Download Electric Charges

Chapter 25
Electricity and Magnetism
Electric Fields: Coulomb’s Law
Reading: Chapter 25
1
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
2
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
Electric Charges
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
15
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
16
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
17
Coulomb’s Law
• Mathematically, the force between two electric charges:
q1q2 ˆ
F12  ke 2 r
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
18
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
19
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
20
Coulomb’s Law
F21  ke
q1q2 ˆ
r21
2
r

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
21
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
22
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
23
Coulomb’s Law
F21  ke
q1q2 ˆ
r21
2
r
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
24
Chapter 25
Electric Field
25
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
26
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 ˆ
F  ke 2 r
r
Then
F
q ˆ
E
 ke 2 r
q0
r
27
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 ˆ
F  ke 2 r
r
F
q ˆ
E
 ke 2 r
q0
r
28
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
qi ˆ
E  ke  2 ri
i ri
29
Electric Field
q ˆ
E  ke 2 r
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
30
Electric Field
q ˆ
E  ke 2 r
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
31
Electric Field
q ˆ
E  ke 2 r
r
z
q1  10 μC q2  10 μC
E
5m
Direction of electric field?

5m


1
6m
2
32
Electric Field
q ˆ
E  ke 2 r
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 cos φ
52  32 4
cos φ 

5
5
E
8
E1
5
33
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 ˆ
FE  ke 2 r
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
34
Coulomb’s Law:
q1q2 ˆ
F12  ke 2 r
r
1
5m
F21
q ˆ
E  ke 2 r
r
E  ke 
i
qi ˆ
r
2 i
ri
F  qE
F1  F21  F31
6m
F31


3
Resultant force:
F31

7m
2
F1
E1
E  E1  E2
E1
E2
F21
5m
E2
6m


1
7m
2
E
35