object (the sphere)
● Some electrons on the rod can move to the
sphere
● When the rod is removed, the sphere is left
with a charge
● The object being charged is always left
with a charge having the same sign as the

39. Grounding neutralizes a charged object

40. Polarization and charging by contact

41. Polarization-Induced Attractions
● Attraction is more common than repulsion
● Charged objects can attract uncharged ones
○ A charged rod attracts a neutral metal ball
○ It redistributes the charge → separation of charge in the
uncharged object. The attractive force is then greater.
Water faucet
comb demo

42. Conduction or Induction?

43. After rubbing the balloon, why does balloon stick to wall?
How do you know that this force is stronger than gravity?

44. Negatively charged paint adheres
to positively charged metal.

45. Charge Distributions
● The excess charge on a conductor resides on the
outer surface concentrating on rough edges and
corners.
● Automobiles are a safe haven from lightening.
● Lightening rods and point discharge

46. Gravitational Fields
•Surround anything with mass
•Vector fields (have magnitude and direction)
•Weaken as you move away from a single mass
•Magnitude of field can be calculated by:

47. ⮚ q0 is the test charge
⮚ Q is the charged object in the area
⮚ E is the electric field experienced
by q0 due to Q
Electric Fields
•Surround charged objects
•Vector fields (magnitude and direction)
•Direction depends on the charge
•Weaken as you move away from isolated one
charge
•Magnitude of field calculated by:

48. Electric Field Strength
The Electric Field Strength at a point in an
Electric Field is the Force per unit positive
test charge exerted on a charge at that
point.
E = F/q
*Vector Quantity
*[N/C]

49. Field of an isolated point charge

50. Coulomb Force is
proportional to 1/r2
Hyperbolic relationship between force and distance

51. ⮚ The number of lines per unit area through the surface is
proportional to the magnitude of the electric field
⮚ The closer the lines the stronger the field, ‘E’.

52. Drawing Electric Field Lines
⮚ Lines begin on positive and end on negative charges.
⮚ No two field lines can cross.
⮚ Number of field lines leaving is proportional to the
charge.
⮚ Strength of the field is proportional to the density of lines.

53. ⮚ Electric field lines are proportional to magnitude of the charge
⮚ Electric field is tangent at any point

54. ⮚If charges are not equal in magnitude the greater charge will
have more field lines
⮚Twice the charge, twice the field lines

55. Double the charge means double the field lines

56. Field the same strength at every point
along the circle

57. The diagram below is a representation of the electric field
arising from?
a. a single negative charge
b. two unlike charges
c. a single positive charge
d. a pair of positive charges
e. a pair of negative charges

58. Must Know what the electric fields looks like
around
1. A positive point charge
2. A negative point charge
3. A positive and negative point charge
4. Two positive point charges
5. Two negative point charges
6. Around and inside a conducting sphere
7. Between 2 parallel plates
NOTE: Point Charges have no dimensions

59. Positive Point Charge
+
+
1. Field emanates from positive charge
2. Perpendicular to the surface
3. Field lines never cross
4. Field weakens as 1/r2

60. 1. Field terminates on it
2. Field perpendicular to
the surface
3. Field lines never cross
4. Field weakens as the
distance increases
Negative Point Charge

61. 1. Inverse square law: 1/r2
2. Double the distance the field is a ¼ the original strength.
3. Less field lines per unit area.
Positive Point Charge

62. 1. Out of the positive
and into the negative
2. Strongest between the
charges
3. Field lines are
perpendicular to the
surface
4. Field lines never
cross
One Positive and one
Negative Point Charge

63. 1. Field zero between
the charges
2. Field lines diverge
3. Field lines never
cross
4. Field lines
perpendicular to
surface
Two Positive Point Charges

64. 1. Field 0 between
the charges
2. Field lines
diverge
3. Field lines never
cross
4. Field lines
perpendicular to
surface
Two Negative Point Charges
Same as positive charge diagram except field lines go into
the charges

65. Negatively Charged
Conducting Sphere
E=0
_
_ _
__
__
_
1. Field ends on the
charge
2. Field ZERO inside
the sphere
3. All excess charge is
on the surface
4. More charge equals
more field lines
It’s NOT
dimensionless

66. E=0
Everywhere
inside
Field lines perpendicular
to surface
Double the
distance, field is ¼
original strength.
Inverse square law

67. 1. Field begins on the
charge
2. Field ZERO inside
the sphere
3. All excess charge is
on the surface
4. More charge equals
more field lines
Positively Charged
Conducting Sphere

68. Edge effects- Electric field lines bulge out slightly around
the edges of Parallel Plates – Field weaker

69. 1. Magnitude - The force on a charge placed in the field divided by
the charge itself.
1. Direction - The direction that the force would be on a positive test
charge placed at that point.
All fields are vectors:

70. The field lines for a large positively charged plate. The field lines
flow away from the plate on both sides. (Note: this is a small
section near the center of a large plate. This is why the field lines
are not coming from the outside rim of the plate.)

71. A uniform electric field is created between two parallel
metal plates if the plates are connected to a battery.
The way the terminals are connected
determines the direction of the field

72. Field around and between charged parallel plates
1. Field comes out of the
positive plate goes into
the negative plate
2. Field is UNIFORM,
same strength
everywhere
3. Field above and below
the plates is zero.

73. ++++++++++++++++++
------------------------
-
Positive
plate
Negative
Plate
E =const.
Uniform field
Parallel Plate Capacitor
Everywhere outside the
plates the field is zero

74. A charged particle
introduced perpendicular
to the electric field will
follow a parabolic path
Like a projectile in a
gravitational field