1. 1 Exam 2 covers Ch. 27-33, Lecture, Discussion, HW, Lab Chapter 27: The Electric Field Chapter 29: Electric potential & work Chapter 30: Electric potential & field (exclude 30.7) Chapter 31: Current & Resistance Chapter 32: Fundamentals of Circuits (exclude 32.8) Chapter 33: The Magnetic Field (exclude 33.5-33.6, 33.9-10, & Hall effect) Exam 2 is Tue. Oct. 27, 5:30-7 pm, 145 Birge

2. 2 Electric field lines Local electric field tangent to field line Density of lines proportional to electric field strength Fields lines can only start on + charge Can only end on - charge. Electric field lines can never cross Oct. 22, 2009 Physics 208 Lecture 15

3. 3 Question Here is a picture of electric field lines. Which choice most accurately ranks the magnitude of the electric field at the different points? A)E 1 =E 3 >E 2 =E 4 B)E 1 =E 2 >E 3 >E 4 C)E 4 =E 3 >E 1 =E 2 D)E 4 =E 2 >E 1 >E 3 E)E 4 <E 3 <E 1 <E 2 1 2 3 4 Oct. 22, 2009 Physics 208 Lecture 15

4. Oct. 22, 2009Physics 208 Lecture 154 Charge Densities Volume charge density: when a charge is distributed evenly throughout a volume  = Q / V dq =  dV Surface charge density: when a charge is distributed evenly over a surface area  = Q / A dq =  dA Linear charge density: when a charge is distributed along a line = Q / dq = d Electric fields and potentials from these charge elements superimpose

5. Oct. 22, 2009Physics 208 Lecture 155 ++++++++++++++++++++ Infinite line of charge, charge density λ r Infinite sheet of charge, charge density η r

6. Oct. 22, 2009Physics 208 Lecture 156 Ring of uniform positive charge y x z Which is the graph of on the z-axis? A) B) C) D) E) z

7. 7 Properties of conductors everywhere inside a conductor Charge in conductor is only on the surface surface of conductor - - - - - - + + + + + +

8. 8 Electric potential: general Electric field usually created by some charge distribution. V(r) is electric potential of that charge distribution V has units of Joules / Coulomb = Volts Electric potential energy difference  U Electric potential difference Depends only on charges that create E-fields

9. 9 Electric Potential Q source of the electric potential, q ‘experiences’ it Electric potential energy per unit charge units of Joules/Coulomb = Volts Example: charge q interacting with charge Q Electric potential energy Electric potential of charge Q

10. 10 Example: Electric 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 Work done by electric fields

11. 11 Potential from electric field Electric field can be used to find changes in potential Potential changes largest in direction of E-field. Smallest (zero) perpendicular to E-field V=VoV=Vo

12. 12 Electric Potential and Field Uniform electric field of What is the electric potential difference V A -V B? A) -12V B) +12V C) -24V D) +24V A x y 2m 5m 2m 5m B

13. Capacitors Energy stored in a capacitor: C = capacitance: depends on geometry of conductor(s) Conductor: electric potential proportional to charge: Example: parallel plate capacitor +Q-Q d Area A 13

14. Question What is the voltage across capacitor 1 after the two are connected? 14 C 2 =3µF V 1 =1V C 1 = 1µF V 2 =0V A.1V B.2V C.0V D.0.25V E.4V

15. 15 Isolated charged capacitor Plate separation increased The stored energy 1)Increases 2)Decreases 3)Does not change A) B) C) Stored energy q unchanged because C isolated q is the same E is the same = q/(Aε 0 ) ΔV increases = Ed C decreases U increases

16. 16 Conductors, charges, electric fields Electrostatic equilibrium No charges moving No electric fields inside conductor. Electric potential is constant everywhere Charges on surface of conductors. Not equilibrium Charges moving (electric current) Electric fields inside conductors -> forces on charges. Electric potential decreases around ‘circuit’

17. 17 Resistance and resistivity Ohm’s Law: ΔV = R I (J =  E or E = ρ J  ΔV = EL and E =  J  /A = ΔV/L R = ρL/A Resistance in ohms ( ) Question 5cm 2cm 1cm I A block is made from a material with resistivity of 10 -4 Ω-m. It has 10 A of current flowing through it. What is the voltage across the block? A. 0.1V B. 0.25V C. 0.5V D. 1.0V E. 5.0V

