1. 03/10/20061 Exam Review I Physics 208

2. 03/10/20062 Chapters 23-28 Coulomb force between charges Work done to move a charge Electric potential as  U/q Electric field as F/q Motion of charged particle in electric field Relation between electric field and electric potential Electric field lines and equipotentials Electric fields in and near conductors Electric flux and Gauss' law Electric field and potential of a point charge, line charge, sheet charge, spherical shell Capacitance of an isolated conductor, and of a pair of conductors Calculating capacitance, parallel plate, cylinder, sphere Energy in a capacitor, energy density, energy in E-field Dielectrics Current and resistance, Ohms law Power dissipation in a resistor Simple circuits (parallel and series) and RC circuits

3. 03/10/20063 Charging processes Triboelectric: -glass rod rubbed with silk  positive -rubber rod rubbed with fur  negative + + + + + + + Less positively charged rod + + + + + Positively charged metal + + + + + + + + + + + + + + + + + - -- - - electron flow Conduction Induction

4. 03/10/20064 If you rub an inflated balloon against your hair, the two materials attract each other, as shown in this figure. Fill in the blank: the amount of charge present in the system of the balloon and your hair after rubbing is _____ the amount of charge present before rubbing. (a) less than (b) the same as (c) more than Quiz on Charge Conservation

5. 03/10/20065 3 pithballs suspended from thin threads are charged by touching them with a charged object. It is found that pithballs 1 and 2 repel each other and pithballs 2 and 3 repel each other. Which of the following statements are correct? 1)1 and 3 carry opposite charge 2)All of them carry charges of the same sign 3)We need to do more experiments to determine the sign of the charges Quiz on charge sign ++ - 1 2 3 -- - ++ +

6. 03/10/20066 Quiz on charge sign cont. 3 objects are brought close to each other, 2 at a time. When objects A and B are brought together, they attract. When objects B and C are brought together, they repel. From this, we conclude that: (a) objects A and C possess charges of opposite sign. (b) all three of the objects possess charges of the same sign. (c) we need to perform additional experiments to determine information about the charges on the objects. + - - A B C - + +

7. 03/10/20067 Answer: (c). In the first experiment, objects A and B may have charges with opposite signs, or one of the objects may be neutral since they can attract one the other even due to induction. The second experiment shows that B and C have charges with the same signs, so that B must be charged. But we still do not know if A is charged or neutral. Answer

8. 03/10/20068 Insulators and conductors One of these isolated charged spheres is copper and the other is rubber. Label which is which and support your answer with an explanation. a) A is rubber and B is copper. b) A is copper and B rubber c) They are both copper Charged rubber rods are placed near a neutral conducting sphere, causing a redistribution of charge on the spheres. Which of the diagrams below depict the proper distribution of charge on the spheres? List all that apply. a)A and D b)C and B c)E

9. 03/10/20069 Coulomb’s Law Electrical force between two stationary charged particles The SI unit of charge is the coulomb (C ), µC = 10 -6 C 1 C corresponds to 6.24 x 10 18 electrons or protons k e = Coulomb constant ≈ 9 x 10 9 N. m 2 /C 2 = 1/(4π  o ) –  o  permittivity of free space = 8.854 x 10 -12 C 2 / N. m 2

10. 03/10/200610 Electric Force

11. 03/10/200611 Electric Force magnitude The electric force between 2 like charged objects is F=0.02 N. If the charge of one of the 2 objects is halved and the distance separating the 2 objects is doubled, what is the new force?

12. 03/10/200612 Electric Force: Newton’s 3rd law

13. 03/10/200613 Forces as vectors 2 small beads with positive charges +3q and +q are fixed at the opposite ends of an horizontal rod. A 3rd small charged bead is free to slide on the rod. a) Does the result depend on the sign of the charge on the bead? b) Find its equilibrium position. a)The result is independent on the sign of the charge of the bead b)Equations to solve the problem (q’ charge of the bead): 12 + F1F1 F2F2 - F1F1 F2F2 d1d1 d2d2

14. 03/10/200614 Electrostatic Potential of 2 like charges

15. 03/10/200615 An electron initially travels horizontally in a uniform electric field pointing upwards with 3 possible directions of the initial velocity of the same magnitude. Which of the following relation is correct? a) v b > v > v a b) v a > v > v b c) v b = v a > v d) v b = v = v a Answer: a) the greatest change in potential  V occurs for the case with the max vertical deflection from the initial position. This occurs when the electron is projected at an angle below the horizontal. E field, potential difference and energy conservation - - - - - - - - - - - + + + + + + + + + + + + + + + ++  K = -  U=-q  V a b x L

16. 03/10/200616 Example E Fields and Potential What is the electric field at point B? What is the electric field at point A? Calculate the force on a Q=-3  C charge placed at point A: x +- B A d 1 =3 m3 m d 2 =4 m 3 m y -12  C +12  C  d F=QE

