1. PHY121 Summer Session II, 2006 Most of information is available at: http://nngroup.physics.sunysb.edu/~chiaki/PHY122-06.http://nngroup.physics.sunysb.edu/~chiaki/PHY122-06 It will be frequently updated. Homework assignments for each chapter due a week later (normally) and are delivered through WebAssign. Once the deadline has passed you cannot input answers on WebAssign. To gain access to WebAssign, you need to obtain access code and go to http://www.webassign.net. Your login username, institutionhttp://www.webassign.net name and password are: initial of your first name plus last name (such as cyanagisawa), sunysb, and the same as your username, respectively. In addition to homework assignments, there is a reading requirement of each chapter, which is very important. The lab session will start next Monday (June 5), for the first class go to A-117 at Physics Building. Your TAs will divide each group into two classes in alphabetic order. Instructor : Chiaki Yanagisawa

2. There will be recitation classes currently planned to be on Fridays at: 9:30 am - 10:15 am, 10:30 am - 11:15 am 3:00 pm - 3:45 pm, 4:00 pm - 4:45 pm. The location will be announced and the times are subject to change. In the recitation classes, quizzes will be given. There will be Office Hours by TAs and the times and locations will be announced. Questions about homework problems should be addressed during Office hours. Certain important announcements will be announce during the lectures and MOST of THEM (NOT ALL) will be posted on the web. Find information about which you want to know on the web or during the lectures as much as possible.

3. Chapter 15: Electric Forces and Electric Fields Properties of electric charges  Two opposite signed charges attract each other  Two equally signed charges repel each other  When a plastic rod is rubbed with a piece of fur, the rod is “positively” charged  When a glass rod is rubbed with a piece of silk, the rod is “negatively” charged  Electric charge is conserved Homework on WebAssign to be set up: 14,22,40,53,64

4. Particle Physics Model of Atoms electrons e - nucleus Old view Semi-modern view Modern view nucleus quarks proton What is the world made of? Electric charge (cont’d)

5. Properties of electric charges  Origin of electric charge Nature’s basic carriers of positive charge are protons, which, along with neutron, are located in the nuclei of atoms, while the basic carriers of negative charge are electrons which orbit around the nucleus of an atoms. Atoms are in general electrically neutral. It is easier to take off electron(s) from an atom than proton(s). By stripping off an electron from the atom, the atom becomes positively charged, while an atom that the stripped off electron is relocated to becomes negatively charged. In 1909 Millikan discovered that if an object is charged, its charge is always a multiple of a fundamental unit of charge, designated by the symbol e : the electric charge is quantized. The value of e in the SI unit is 1.60219x10 -19 coulomb C.

6. Electron: Considered a point object with radius less than 10 -18 meters with electric charge e= -1.6 x 10 -19 Coulombs (SI units) and mass m e = 9.11 x 10 - 31 kg Proton: It has a finite size with charge +e, mass m p = 1.67 x 10 -27 kg and with radius –0.805 +/-0.011 x 10 -15 m scattering experiment –0.890 +/-0.014 x 10 -15 m Lamb shift experiment Neutron: Similar size as proton, but with total charge = 0 and mass m n = –Positive and negative charges exists inside the neutron Pions: Smaller than proton. Three types: + e, - e, 0 charge. –0.66 +/- 0.01 x 10 -15 m Quarks: Point objects. Confined to the proton, neutron, pions, and so forth. – Not free – Proton (uud) charge = 2/3e + 2/3e -1/3e = +e – Neutron (udd) charge = 2/3e -1/3e -1/3e = 0 –An isolated quark has never been found  Electric charges Properties of electric charges

7. Two kinds of charges: Positive and Negative Like charges repel - unlike charges attract Charge is conserved and quantized 1.Electric charge is always a multiple of the fundamental unit of charge, denoted by e. 2.In 1909 Robert Millikan was the first to measure e. Its value is e = 1.602 x 10 −19 C (coulombs). 3.Symbols Q or q are standard for charge. 4.Always Q = Ne where N is an integer 5.Charges: proton, + e ; electron, − e ; neutron, 0 ; omega, − 3e ; quarks, ± 1/3 e or ± 2/3 e – how come? – quarks always exist in groups with the N×e rule applying to the group as a whole. Properties of electric charges

8. Insulators and Conductors  Definition In conductors, electric charges move freely in response to an electric force. All other materials are called insulators. Insulators : glass, rubber, etc. When an insulator is charged by rubbing, only the rubbed area becomes charged, and there is no tendency for the charge to move into other regions of the material. Conductors : copper, aluminum, silver, etc. When a small area of a conductor is charged, the charge readily distributes itself over the entire surface of the material. Semiconductors : silicon, germanium, etc. Electrical properties of semiconductor materials are somewhere between insulators and conductors.

