- Coulomb's law describes the electric force between two point charges. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. - The document discusses various methods of charging objects, including rubbing, conduction, and induction. It also describes the properties of conductors and insulators. - Examples are provided to demonstrate how to use Coulomb's law to calculate the electric force between charges, including resolving forces into components. Equilibrium situations involving electric forces and other forces are also analyzed.

1. Electric Charge and
Electric Field

2. ELECTRIC CHARGES &
ELECTRIC FIELDS
*Properties of electric charges
*Coulomb’s law
*Electric field
*Electric field of continuous charge
distribution
*Electric field lines
*Motion of charged particles in a
uniform electric field

3. Learning Outcomes
• On the completion of this chapter students
should be able to:
• Draw, explain, write the strength and
determine the electric field around a
charged particle and a configuration of
charged particle and the electric forces
experienced by or exerted upon any
charged particle or any configuration of
charged particles.

4. Static Electricity; Electric Charge and Its
Conservation
Objects can be charged by rubbing – posses net
electric charge
Ex – combing your hair , touched a metal
doorknob after sliding the carpet
(a) Rub a plastic ruler and (b) bring it close to some tiny pieces of paper.

5. Static Electricity;
Electric Charge and Its
Conservation
• Benjamin Franklin(1706-
1790)
• Positive charge – possessed
by protons
• Negative charge –
possessed by electrons
• Charges of same sign repel
• Charges of opposite signs
attract

6. (a)A negatively charged rubber rod suspended by a thread is
attracted to a positively charged glass rod.
(b) A negatively charged rubber rod is repelled by another
negatively charged rubber rod.

7. Electric Charge in the Atom
Atom:
Nucleus
(small, massive, positiv
e charge)
Electron cloud
(large, very low
density, negative
charge)

8. Electric Charge in the Atom
Atom is electrically neutral.
Rubbing charges objects by moving electrons
from one to the other.

9. Electric Charge in the Atom
Polar molecule: neutral overall, but charge not
evenly distributed
Diagram of a water molecule. Because it has opposite charges on different
ends, it is called a “polar” molecule.

10. Conductor:
Charge flows freely
Metals
Insulator:
Almost no charge flows
Most other materials
Some materials are semiconductors.
Insulators and Conductors
(a) A charged metal sphere and a neutral metal sphere.
(b) (b) The two spheres connected by a conductor (a metal nail), which conducts
charge from one sphere to the other.
(c) (c) The two spheres connected by an insulator (wood); almost no charge is
conducted.

11. Induced Charge
Metal objects can be charged by conduction:
A neutral metal rod in (a) will acquire a positive charge if placed in contact (b) with
a positively charged metal object. (Electrons move as shown by the orange arrow.)
This is called charging by conduction.
- +ve charged metal is
brought close to
uncharged object
-If the 2 object
touch, free e- in neutral
are attracted to +ve
charged and pass
over to it.
- so,nuetral metal rod
now will miss –ve e
and will have net +ve
charge

12. Charging a metallic object by induction (that
is, the two objects never touch each other).
(a) A neutral metallic sphere, with equal numbers
of positive and negative charges.
(b) The electrons on the neutral sphere are
redistributed when a charged rubber rod is
placed near the sphere.
(c) When the sphere is grounded, some of its
electrons leave through the ground wire.
(d) When the ground connection is removed, the
sphere has excess positive charge that is
nonuniformly distributed.
(e) When the rod is removed, the remaining
electrons redistribute uniformly and there is a
net uniform distribution of positive charge on
the sphere.

13. They can also be charged by induction, either
while connected to ground or not:
Induced Charge
Charging by induction.
Inducing a charge on an object connected to ground.

14. They can also be charged by induction, either
while connected to ground or not:
Induced Charge
Charging by induction.
Inducing a charge on an object connected to ground.
• both object do not touch
•Free electron of metal rod do
not leave the rod- they will
move within the metal toward
the external +ve charged and
leaving charged at opposite
end
•So, charged is induced at the
2 end of metal rod

15. Induced Charge
Nonconductors won’t become charged by
conduction or induction, but will experience
charge separation:

16. The electroscope
can be used for
detecting charge.
Induced Charge; the
Electroscope

17. Coulomb’s Law
Experiment shows that the electric force
between two charges is proportional to the
product of the charges and inversely
proportional to the distance between them.

18. Experiment shows that the electric force
between two charges is proportional to the
product of the charges and inversely
proportional to the distance between them.
Coulomb’s Law
Coulomb’s law, Eq. 21–1, gives the force between two point charges, Q1
and Q2, a distance r apart.