18. 18 Current conservation I in I out I out = I in I1I1 I2I2 I3I3 I 1 =I 2 +I 3 I2I2 I3I3 I1I1 I 1 +I 2 =I 3

19. 19 Resistors in Series and parallel Series I 1 = I 2 = I R eq = R 1 +R 2 R1R1 R2R2 = R 1 +R 2 2 resistors in series: R  L Like summing lengths R1R1 R2R2 = I I I I1I1 I2I2 I 1 +I 2 Parallel V 1 = V 2 = V R eq = (R 1 -1 +R 2 -1 ) -1

20. 20 Quick Quiz What happens to the brightness of bulb A when the switch is closed? A.Gets dimmer B.Gets brighter C.Stays same D.Something else

21. 21 Quick Quiz What is the current through resistor R 1 ? R 1 =200Ω R 2 =200Ω R 3 =100Ω R 4 =100Ω 9V R eq =100Ω R eq =50Ω 9V A. 5 mA B. 10 mA C. 20 mA D. 30 mA E. 60 mA 6V 3V

22. Oct. 22, 2009Physics 208 Lecture 1522 Power dissipation (Joule heating) Charge loses energy from c to d. Ohm’s law: Energy dissipated in resistor as Heat (& light) in bulb Power dissipated in resistor = Joules / s = Watts

23. 23 Capacitors as circuit elements Voltage difference depends on charge Q=CV Current in circuit Q on capacitor changes with time Voltage across cap changes with time

24. 24 Capacitors in parallel and series ΔV 1 = ΔV 2 = ΔV Q total = Q 1 + Q 2 C eq = C 1 + C 2 Q 1 =Q 2 =Q ΔV = ΔV 1 +ΔV 2 1/C eq = 1/C 1 + 1/C 2 Parallel Series

25. 25 Example: Equivalent Capacitance C 1 = 30  F C 2 = 15  F C 3 = 15  F C 4 = 30  F C2C2 V C3C3 C1C1 C4C4 Parallel combination C eq =C 1 ||C 2 in series

26. 26 RC Circuits R C  R C Start w/uncharged C Close switch at t=0 Start w/charged C Close switch at t=0 Time constant ChargeDischarge

27. 27 Question What is the current through R 1 Immediately after the switch is closed? 10V R 1 =100Ω R 2 =100Ω C=1µF A. 10A B. 1 A C. 0.1A D. 0.05A E. 0.01A

28. 28 Question What is the current through R 1 a long time after the switch is closed? 10V R 1 =100Ω R 2 =100Ω C=1µF A. 10A B. 1 A C. 0.1A D. 0.05A E. 0.01A

29. 29 Question What is the charge on the capacitor a long time after the switch is closed? A. 0.05µC B. 0.1µC C. 1µC D. 5µC E. 10µC 10V R 1 =100Ω R 2 =100Ω C=1µF

30. 30 RC Circuits What is the value of the time constant of this circuit? A) 6 ms B) 12 ms C) 25 ms D) 30 ms

31. 31 F B on a Charge Moving in a Magnetic Field, Formula F B = q v x B F B is the magnetic force q is the charge v is the velocity of the moving charge B is the magnetic field SI unit of magnetic field: tesla (T) CGS unit: gauss (G): 1 T = 10 4 G (Earth surface 0.5 G)

32. 32 Magnetic Force on a Current S N I Current Magnetic field Magnetic force Force on each charge Force on length of wire Force on straight section of wire, length L

33. Oct. 22, 2009Physics 208 Lecture 1533 Law of Biot-Savart Each short length of current produces contribution to magnetic field. r  I in plane of page dsds B out of page dsds dBdB r = permeability of free space r = distance from current element Field from very short section of current

34. 34 Magnetic field from long straight wire: Direction What direction is the magnetic field from an infinitely-long straight wire? I x y = permeability of free space r = distance from wire

35. Oct. 22, 2009Physics 208 Lecture 1535 Magnetic field from loop Which of these graphs best represents the magnetic field on the axis of the loop? BzBz BzBz BzBz BzBz A. B. C. D. z z z z z x y I