1. PHYS 1902: 2018
Electromagnetism: 1
Lecturer: Prof. Geraint F. Lewis

2. SPOILER
WARNING!

3. Electromagnetism - The Whole Thing

4. EM Module By the end of this module, you should be able to:
describe electric and magnetic fields and their effects on charges and currents, understanding each field as an alternative way of describing the corresponding force.
relate each of Maxwell's equations to the properties of the fields it describes
understand the ways that fields are created and use Maxwell's equations to calculate the fields produced
describe the relationships between electric and magnetic fields and appreciate that light is a consequence of this relationship

5. Where to get help - Textbook, especially broblems Workshop tutorials
Duty Tutor
Note!
A lot of work will be on the board, & slides may not be in step with lecture. Also, examples are only worked out on the board!

6. Chapter 21
Electric Charge and Electric Field

7. Electric Charge Some things “have” charge just like they “have” mass
Unlike mass, charge can come in two types:
Positive
Negative
Opposite signs attract, like signs repel
SI Unit of charge is the Coulomb (C)

8. Coulomb’s Law Remember: force is a vector
Charles-Augustin de Coulomb
(from Wikipedia)
Remember:
force is a vector
direction is determined by the sign of the charge
(Permittivity of Free Space)

9. Superposition Principle

10. A Simple Problem

11. Another Simple Problem
In which direction is the net force on the charge Q?

12. The Electric Field Defined as: Of a point charge:
Just like forces, there is a superposition principle for the electric field

13. The electric field is a “vector field”

14. The Electric Field The “test charge” is taken to be positive.
Electric field ”points” away from positive charges.
Electric field “points” towards negative charges.

15. Electric Field Lines
This is a general property of vector fields.

16. Electric Field Lines

17. A Problem What is the electric field at the origin?
What do the field lines look like?

18. What is the electric field at point P?
Example 21.11
What is the electric field at point P?

19. What is the electric field at point P?
Example 21.12
What is the electric field at point P?
𝐸 𝑥 = 𝑑 𝐸 𝑥

20. Electric Dipole

21. Torque on an Electric Dipole

22. Torque on an Electric Dipole

23. Potential Energy for a Dipole

24. Chapter 22
Gauss’s Law

25. Charge in a Volume

26. Charge and Electric Flux
Goal: Relate charge inside a closed surface to electric “flux” through that surface

27. Electric Flux

28. Electric Flux

29. Electric Flux

30. Surfaces are Oriented

31. Electric Flux

32. Electric Flux-Point Charge
Consider a ”closed” spherical surface centred on a point charge, q.
At each point on the sphere, the electric field points radially outwards (spherical symmetry).
At each point on the sphere, the ”normal” to the surface is also radial. Choose the normal pointing “towards infinity”.
Each infinitesimal vector area, dA, also points radially outwards.
So, what is the electric flux through the surface of the sphere?

33. Electric Flux-Point Charge
Let’s add a second sphere, at double the radius of the first.
The relative size of the area of this new sphere is 4 times that of the old.
The magnitude of the electric field through the larger sphere is ¼ of the smaller sphere.
So, the electric flux through the larger sphere is the same as that through the smaller sphere.
Φ 𝐸 = 𝐸 . 𝑑𝐴 = 𝑞 𝜖 0

34. Electric Flux-Point Charge

35. Gauss’s Law
The total electric flux through a closed surface is equal to the total (net) electric charge inside the surface, divided by ε0.

36. What about other shapes?
𝑟 2 = 𝑥 2 + 𝑦 2 +( 𝑎 2 ) 2

37. Choices of Surfaces

38. Application: Conductors

39. Conducting Sphere: 22.5

40. Infinite Line of Charge: 22.6

41. Infinite Plane Sheet: 22.7

42. Finite Charged Plates Infinite Charged Plates
Parallel Plates: 22.8
Finite Charged Plates Infinite Charged Plates

43. Uniformly Charged Sphere: 22.9

44. Application: Conductors
Faraday’s Bucket

45. Application: Faraday Cage
Why are microwaves confined to the inside, but light can escape?

46. Surface of a Conductor

47. Chapter 23
Electric Potential

48. Electric Potential Energy
Electric force is conservative
(work done by a conservative force)

49. Electric Potential Energy in a Uniform Field

50. Electric Potential Energy in a Uniform Field

51. Electric Potential Energy in a Uniform Field

52. Electric Potential Energy in a Uniform Field

53. Electric Potential Energy in a Uniform Field

54. Electric Potential Energy of Two Charges

55. Electric Potential Energy of Two Charges

56. Electric Potential Energy of Two Charges

57. Electric Potential Energy of Point Charges

58. What happens?

59. Electric Potential

60. Electric Potential of a Uniform Field
Can speak of the electric potential (voltage) at any point, without reference to a test charge

61. Electric Potential of a Point Charge

62. Electric Potential of Many Point Charges

63. Equipotential surfaces
Visual means of expressing the electric potential

64. Equipotential surfaces

65. Equipotential surfaces

66. Electric Potential and Electric Field.

67. Electric Potential for a Conductor

68. Example 23.10

69. Example 23.11

70. Example 23.12

71. Potential Gradients