19. Properties of electric force
between two stationary charge
particles: The electric force..
• is inversely proportional to square of the
separation between particles and directed along
the line joining them
• is proportional to the product of the charges q1
and q2 on the two particles
• is attractive if charges are of opposite sign and
repulsive if the charges are of the same sign
• Is a conservative force

20. Coulomb’s Law equation
• An equation giving the magnitude of electric
force between two point charges
• (Point charges defined as a particle of zero
size that carries an electric charge)
2
21
ee
r
qq
kF
Where ke is called the Coulomb constant and
ke = 8.9875 x 109 Nm2C-2 (S.I units) or
ke = 1/ 4πЄ0 and
Є0 = permittivity of free space
= 8.8542 x 10-12 C2N-1m-2

21. Coulomb’s law:
This equation gives the magnitude of
the force between two charges.
Coulomb’s Law

22. Coulomb’s Law
The force is along the line connecting the
charges, and is attractive if the charges are
opposite, and repulsive if they are the same.
The direction of the static
electric force one point
charge exerts on another
is always along the line
joining the two
charges, and depends on
whether the charges have
the same sign as in (a)
and (b), or opposite signs
(c).

23. Coulomb’s Law
Unit of charge: coulomb, C
The proportionality constant in Coulomb’s
law is then:
Charges produced by rubbing are
typically around a microcoulomb:

24. Coulomb’s Law
Electric charge is quantized in units
of the electron charge.

25. Coulomb’s Law
The proportionality constant k can also be
written in terms of , the permittivity of free
space:
(16-2)

26. Two point charges separated by a distance r exert a force on
each other that is given by Coulomb’s law. The force F21
exerted by q2 on q1 is equal in magnitude and opposite in
direction to the force F12 exerted by q1 on q2. When the
charges are of the same sign, the force is repulsive.
Electric Force is a vector

27. When the charges are of opposite signs, the
force is attractive.

28. rF ˆ
2
21
e12
r
qq
k
Where, is a unit vector directed from q1 to q2.
Since the force obeys Newton’s third law, then
F12 = - F21
rˆ

30. Example: Question 1
• The electron and proton of a hydrogen
atom are separated by a distance of
approximately 5.3 x 10-11 m. Find the
magnitude of the electric force.

31. Example: Solution 1
2
21
ee
r
qq
kF
11
219
9
e
5.3x10
)(1.6x10
x8.99x10F
Fe = 8.2 x 10-8 N

32. Coulomb’s Law
Example 2: Three charges in a line.
Three charged particles are arranged in a
line, as shown. Calculate the net electrostatic
force on particle 3 (the -4.0 μC on the right) due
to the other two charges.

33. Exercise
1. What is the magnitude of the force a +25
µC charge exerts on a +2.5 mC charge
28 cm away?

34. Exercise
2. Three point charges, Q1 = 3 µC, Q2 = -5 µC,
and Q3 = 8 µC are placed on the x-axis as
shown in Figure 1. Find the net force on the
charge Q2 due to the charges Q1 and Q3.
Q1
20 cm 30 cm
Q2 Q3

35. Exercise
3. Particles of charge +75, +48 and -85 µC
are placed in a line . The center one is
0.35 m from each of the others. Calculate
the net force on each charge due to the
other two.

36. Coulomb’s Law
Example 3: Electric force using vector components.
Calculate the net electrostatic force on charge Q3 shown in the figure due to the
charges Q1 and Q2.

37. Coulomb’s Law
Approach
1. We use Coulomb’s law to find the
magnitude of the individual
forces.
2. The direction of each force will be
along the line connecting Q3 to
Q1 or Q2.
3. The forces F31 and F32 have the
directions shown in figure,
Q1 exerts an attractive force on
Q3
Q2 exerts a repulsive force on Q3
4. The forces F31 and F32 are not in
the same line, so to find the
resultant force on Q3, we resolve
F31 and F32 into x and y
components and perform vector
addition.

38. Exercise
1. Three charged particles are placed at the
corners of an equilateral triangle of side
1.20 m . The charges are +7.0µC, -
8.0µC and -6.0µC. Calculate the
magnitude and direction of the net force
on Q1 due to the other two.

39. Electrical Force with Other
Forces, Example
The spheres are in equilibrium.
Since they are separated, they exert
a repulsive force on each other.
– Charges are like charges
Model each sphere as a particle in
equilibrium.
Proceed as usual with equilibrium
problems, noting one force is an
electrical force.
Section 23.3

40. Electrical Force with Other
Forces, Example cont.
The force diagram includes the
components of the tension, the
electrical force, and the weight.
Solve for |q|
If the charge of the spheres is not
given, you cannot determine the sign
of q, only that they both have same
sign.
Section 23.3

41. Examples
Two indentical small spheres, each having a
mass of 3.00 x 10-2 kg, hang in equilibrium
as shown in Figure. The length, L of each
string is 0.150m and the θ= 5.000. Find the
magnitude of the charge on each sphere.

42. • Two kinds of electric charge – positive and
negative.
• Charge is conserved.
• Charge on electron:
e = 1.602 x 10-19 C.
• Conductors: electrons free to move.
• Insulators: nonconductors.
Summary

43. • Charge is quantized in units of e.
• Objects can be charged by conduction or
induction.
• Coulomb’s law:
Summary