1. Fundamental Physics II PETROVIETNAM UNIVERSITY FUNDAMENTAL SCIENCES DEPARTMENT Vungtau, December 2012 Pham Hong Quang E-mail: quangph@pvu.edu.vn

2. Gi ơ i thiê ̣ u môn ho ̣ c Pham Hong Quang 2 1. Tên môn h ọ c: V ậ t lý 2 (Physics 2) 2. S ố tín ch ỉ : 03 (2 Lý thuy ế t + 1 Thí nghi ệ m) 4. Phân b ổ th ờ i gian: - Lên l ớ p: 30 ti ế t (6 ti ế t/tu ầ n) + Lý thuy ế t: 24 ti ế t + Bài t ậ p: 6 ti ế t - Thí nghi ệ m: 30 ti ế t (2 ti ế t/tu ầ n) - Ki ể m tra gi ữ a k ỳ :2 ti ế t - Thi k ế t thúc h ọ c k ỳ :90 phút - T ự ho ̣ c: 60 gi ờ

3. Ta ̀ i liê ̣ u Pham Hong Quang Faculty of Fundamental Sciences 3 Ta ̀ i liê ̣ u chinh: [1] C ơ s ở V ậ t lý, T ậ p IV, V, VI: Đi ệ n và T ừ h ọ c, Quang h ọ c, David Halliday, Robert Resnik, Jearl Walker, b ả n d ị ch ti ế ng Vi ệ t, NXB Giáo d ụ c (1999). Sách tham kh ả o: [2] Fundamentals of physics, 8th ed., Extended, David Halliday, Robert Resnick and Jearl Walker, John Wiley & Sons (2008).

4. Đanh gia đ iê ̉ m Pham Hong Quang Faculty of Fundamental Sciences 4 Lý thuy ế t (h ệ s ố 2) Tham d ự l ớ p đầ y đủ : 5 % Bài t ậ p: 25 % Đi ể m ki ể m tra gi ữ a k ỳ : 20 % Đi ể m thi k ế t thúc môn h ọ c: 50 % Thí nghi ệ m (h ệ s ố 1) Th ự c hi ệ n t ấ t c ả các bài thí nghi ệ m (bao g ồ m tóm t ắ t lý thuy ế t tr ướ c và x ử lý s ố li ệ u sau thí nghi ệ m):50% Thi v ấ n đ áp:50%

5. 5 CHAPTER I Pham Hong Quang 5 PetroVietnam University Electric Charges, and Electric Fields

6. Chapter 1 Electric Charges, and Electric Fields Pham Hong Quang Faculty of Fundamental Sciences 6 1.Electric Charge 2. Insulators and Conductors 3. Coulomb’s Law 4. The Electric Field 5. Electric Field Lines 6. Shielding and Charging by Induction 7. Electric Flux and Gauss’s Law 8.Potentials

7. 1.1 Electric Charge Pham Hong Quang Faculty of Fundamental Sciences 7 The effects of electric charge were first observed as static electricity: After being rubbed on a piece of fur, an amber rod acquires a charge and can attract small objects.

8. 1.1 Electric Charge Pham Hong Quang Faculty of Fundamental Sciences 8 Charging both amber and glass rods shows that there are two types of electric charge; like charges repel and opposites attract.

9. 1.1 Electric Charge Pham Hong Quang Faculty of Fundamental Sciences 9 All electrons have exactly the same charge; the charge on the proton (in the atomic nucleus) has the same magnitude but the opposite sign:

10. 1.1 Electric Charge Pham Hong Quang Faculty of Fundamental Sciences 10 The electrons in an atom are in a cloud surrounding the nucleus, and can be separated from the atom with relative ease.

11. 1.1 Electric Charge Pham Hong Quang Faculty of Fundamental Sciences 11 When an amber rod is rubbed with fur, some of the electrons on the atoms in the fur are transferred to the amber:

12. 1.1 Electric Charge Pham Hong Quang Faculty of Fundamental Sciences 12 We find that the total electric charge of the universe is a constant: Electric charge is conserved. Also, electric charge is quantized in units of e. The atom that has lost an electron is now positively charged – it is a positive ion The atom that has gained an electron is now negatively charged – it is a negative ion

13. 1.1 Electric Charge Pham Hong Quang Faculty of Fundamental Sciences 13 Insulators and Conductors Conductor: A material whose conduction electrons are free to move throughout. Most metals are conductors. Insulator: A material whose electrons seldom move from atom to atom. Most insulators are non-metals.

