Download Electric Charges

Chapter 20
Electric Forces and Fields:
Coulomb’s Law
Reading: Chapter 20
1
Electric Charges
 There are two kinds of electric charges
- Called positive and negative
 Negative charges are the type possessed by
electrons
 Positive charges are the type possessed by protons
 Charges of the same sign repel one another and
charges with opposite signs attract one another
Electric charge is always conserved in isolated system
Neutral – equal number of positive
and negative charges
Positively charged
2
Electric Charges: Conductors and Isolators
 Electrical conductors are materials in which
some of the electrons are free electrons
 These electrons can move relatively freely
through the material
 Examples of good conductors include copper,
aluminum and silver
 Electrical insulators are materials in which all
of the electrons are bound to atoms
 These electrons can not move relatively freely
through the material
 Examples of good insulators include glass, rubber
and wood
 Semiconductors are somewhere between
insulators and conductors
3
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Coulomb’s Law
• Mathematically, the force between two electric charges:
q1q2
F12  ke 2
r
• The SI unit of charge is the coulomb (C)
• ke is called the Coulomb constant
– ke = 8.9875 x 109 N.m2/C2 = 1/(4πeo)
– eo is the permittivity of free space
– eo = 8.8542 x 10-12 C2 / N.m2
Electric charge:

electron
e = -1.6 x 10-19 C

proton
e = 1.6 x 10-19 C
16
Coulomb’s Law
| q1 || q2 |
F12  F21  ke
r2
Direction depends on the sign of
the product
q1q2
F21  F12
opposite directions,
the same magnitude
1
2


F21
F12
q1q2  0
1
2


F21
F12
q1q2  0
1

F21
F12
2

q1q2  0
The force is attractive if the charges are of opposite sign
The force is repulsive if the charges are of like sign
Magnitude:
F12  F21  ke
| q1 || q2 |
r2
17
Coulomb’s Law: Superposition Principle
• The force exerted by q1 on q3 is F13
• The force exerted by q2 on q3 is F23
• The resultant force exerted on q3 is the vector
sum of F13 and F23
18
Coulomb’s Law
F21  ke
q1q2
r2

1
q1  1μC q2  2 μC
q3  3 μC
Magnitude:
5m

2
6m
Resultant force:

F23 3
F13
F3  F21  F31
F13
F3
F23
6
| q3 || q2 |
 3  106
9 2  10
4
F23  ke

8.9875

10
N

15

10
N
2
2
r
6
6
| q3 || q1 |
 3  106
9 10
4
F13  ke

8.9875

10
N

2.2

10
N
2
2
r
11
F3  F23  F13  (15  104  2.2  104 )N  12.8  104 N
19
Coulomb’s Law
F21  ke
q1q2 ˆ
r21
2
r

1
q1  1μC q2  2 μC
5m
6m

F12 2
F32

Resultant force:
F2  F12  F32
3
F2
q3  3 μC
Magnitude:
F12
F32
6
| q3 || q2 |
 3  106
9 2  10
4
F32  ke

8.9875

10
N

15

10
N
2
2
r
6
6
| q1 || q2 |
 2  106
9 10
4
F12  ke

8.9875

10
N

7.2

10
N
2
2
r
5
F2  F32  F12  (15  104  7.2  104 )N  7.8  104 N
20
Coulomb’s Law
F21  ke
q1q2 ˆ
r21
2
r

F31 1
q1  1μC q2  2 μC
5m
F21

2
6m

Resultant force:
F1  F21  F31
3
F1
q3  3 μC
Magnitude:
F31
F21
6
| q3 || q1 |
 3  106
9 10
4
F31  ke