9. Insulators and Conductors  Charging a material Charging by contact

10. Insulators and Conductors  Charging a material Charging by induction Induction : A process in which a donor material gives opposite signed charges to another material without losing any of donor’s charges

11. Insulators and Conductors  Insulator Polarization Polarization in an insulator by induction ++ -

12. Coulomb’s Law  Coulomb’s law - The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them r : distance between two charges q 1,q 2 : charges k e : Coulomb constant 8.9875 x10 9 Nm/C 2 - The directions of the forces the two charges exert on each other are always along the line joining them. - When two charges have the same sign, the forces are repulsive. - When two charges have opposite signs, the forces are attractive. ++ r q1q1 q2q2 -- r q1q1 q2q2 +- r q1q1 q2q2 F 21 F 12 F 21 F 12 F 21

13. Coulomb’s Law  Coulomb’s law and units SI unit Exact by definition charge of a proton r : distance between two charges (m) q 1,q 2 : charges (C) k e : Coulomb’s constant

14. Coulomb’s Law  Example : Electric forces vs. gravitational forces electric force gravitational force ++ r q q Gravitational force is tiny compared with electric force! ++ 0 0 proton neutron  particle

15. Coulomb’s law  Example : Forces between two charges +- r F 12 F 21

16. Coulomb’s law  Superposition of forces Principle of superposition When two charges exert forces simultaneously on a third charge, the total force acting on that charge is the vector sum of the forces that the two charges would exert individually.  Example : Vector addition of electric forces on a line +- 2.0 cm F 13 F 23 + q1q1 q2q2 q3q3 4.0 cm

17. Coulomb’s Law  Example 15.2: May the force be zero + 2.0 cm-x F 13 F 23 + q1q1 q3q3 q2q2 2.0 cm - x Three charges lie along the x-axis as in Fig. The positive charge q 1 =15  C is at x=2.0 cm, and the positive charge q 2 =6.0  C is at the origin. Where must a negative charge q 3 be placed on the x-axis so that the resultant electric force on it is zero?

18. Coulomb’s law  Example : Vector addition of electric forces in a plane + + + 0.50 m 0.40 m 0.30 m q 1 =2.0  C Q=2.0  C  

19. Electric Field  Electric field and electric forces + + + + + + + + + A B + + + + + + + + A P remove body B Existence of a charged body A modifies property of space and produces an “electric field”. When a charged body B is removed, although the force exerted on the body B disappeared, the electric field by the body A remains. The electric force on a charged body is exerted by the electric field created by other charged bodies.

20.  Electric field and electric forces (cont’d) + + + + + + + + A Test charge + + + + + + + + A P placing a test charge To find out experimentally whether there is an electric field at a particular point, we place a small charged body (test charge) at the point. Electric field is defined by (N/C in SI units) The force on a charge q: Electric Field

21.  Electric field of a point charge +- P P q0q0 q0q0 qq S S + + P q0q0 q S P’ Electric Field unit vector

22. Electric Field Lines  An electric field line is an imaginary line or curve drawn through a region of space so that its tangent at any point is in the direction of the electric-field vector at that point.  Electric field lines show the direction of at each point, and their spacing gives a general idea of the magnitude of at each point.  Where is strong, electric field lines are drawn bunched closely together; where is weaker, they are farther apart.  At any particular point, the electric field has a unique direction so that only one field line can pass through each point of the field. Field lines never intersect.

23. E-field lines begin on + charges and end on - charges. (or infinity) They enter or leave charge symmetrically. The number of lines entering or leaving a charge is proportional to the charge. The density of lines indicates the strength of E at that point. At large distances from a system of charges, the lines become isotropic and radial as from a single point charge equal to the net charge of the system. No two field lines can cross.  Field line drawing rules: Electric Field Lines

24.  Field line examples

25. Electric Field Lines  Field line examples (cont’d)

26.  An electric dipole is a pair of point charges with equal magnitude and opposite sign separated by a distance d. qd d electric dipole moment  Water molecule and its electric dipole Electric Field Lines

