1. Electricity and Magnetism
Demo equipment
Round balloons, long balloons, rabbit fur, bubble soap, 2x4, watch glass, Bakelite rod, glass rod, aluminum soda can
Underlying a whole lot of phenomena
Ch. 18–24

2. Outline Stationary charges Moving charges Magnetism Magnetic Induction
forces, potential, fields
Moving charges
current, resistance, circuits
Magnetism
another effect of moving charges
Magnetic Induction
Pushing charges with magnetism

3. Objectives Determine electric force using Coulomb’s Law.
Explain forces in terms of electric fields.
Determine energies from electric potential.

4. Electric Charge
§18.1–18.2

5. Conductors and Insulators
Conductor: charges can move freely
Insulator: charges cannot move
§18.3

6. Charging Charge is conserved Charges can be separated
Charges can transfer from one object to another
§18.4

7. Electric Forces Between Objects
Demo: balloon and fur
balloon attracts fur
balloon repels other balloon
always between objects
§ 18.5

8. Coulomb’s Law kq1q2 F = d2 Nm2 k = 8.992  109 C2
C = coulomb (unit of electric charge)

9. Coulomb’s Law kq1q2 F = d2 Force is attractive for opposite charges
Force is repulsive for like charges
Proportional to the inverse square of the separation

10. Question
A hydrogen atom consists of a positive proton and a negative electron. How does the force between the electron and proton change when the electron moves twice as close?
The force becomes twice (2) as much.
The force becomes half (1/2) as much.
The force remains the same.
The force becomes four times (4×) as much.
The force becomes one-fourth (1/4) as much.

11. tells us something about matter
Charge Polarization
tells us something about matter

12. Scenario
A bag contains equal numbers of positive and negative charges. The charges can move around inside the bag, but they cannot leave the bag. The bag is placed near a very large, immobile + charge. + – +

13. Quick Question
What sort of force exists between the + charges in the bag and the large + charge?
The + charges are attracted to the charge.
The + charges are repelled by the charge.
The + charges are neither attracted nor repelled. + – +

14. Quick Question
What sort of force exists between the – charges in the bag and the large + charge?
The – charges are attracted to the charge.
The – charges are repelled by the charge.
The – charges are neither attracted nor repelled. + – +

15. Quick Question
In which direction do the + charges in the bag accelerate due to the large + charge?
Toward the charge.
Away from the charge.
The + charges will not accelerate. + – +

16. Quick Question
In which direction do the – charges in the bag accelerate due to the large + charge?
Toward the charge.
Away from the charge.
The – charges will not accelerate. + – +

17. Question
After the charges re-distribute, which force to the external + charge will be stronger?
The attraction to the – charges.
The repulsion to the + charges.
The attraction and repulsion will exactly cancel. + – +

18. Question
What sort of force exists between the bag overall and the large + charge?
The bag is attracted to the charge.
The bag is repelled by the charge.
The bag is neither attracted nor repelled.
Demo: balloon and uncharged objects: wall, aluminum can, soap bubbles, 2”x4” + – +

19. Group Question
What sort of force on the bag will exist if the external charge is negative?
The bag is attracted to the charge.
The bag is repelled by the charge.
The bag is neither attracted nor repelled. + – –

20. around electric charges
Electric Fields
around electric charges
§ 18.6

21. Electric Field
Field E relates the electric force F on an object to its charge q
F = qE
Field is a vector

22. Electric field Magnitude is the force in N on a +1 C charge
Direction is the direction of the force exerted on a positive charge
Vectors point away from positive charges and toward negative charges
Unit = N/C

23. Question
A positive charge experiences a force F to the right in an electric field. How does the force change if the field strength doubles?
The force becomes 1/4 what it was (F/4).
The force becomes 1/2 what it was (F/2).
The force remains the same (F).
The force becomes 2 what it was (2F).
The force becomes 4 what it was (4F).
The force reverses direction (–F).

24. Fields and Newton’s Third Law
Field notation is unilateral
Remember that forces are always between objects
A charge’s field acts on other charges
Never on itself

25. Visualizing Fields
Field vectors
Field lines

26. Field Vectors

27. Board Work
Draw field vectors to describe the electric field of a single positive charge. +

28. Field Lines

29. Field Lines
Magnitude of the force on a charge is greater where field lines are close together
Direction of the force is parallel to field lines
Force on a positive charge is along field lines
Force on a negative charge is opposite field lines

30. Question Green arrows are field lines.B C D
Green arrows are field lines.
Particles A–D have the same charge. Which experiences the greatest force from the field?
E. All four forces are equal.

31. Question Green arrows are field lines.
Particles A–D have the same charge. Which experiences the greatest force from the field? C A B D
E. All four forces are equal.

32. Board Work
Draw field lines to describe the electric field of a single positive charge. +

33. Board Work
Draw field lines to describe the electric field of an electric dipole. + −

34. Question
What is the nature of the electric field near an infinite plane of electric charge?

35. Conductors exclude E fields
Shielding
Conductors exclude E fields
§18.8

36. A Conductor in an E Field
Charges move in an E field
Charges make their own field
Charges rearrange until there is zero field inside the conductor
Then they stop

37. Conductors Exclude E fields
There can never be a static electric field inside a conductor.

38. Quantifying field lines
Gauss’s Law
Quantifying field lines
§18.9

39. Electric Flux
Through a closed surface

40. Electric Flux FE
Conceptually, the number of electric field lines passing through a surface E
FE = EA
A = area of the surface

41. Electric Flux FE
Previous formula only works when field is normal to the surface E
FE = 0

42. Electric Flux FE E q Area in profile is A cos q
q = angle of E field from surface normal
FE = EA cos q = E·A
A = “Area vector” normal to surface

43. Gauss’s Law
Flux through an enclosing surface is proportional to charge enclosed
FE = q/e0
e0 = “vacuum permittivity” = 8.85×10–12 C2/(Nm2)

44. Gauss’s law Use flux to find field around a point charge
The answer should be Coulomb’s law

45. Field of a Point Charge What is area A of spherical shell?
AP Physics L04_flux
Field of a Point Charge
What is area A of spherical shell?
FE = Qin/e0 = EA
Find E

46. Field around a Point Charge
Shell Area = 4pr2
FE = q/e0 = EA +q q
e0A q
e04pr2 R
E = = q
4pe0 r2 = kq r2 =
if k = 1
4pe0

47. Gauss’s Law Example Infinite line of uniform charge density (Q/L) = l
Cylindrical surface with charge on axis
Area of surface = 2prL + ends
Qin = Ll
FE = Qin/e0 = Ll/e0
FE = E(2prL)
Ll/e0 = E(2prL)
2pe0 1 l r
E = Q

48. Gauss’s Law Example Infinite plane of uniform charge density (Q/A) = s
Area of surface = 2A + edges
Qin = As
FE = Qin/e0 = As/e0
FE = E(2A)
As/e0 = E(2A)
E = ½ s/e0 Q

49. Gauss’s law examples
Field within a spherical shell of uniform charge density
Field within a sphere of uniform charge density
Charge distribution in a conductor
Field around charge at center of a neutral, hollow conducting sphere