1. Coulomb’s Law and Electric Field
Chapter 24: all
Chapter 25: all

2. Electric charge Able to attract other objects Two kinds
Positive – glass rod rubbed with silk
Negative – plastic rod rubbed with fur
Like charges repel
Opposite charge attract
Charge is not created, it is merely transferred from one material to another

3. Elementary particles Proton – positively charged
Electron – negatively charged
Neutron – no charge
Nucleus – in center of atom, contains protons and neutrons
Quarks – fundamental particles – make up protons and neutrons, have fractional charge

4. ions Positive ions – have lost one or more electrons
Negative ions – have gained one or more electrons
Only electrons are lost or gained under normal conditions

5. Conservation of charge
The algebraic sum of all the electric charges in any closed system is constant.

6. Electrical interactions
Responsible for many things
The forces that hold molecules and crystals together
Surface tension
Adhesives
Friction

7. Conductors Permit the movement of charge through them
Electrons can move freely
Most metals are good conductors

8. Insulators Do not permit the movement of charge through them
Most nonmetals are good insulators
Electrons cannot move freely

9. Charging by induction
See pictures on pages

10. Coulomb’s Law Point charge – has essentially no volume
The electrical force between two objects gets smaller as they get farther apart.
The electrical force between two objects gets larger as the amount of charge increases

11. Coulomb’s Law r is the distance between the charges
q1 and q2 are the magnitudes of the charges
k is a constant
8.99 x 109 N∙m2/C2

12. Coulombs SI unit of charge, abbreviated C
Defined in terms of current – we will talk about this later

13. Coulomb’s law constant
k is defined in terms of the speed of light
k = 10-7c
k = 1/4pe0
e0 is another constant that will be more useful later
e0 = 8.85 x C2/N∙m2

14. The coulomb Very large amount of charge Charge on 6 x 1018 electrons
Most charges we encounter are between 10-9 and 10-6 C
1 mC = 10-6 C

15. Examples
See pages

16. Electric Field
A field is a region in space where a force can be experienced.
Or: a region in space where a quantity has a definite value at every point.

17. Electric Field Produced by a charged particle.
The force felt by another charged particle is caused by the electric field.
We can check for an electric field with a test charge, qt. If it experiences a force, there is an electric field.

18. Electric field
The definite quantity is a ratio of the electric force experienced by a charge to the amount of the charge.
Vector quantity measured in N/C.

19. Electric field
To determine the field from a point charge, Q, we place a test charge, qt, at some position and determine the force acting on it. Q qt F

20. Direction of E
If the test charge is positive, E has the same direction as F.
If the test charge is negative, E has the opposite direction as F.

21. Electric Field - Point Charge

22. Electric Field
The field is there, independent of a test charge or anything else!
The electric field vector points in the direction a positive charge would be forced.

23. Example 1
Two charges, Q1 = +2 x 10-8 C and Q2 = +3 x 10-8 C are 50 mm apart as shown below.
What is the electric field halfway between them? E2 E1 Q1 Q2
50 mm

24. Example 1
At the halfway point, r1 = r2 = 25 mm.
Magnitudes of fields:

25. Example 1
E1 = 2.9 x 105 N/C
E2 = 4.3 x 105 N/C
E1 is to the right and E2 is to the left.
E2 = x 105 N/C
E = E1 + E2 = x 105 N/C

26. Example 2
For the charges in Example 1, where is the electric field equal to zero?
Since the fields are in opposite directions between the charges, the point where the field is zero must be between them. E2 E1 Q1 Q2

27. Example 2
r1 + r2 = s, so r2 = s – r1

28. Example 2

29. Field Diagrams
To represent an electric field we use lines of force or field lines.
These represent the sum of the electric field vectors.

30. Field Diagrams

31. Field Diagrams

32. Field Diagrams
At any point on the field lines, the electric field vector is along a line tangent to the field line.

33. Field Diagrams

34. Field Diagrams
Lines leave positive charges and enter negative charges.
Lines are drawn in the direction of the force on a positive test charge.
Lines never cross each other.
The spacing of the lines represents the strength or magnitude of the electric field.

35. Point Charges Lines leave or enter the charges in a symmetric pattern.
The number of lines around the charge is proportional to the magnitude of the charge.

36. Point Charges

37. Point Charges

38. Gauss’s Law
Electric flux through a closed surface is proportional to the total number of field lines crossing the surface in the outward direction minus the number crossing in the inward direction.

39. Example 25-9 (see page 563)
Field of a charged sphere is the same as if it were a point charge

40. Example (see page 564)
Field of a infinite line of charge is

41. Other scenarios
See table on page 567

42. Example 3 Two parallel metal plates are 2 cm apart.
An electric field of 500 N/C is placed between them.
An electron is projected at 107 m/s halfway between the plates and parallel to them.
How far will the electron travel before it strikes the positive plate?

43. Example 3
Two charged parallel plates create a uniform electric field in the space between them.

44. Example 3 E vo
This is just like a projectile problem except that the acceleration is not a given value.

45. Example 3
= 8.8 x 1013 m/s2

46. Example 3
8.8 x 1013 m/s2 is the vertical acceleration of the electron.
Horizontally, the acceleration is zero.
x = vt
v = 1 x 107 m/s & t = ?

47. Example 3 = 1.5 x 10-8 s Back to vertical direction:
y = yo + vot + 1/2at2
y = 1/2at2
= 1.5 x 10-8 s

48. Example 3 Back to horizontal direction: x = vt
x = (1 x 107 m/s)(1.5 x 10–8 s)
x = 0.15 m = 15 cm

49. Dipoles A pair of charges with equal and opposite sign.
Induced dipoles, molecular dipoles, etc.…