27.  Millikan’s experiment Millikan Oil-Drop Experiment D if v<0 (i.e. Eq<mg) D if v>0 (i.e. Eq>mg) drag force If the oil drop moves downward, the drag force points upward. When Eq=mg+D, the drop reaches the terminal velocity. Knowing the terminal velocity, mass of the drop, and the magnitude of the electric field, the charge of the drop can be measured. E=0 When the drag force, which is proportional to the velocity of the drop, becomes equal to mg, the drop reaches the terminal velocity. E=0

28.  Some definitions Electric Flux and Guass’s Law Closed surface : A closed surface has an inside and outside. Electric flux : A measure of how much the electric field vectors penetrate through a given surface.  Electric flux A (area)  electric flux:

29. Calculating Electric Flux  Example : Electric flux through a cube L

30. Calculating Electric Flux  Example : Electric flux through a sphere + +q r=0.20 m q=3.0  C A=2  r 2

31. Gauss ’s Law  Preview: The total electric flux through any closed surface (a surface enclosing a definite volume) is proportional to the total (net) electric charge inside the surface.  Case 1: Field of a single positive charge q + r=R A sphere with r=R at r=R The flux is independent of the radius R of the surface.

32. Gauss ’s Law  Case 2: More general case with a charge +q + + surface perpendicular to

33. Gauss’s Law  Case 3: An closed surface without any charge inside + Electric field lines that go in come out. Electric field lines can begin or end inside a region of space only when there is charge in that region.  Gauss’s law The total electric flux through a closed surface is equal to the total (net) electric charge inside the surface divided by  

34. Applications of Gauss’s Law  Example 15.8: Field of an infinite plane sheet of charge + + + + + + ++ + + + Gaussian surface two end surfaces Note:

35. Gauss’s Law  Example : Field between oppositely charged parallel conducting plane + + + + + + + + + - - - - - - - - - plate 1 plate 2 a b c S1S1 S2S2 S3S3 S4S4 Solution 1: No electric flux on these surfaces Solution 2: inward flux outward flux At Point a : b : c :

36.  Trajectory of a charged particle in a uniform electric field Application of Gauss’s Law

37. Applications of Gauss’s Law  Example : Field of an infinite line of charges line charge density Gaussian surface chosen according to symmetry

38. Applications of Gauss’s Law  Example : Field of a uniformly charged sphere Gaussian surface r=R R + + + + + + ++ ++ + +

39. Applications of Gauss’s Law  Example 15.7 : Field of a charged spherical shell Gaussian surface + + ++ ++ + + a b Total charge on the shell = Q

40. Applications of Gauss’s Law  Charge distribution and field The charge distribution the field The symmetry can simplify the procedure of application  Electric field by a charge distribution on a conductor When excess charge is placed on a solid conductor and is at rest, it resides entirely on the surface, not in the interior of the material (excess charge = charge other than the ions and free electrons that make up the material conductor A Gaussian surface inside conductor Charges on surface Conductor

41. Applications of Gauss’s Law  Electric field by a charge distribution on a conductor (cont’d) A Gaussian surface inside condactor Charges on surface Conductor Draw a Gaussian surface inside of the conductor E=0 everywhere on this surface (inside conductor) The net charge inside the surface is zero There can be no excess charge at any point within a solid conductor Any excess charge must reside on the conductor’s surface E on the surface is perpendicular to the surface Gauss’s law E at every point in the interior of a conducting material is zero in an electrostatic situation (all charges are at rest). If E were non-zero, then the charges would move

42. Charges on Conductors  Case 1: charge on a solid conductor resides entirely on its outer surface in an electrostatic situation + + + + + + ++ + + + + ++ + +  Case 2: charge on a conductor with a cavity + + + + + + ++ + + + + ++ + + Gauss surface The electric field at every point within a conductor is zero and any excess charge on a solid conductor is located entirely on its surface. If there is no charge within the cavity, the net charge on the surface of the cavity is zero.

43. Charges on Conductors  Case 3: charge on a conductor with a cavity and a charge q inside the cavity + + + + + + ++ + + + + ++ + + Gauss surface + - - -- - - - The conductor is uncharged and insulated from charge q. The total charge inside the Gauss surface should be zero from Gauss’ law and E=0 on this surface. Therefore there must be a charge –q distributed on the surface of the cavity. The similar argument can be used for the case where the conductor originally had a charge q C. In this case the total charge on the outer surface must be q+q C after charge q is inserted in cavity.