14. 1.1 Electric Charge Pham Hong Quang Faculty of Fundamental Sciences 14 If a conductor carries excess charge, the excess is distributed over the surface of the conductor. Insulators and Conductors

15. 1.1 Electric Charge Pham Hong Quang Faculty of Fundamental Sciences 15 Semiconductors have properties intermediate between conductors and insulators; their properties change with their chemical composition. Photoconductive materials become conductors when light shines on them. Insulators and Conductors

16. 1.2 Coulomb’s Law Pham Hong Quang Faculty of Fundamental Sciences 16 Coulomb’s law gives the force between two point charges: The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if the charges are like.

17. 1.2 Coulomb’s Law Pham Hong Quang Faculty of Fundamental Sciences 17 The forces on the two charges are action- reaction forces.

18. 1.2 Coulomb’s Law Pham Hong Quang Faculty of Fundamental Sciences 18 If there are multiple point charges, the forces add by superposition.

19. 1.2 Coulomb’s Law Pham Hong Quang Faculty of Fundamental Sciences 19 Coulomb’s law is stated in terms of point charges, but it is also valid for spherically symmetric charge distributions, as long as the distance is measured from the center of the sphere.

20. 1.3 The Electric Field Pham Hong Quang Faculty of Fundamental Sciences 20 Definition of the electric field: Here, q 0 is a “test charge” – it serves to allow the electric force to be measured, but is not large enough to create a significant force on any other charges.

21. 1.3 The Electric Field Pham Hong Quang Faculty of Fundamental Sciences 21 If we know the electric field, we can calculate the force on any charge: The direction of the force depends on the sign of the charge – in the direction of the field for a positive charge, opposite to it for a negative one.

22. 1.3 The Electric Field Pham Hong Quang Faculty of Fundamental Sciences 22 The electric field of a point charge points radially away from a positive charge and towards a negative one. The electric field due to the point charge q at r is E = kq/r 2

23. 1.3 The Electric Field Pham Hong Quang Faculty of Fundamental Sciences 23 Just as electric forces can be superposed, electric fields can as well.

24. 1.3 The Electric Field Pham Hong Quang Faculty of Fundamental Sciences 24 Electric field lines are a convenient way of visualizing the electric field. Electric field lines: 1.Point in the direction of the field vector at every point 2.Start at positive charges or infinity 3.End at negative charges or infinity 4.Are more dense where the field is stronger Electric Field Lines

25. 1.3 The Electric Field Pham Hong Quang Faculty of Fundamental Sciences 25 The charge on the right is twice the magnitude of the charge on the left (and opposite in sign), so there are twice as many field lines, and they point towards the charge rather than away from it.

26. 1.3 The Electric Field Pham Hong Quang Faculty of Fundamental Sciences 26 Combinations of charges. Note that, while the lines are less dense where the field is weaker, the field is not zero where there are no lines. In fact, there is only one point within the figures below where the field is zero – can you find it?

27. 1.3 The Electric Field Pham Hong Quang Faculty of Fundamental Sciences 27 A parallel-plate capacitor consists of two conducting plates with equal and opposite charges. Here is the electric field:

28. 1.3 The Electric Field Pham Hong Quang Faculty of Fundamental Sciences 28 Shielding and Charge by Induction Since excess charge on a conductor is free to move, the charges will move so that they are as far apart as possible. This means that excess charge on a conductor resides on its surface, as in the upper diagram.

29. 1.3 The Electric Field Pham Hong Quang Faculty of Fundamental Sciences 29 When electric charges are at rest, the electric field within a conductor is zero.

30. 1.3 The Electric Field Pham Hong Quang Faculty of Fundamental Sciences 30 The electric field is always perpendicular to the surface of a conductor – if it weren’t, the charges would move along the surface.

31. 1.3 The Electric Field Pham Hong Quang Faculty of Fundamental Sciences 31 The electric field is stronger where the surface is more sharply curved.