17. 03/10/200617 Example E Potential Calculate the electric potential at B Calculate the work YOU must do to move a Q=+5 mC charge from A to B. Calculate the electric potential at A x + - B A d 1 =3 m3 m d 2 =4 m 3 m y -12  C+12  C d

18. 03/10/200618 Gauss’ Law

19. 03/10/200619 Electric Flux

20. 03/10/200620 The electric charge density for plate 1 is -  and for plate 2 is +  The magnitude of the electric field associated with plate 1 is:  /(2  0 ) and the filed lines are shown in the figure. When they are placed parallel one to the other, the Magnitude of the field is: 1.  /  0 between and ±  /(2  0 ) outside 2.  /  0 between and 0 outside 3. None of the above Plane charge density

21. 03/10/200621 Insulator and Conductor sphere A solid nonconductive spherical ball of diameter d = 2R = 1.0 cm is uniformly charged such that is has an electric field of 20 kV/m at its surface. 1.How much charge is on the ball? Chose gauss surface with r = R 2. What is the magnitude of the electric field halfway to the center of the ball? 3. If the ball were made of a conductive material, how would the answers to 1) and 2) change? R uniform charge distribution inside the insulating shell 1. Same (all charge on surface)2. E = 0 (field inside a conductor is 0)

22. 03/10/200622 Capacitors C  Q/V Parallel PlateC =   A/d Adding –Series V eq =V 1 +V 2 Q eq = Q 1 =Q 2 –Parallel V eq =V 1 =V 2 Q eq = Q 1 +Q 2

23. 03/10/200623 The parallel plates of a capacitor with vacuum between them are given equal and opposite charge. If the plates are pushed closer from a distance d to D < d, does the energy stored in the capacitor 1)Increase 2)Decrease 3)Remain equal Energy stored in a parallel plate capacitor

24. 03/10/200624 Metal slab in a capacitor In the slab E = 0 and we have 2 equivalent capacitors in series In the other case the capacitance between the 2 bottom plates is (for the other 2 plates at the same potential 1/C  0)

25. 03/10/200625 Capacitor with slab of dielectric A dielectric slab is introduced between the plates of a capacitor. The capacitor is charged and then the dielectric is removed. Which of the following statements are correct: 1)The stored energy increases 2)The capacitance increases 3)The potential difference decreases 0 = quantities in vacuum

26. 03/10/200626 Calculate the equivalent Capacitance C 1 = 10  F C 2 = 20  F C 3 = 30  F C 4 = 40  F V = 50 Volts Compare V 1 with V 4 C2C2 V C3C3 C1C1 C4C4 parallel C 1, C 23, C 4 in series C 1 V 4

27. 03/10/200627 Resistors R = V/I R=  L/A P = RI 2 Adding –Series V eq =V 1 +V 2 I eq = I 1 =I 2 –Parallel V eq =V 1 =V 2 I eq = I 1 +I 2

28. 03/10/200628 Resistors in Series

29. 03/10/200629 Resistors in Parallel

30. 03/10/200630 Light bulbs in Series Since the wire has R =0 all current will flow through it and bulb B will fade. Instead A will look brigther since the current in A increaseas from I = V/(R A +R B ) to I = V/R A Consider the resistance of the wire negligible

31. 03/10/200631 Which of the following statements are correct? 1.A looks dimmer than B 2.A looks as bright as B 3.A looks brighter than B Light Bulbs of Different Power in Parallel A 100 W B 60 W R A I B R A I A 2 > R B I B 2 What happens if A and B are connected in series?

32. 03/10/200632 Resistors in series and parallel

33. 03/10/200633 Kirchhoff’s Rules Junction Rule:  I in =  I out A statement of Conservation of Charge  Loop Rule: A statement of Conservation of Energy I 1 = I 2 + I 3 -

34. 03/10/200634 Kirchhoff’s laws R 1 = 10  R 2 = 20  R 3 = 30  V 1 = 50 Volts V 2 = 10 Volts 2 loops Chose 2 currents and their verse Calculate total power delivered by the batteries R2R2 V1V1 R3R3 R1R1 +-+- - + V2V2 I1I1 I2I2

35. 03/10/200635 RC Circuits: CHARGE OF C R C  S1S1 Calculate current immediately after switch is closed. Calculate current after switch has been closed for 2 time constants Calculate current after switch has been closed for a very long time Calculate charge on capacitor after switch has been closed for a long time R=10 , C=30 mF and  =20 Volts I =  /R = 2 A  =RC = 0.3 s

36. 03/10/200636 RC Circuits You are given a 5-pack of R=2  resistors and a 5-pack of C=2  F capacitors. How do you configure them to produce a circuit of 21  s time constant RC circuit? Time constant,  = RC = 21  s = 7 * 3  s = 7  * 3  F