8.9875

10
N

2.2

10
N
2
2
r
11
6
| q1 || q2 |
 2  106
9 10
4
F21  ke

8.9875

10
N

7.2

10
N
2
2
r
5
F1  F21  F31  (7.2  104  2.2  104 )N  5  104 N
21
Coulomb’s Law
F21  ke
q1q2
r2
1
5m
q1  1μC q2  2 μC
F21
F1  F21  F31
6m
F31


q3  3 μC
Resultant force:
F31

7m
3
F21
F1
2
Magnitude:
6
6
| q1 || q2 |
10

2

10
9
4
F21  ke

8.9875

10
N

5

10
N
2
2
r
6
6
6
| q3 || q1 |
10

3

10
9
3
F31  ke

8.9875

10
N

1.1

10
N
2
2
r
5

5m
F13
1
F23
7m
F3

F23
6m


3
F13
2
5m
1
F32
6m
F12


3
F1
F12
7m
F32
2
22
Conservation of Charge
Electric charge is always conserved in isolated system
Two identical sphere
q1  1μC
q2  2 μC
They are connected by conducting wire. What is the electric
charge of each sphere?
The same charge q. Then the
conservation of charge means that :
2q  q1  q2
For three spheres:
q1  1μC q2  2 μC
q
q1  q2 1  2

μC  0.5 μC
2
2
q3  3 μC
3q  q1  q2  q3
q
q1  q2  q3 1  2  3

μC  1μC
3
3
23
Chapter 20
Electric Field
24
Electric Field
 An electric field is said to exist in the region of space around a
charged object
 This charged object is the source charge
 When another charged object, the test charge, enters this electric
field, an electric force acts on it.
The electric field is defined as the electric force on the test charge
per unit charge
F
E
q0
 If you know the electric field you can find the force
F  qE
If q is positive, F and E are in the same direction
If q is negative, F and E are in opposite directions
25
Electric Field
 The direction of E is that of the force on a positive test charge
 The SI units of E are N/C
E
Coulomb’s Law:
F
q0
qq0
F  ke 2
r
Then
E
F
q
 ke 2
q0
r
26
Electric Field
 q is positive, F is directed away
from q
 The direction of E is also away
from the positive source charge
 q is negative, F is directed toward q
 E is also toward the negative
source charge
qq0
F  ke 2
r
E
F
q
 ke 2
q0
r
27
Electric Field: Superposition Principle
• At any point P, the total electric field due to a group of
source charges equals the vector sum of electric
fields of all the charges
E   Ei
i
28
Electric Field
q
E  ke 2
r

1
q1  1μC q2  2 μC
Magnitude:
5m

2
6m
Electric Field:
E2
E1
E  E1  E2
E1
E
E2
6
| q2 |
9 2  10
2
E2  ke 2  8.9875  10
N
/
C

5

10
N /C
2
r
6
6
| q1 |
9 10
2
E1  ke 2  8.9875  10
N
/
C

0.7

10
N /C
2
r
11
E  E2  E1  (5  102  0.7  102 )N / C  4.3  102 N / C
29
Electric Field
q
E  ke 2
r
Electric field
E1
5m
q1  1μC q2  2 μC
E2
E  E1  E2
6m
E1
E2