32. 1.4 Electric field due to a continuous distribution Pham Hong Quang Faculty of Fundamental Sciences 32 Instead of summing the charge we can imagine a continuous distribution and integrate it. This distribution may be over a volume, a surface or just a line. E = ∫dE = ∫ kdq i /r 2

33. 1.4 Electric field due to a continuous distribution Pham Hong Quang Faculty of Fundamental Sciences 33 Electric field due to a line of uniform + charge of length L with linear charge density equal to λ

34. 1.4 Electric field due to a continuous distribution Pham Hong Quang Faculty of Fundamental Sciences 34 What is the electric field from an infinitely long wire with linear charge density of +100 nC/m at a point 10 cm away from it. What do the lines of flux look like?

35. 1.4 Electric field due to a continuous distribution Pham Hong Quang Faculty of Fundamental Sciences 35 The electric field on the axis of a uniformly charged ring with linear charge density l = Q/2pR. =0 at z=0 =0 at z=infinity =max at z=0.7R

36. 1.5 Electric Flux and Gauss’s Law Pham Hong Quang Faculty of Fundamental Sciences 36 Electric flux is a measure of the electric field perpendicular to a surface:

37. 1.5 Electric Flux and Gauss’s Law Pham Hong Quang Faculty of Fundamental Sciences 37 Gauss’s law states that the electric flux through a closed surface is proportional to the charge enclosed by the surface:

38. 1.5 Electric Flux and Gauss’s Law Pham Hong Quang Faculty of Fundamental Sciences 38 Gauss’s law can be used to find the electric field in systems with simple configurations.

39. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 39 Gravitational force: F=Gm 1 m 2 /r 2 Electrostatic force: F=Gq 1 q 2 /r 2 One thing is in common: both of these forces are conservative What does it mean for a force or field to be conservative? The work done by the force is independent of path!

40. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 40 Gravitational force

41. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 41 Electrostatic force We can assign the Reference Point of Electric Potential Energy where W is the work done by the electric force field. If we take U ∞ = 0 then, U = - W ∞ The potential energy of a charge at a point is equal to the negative of the work done by the field in bringing the charge from infinity to that point.

42. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 42 Electric Potential is the potential energy per unit charge. V = U/q  V =  U/q = -W/q V = - W ∞ /q Note that the work you apply to a charge is the negative of the work that the field applies on the charge (when there is no change in kinetic energy).  V = W applied /q or W applied = q  V The units of J/C is defined to be the volt (V).

43. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 43 Notes Electric field always points from higher electric potential to lower electric potential. A positive charge accelerates from a region of higher electric potential energy (or higher potential) toward a region of lower electric potential energy (or lower potential). A negative charge accelerates from a region of lower potential toward a region of higher potential.

44. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 44 Equipotential Surfaces An equipotential surface is a surface on which the electric potential is the same everywhere.

45. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 45 1.The net electric force does no work as a charge moves on an equipotential surface. 2.The electric field created by any charge or group of charges is everywhere perpendicular to the associated equipotential surfaces and points in the direction of decreasing potential. What will happen if the electric field E is not perpendicular to the equipotential surface? Equipotential Surfaces, Cont.

46. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 46 Calculating the Potential from the Field

47. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 47 Calculating the Field from the Potential The potential gradient gives the component of the electric field along the displacement Δ s

48. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 48 Potential due to a Point Charge: With the understanding that V ∞ = 0 Notice that: 1.V is a scalar (much easier to handle than a vector!) 2.V can be positive or negative! Potential due to a Group of Point Charges:

49. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 49 Potential Due to a Continuous Charge Distribution

50. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 50 Line of Charge A thin nonconducting rod of length L has a positive charge of uniform linear density λ. Let us determine the electric potential V due to the rod at point P, a perpendicular distance d from the left end of the rod.

51. 1.6 Electric Potential Pham Hong Quang Faculty of Fundamental Sciences 51 Charged Disk we calculated the magnitude of the electric field at points on the central axis of a plastic disk of radius R that has a uniform charge density σ on one surface. Here we derive an expression for V(z), the electric potential at any point on the central axis.

52. 52 Pham Hong Quang 52 PetroVietnam University Thank you!