Understanding Electric Charge and Forces in Physics: A Comprehensive Guide

1. PHY127 Summer Session II • Most of information is available at: • http://nngroup.physics.sunysb.edu/~chiaki/PHY127-08 • The website above is the point of contact outside the class for important • messages, so regularly and frequently check the website. • At the end of class a quiz is given for the previous chapter covered in • the class. Bring a calculator (no wireless connection), a pencil, an eraser, • and a copy of lecture note for the chapter. • The lab session is an integrated part of the course and make sure that • you will attend all the sessions. See the syllabus for the detailed • information and the information (e.g. lab manuals) at the website above. • 5 homework problems for each chapter are in general due a week later • at 11:59 pm and are delivered through MasteringPhysics website at: • http://www.masteringphysics.com. You need to open an account. • In addition to homework problems, there is naturally a reading • requirement of each chapter, which is very important.

2. Chapter 20: Electric Charge/Force/Field • When a plastic rod is rubbed with a piece of fur, the rod is “negatively” charged • When a glass rod is rubbed with a piece of silk, the rod is “positively” charged Electric charge • Two equally signed charges repel each other • Two opposite signed charges attract each other • Electric charge is conserved

3. Electric charge (cont’d)

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

5. Electric charge (cont’d) • 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 me= 9.11 x 10 - 31 kg • Proton: It has a finite size with charge +e, mass mp= 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 mn= • 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 and neutron, • 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

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

7. Charging by contact

8. Charging by induction (cont’d)

9. Conductors : material in which charges can freely move. metal • Insulators : material in which charges are not readily transported. wood • Semiconductors : material whose electric property is in between. silicon • Induction : A process in which a donor material gives opposite signed charges to another material without losing any of donor’s charges Conductors, insulators, and induced charges

10. 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 q1,q2 : charges k : a proportionality constant Coulomb’s law - 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. q2 q2 q2 q1 q1 q1 + + - - + - r r r F2 on 1 F2 on 1 F1 on 2 F1 on 2 F2 on 1 F1 on 2

11. Coulomb’s law and units r : distance between two charges (m) q1,q2 : charges (C) k : a proportionality constant (=ke) SI units Coulomb’s law Exact by definition charge of a proton

12. Example: Electric forces vs. gravitational forces q q electric force + + r gravitational force neutron 0 proton Coulomb’s law + + aparticle 0 Gravitational force is tiny compared with electric force!

13. Example: Forces between two charges + - r F2 on 1 F1 on 2 Coulomb’s law

14. Superposition of forces Principle of superposition of kforces 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 Coulomb’s law q3 q2 q1 F2 on 3 F1 on 3 + + - 2.0 cm 4.0 cm

15. Example: Vector addition of electric forces in a plane q1=2.0 mC + 0.50 m Q=4.0 mC 0.30 m a 0.40 m + a 0.30 m 0.50 m + Coulomb’s law q2=2.0 mC force due to q2

16. Electric field and electric forces B A A P + + + + + + + + + + + + + + + + + remove body B Electric field and electric forces • 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.

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

18. Electric field of a point charge q0 q0 P P q q + - S S Electric field and electric forces + q0 P q + S P’

19. Electric field by a continuous charge distribution Electric field and electric forces

20. Electric field by a continuous charge distribution (cont’d) These may be considered in 1, 2 or 3 dimensions. There are some usual conventions for the notation: Charge per unit length is λ ;units C/m i.e, dq = λ dl Charge per unit area isσ ;units C/m2 i.e, dq = σ dA Charge per unit volume isρ ; units C/m3 i.e, dq = ρdV Electric field and electric forces

21. Example : Electron in a uniform field y - x O - 1.0 cm 100 V + • Two large parallel conducting plates connected to a battery produce uniform electric field Electric field and electric forces • Since the electric force is constant, the acceleration is constant too • From the constant-acceleration formula: when • The electron’s kinetic energy is: • The time required is:

22. 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. Electric field lines • 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. Field line drawing rules: • Field line examples • 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. Electric field lines

24. Field line examples (cont’d) Electric field lines (cont’d)

25. An electric dipole is a pair of point charges with equal magnitude and opposite sign separated by a distance d. electric dipole moment qd Electric Dipoles d • Water molecule and its electric dipole

26. Force and torque on an electric dipole Electric Dipoles torque: electric dipole moment: work done by a torque t during an infinitesimal displacement df :

27. Force and torque on an electric dipole (cont’d) potential energy for a dipole in an electric field Electric Dipoles

28. Trajectory of a charged particle in a uniform electric field Exercises

29. Cathode ray tube Exercises

30. Electric field by finite line charge Exercises

31. Electric field by a ring charge Exercises

32. Electric field by a uniformly charged disk Exercises

33. Electric field by infinite plate charge + Exercises + + + + + +

34. Electric field by two oppositely charged parallel planes Exercises

35. Far field by an electric dipole Exercises