1
7m
2
E
Magnitude:
6
| q2 |
9 2  10
2
E2  ke 2  8.9875  10
N
/
C

5

10
N /C
2
r
6
6
| q1 |
9 10
2
E1  ke 2  8.9875  10
N
/
C

0.37

10
N /C
2
r
5
30
Electric Field
q
E  ke 2
r
z
q1  10 μC q2  10 μC
E
5m
Direction of electric field?

5m


1
6m
2
31
Electric Field
q
E  ke 2
r
E

q1  10 μC q2  10 μC
E2
5m
E2 Electric field
E  E1  E2
E1

5m


1
6m
2
Magnitude:
6
| q2 |
10

10
3
E2  E1  ke 2  8.9875  109
N
/
C

3.6

10
N /C
2
r
5
E  2E1 cosφ
52  32 4
cosφ

5
5
E
8
E1
5
32
Example
l  1m
q1  10 μC q2  10 μC
m1  m2  m
1  2
l  1m
T
1
2


FE
Electric field
r
mg
T  mg  FE  0
g
q1q2
FE  ke 2
r
T cos  2  mg
T sin  2  FE
tan 1 
FE
q1q2
tan  2 
 ke 2
mg
r mg
 2  1
FE
qq
 ke 21 2
mg
r mg
33
σ
E plane =2πk eσ=
2ε
0
E plane
σ>0
E plane
E plane
|σ|
 2πk e |σ|=
2ε
0
Q0
Q=σA
E plane
σ<0
E plane
Q0
Q=σA
34
Important Example
Find electric field
    
     
    
     
E
E
σ>0
-σ<0
E
σ<0
σ>0
σ
E 
2ε0
E
σ
E 
2ε
0
35
Important Example
    
     
Find electric field
σ
E 
2ε0
σ
E 
2ε
0
σ>0
    
     
σ<0
E  E  E 
E
E
E
E
E
E
σ>0
σ<0
E  E  E   0
σ
E  E  E 
ε
0
E  E  E   0
36
Important Example
    
     
    
     
E 0
σ Q
E

ε
ε
0
0A
E 0
σ 0
σ  0
σ>0
E
σ<0
37
Electric field due to a thin uniformly charged spherical shell
• When r < a, electric field is ZERO: E = 0
A1
r1
E 2
the same
solid angle
E1
r2
q1  A1
q2  A2
A1  r12 
A2  r22 
q1
A1
 r12 
E1  ke 2  ke 2  ke
 ke
r1
r1
r12
q2
A2
 r22 
E2  ke 2  ke 2  ke
 ke
2
r2
r2
r2
E1  E2
E1  E2  0
A2
Only because in Coulomb law
1
E 2
r
38
Motion of Charged Particle
39
Motion of Charged Particle
• When a charged particle is placed in an electric field, it experiences
an electrical force
• If this is the only force on the particle, it must be the net force
• The net force will cause the particle to accelerate according to
Newton’s second law
F  qE
- Coulomb’s law
F  ma
- Newton’s second law
q
a E
m
40
Motion of Charged Particle
What is the final velocity?
F  qE
F  ma
- Coulomb’s law
- Newton’s second law
vf
|q|
ay  
E
m
Motion in x – with constant velocity
v0
Motion in x – with constant acceleration
t
l
v0
|q|
ay  
E
m
- travel time
v x  v0
After time t the velocity in y direction becomes
|q|
vy  ayt  
Et
m
then
q

v f  v02   Et 
m 
2
vy
vf
41
Chapter 20
Conductors in Electric Field
42
Electric Charges: Conductors and Isolators
 Electrical conductors are materials in which
some of the electrons are free electrons
 These electrons can move relatively freely
through the material
 Examples of good conductors include copper,
aluminum and silver
 Electrical insulators are materials in which all
of the electrons are bound to atoms
 These electrons can not move relatively freely
through the material
 Examples of good insulators include glass, rubber
and wood
 Semiconductors are somewhere between
insulators and conductors
43
Electrostatic Equilibrium
Definition:
when there is no net motion of charges
within a conductor, the conductor is
said to be in electrostatic equilibrium
Because the electrons can move freely through the
material
 no motion means that there are no electric forces
 no electric forces means that the electric field
inside the conductor is 0
If electric field inside the conductor is not 0, E  0 then
there is an electric force F  qE and, from the second
Newton’s law, there is a motion of free electrons.
F  qE
44
Conductor in Electrostatic Equilibrium
• The electric field is zero everywhere inside the
conductor
• Before the external field is applied,
free electrons are distributed
throughout the conductor
• When the external field is applied, the
electrons redistribute until the
magnitude of the internal field equals
the magnitude of the external field
• There is a net field of zero inside the
conductor
45
Conductor in Electrostatic Equilibrium
• If an isolated conductor carries a charge, the charge
resides on its surface
E 0
46