Exam 2 covers Ch. 27-33, Lecture, Discussion, HW, Lab

1. Exam 2 covers Ch. 27-33,Lecture, Discussion, HW, Lab Exam 2 is Tue. Oct. 27, 5:30-7 pm, 145 Birge • 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)

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 Physics 208 Lecture 15

3. 4 3 1 2 Question Here is a picture of electric field lines. Which choice most accurately ranks the magnitude of the electric field at the different points? E1=E3>E2=E4 E1=E2>E3>E4 E4=E3>E1=E2 E4=E2>E1>E3 E4<E3<E1<E2 Physics 208 Lecture 15

4. 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 Physics 208 Lecture 15

5. Infinite line of charge, charge density λ r + + + + + + + + + + + + + + + + + + + + r Infinite sheet of charge, charge density η Physics 208 Lecture 15

6. Ring of uniform positive charge A) B) C) D) E) Which is the graph of on the z-axis? z y x z Physics 208 Lecture 15

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

8. Electric potential: general Electric potential energy difference U • 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 difference Depends only on charges that create E-fields

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

10. Example: Electric Potential y Calculate the electric potential at B B x d d2=4 m -12 μC +12 μC A - + Calculate the electric potential at A d1=3 m 3 m 3 m Calculate the work YOU must do to move a Q=+5 mC charge from A to B. Work done by electric fields

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=Vo

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

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

14. Question What is the voltage across capacitor 1 after the two are connected? C1=1µF C2=3µF V1=1V V2=0V 1V 2V 0V 0.25V 4V

15. Isolated charged capacitor • Plate separation increased • The stored energy • Increases • Decreases • Does not change Stored energy A) B) C) q unchanged because C isolated q is the same E is the same = q/(Aε0) ΔV increases = Ed C decreases U increases

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

18. Current conservation I2 I1 I3 I1=I2+I3 I1 I3 I2 I1+I2=I3 Iin Iout Iout = Iin

19. Resistors in Series and parallel R1 R2 • Parallel • V1 = V2 = V • Req = (R1-1+R2-1)-1 • Series • I1 = I2 = I • Req = R1+R2 I1+I2 I R1 R1+R2 I = = I1 I2 I R2 2 resistors in series: R  L Like summing lengths

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

21. Quick Quiz R1=200Ω R4=100Ω 9V R2=200Ω R3=100Ω 3V 6V Req=100Ω 9V Req=50Ω What is the current through resistor R1? 5 mA 10 mA 20 mA 30 mA 60 mA

22. 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 Physics 208 Lecture 15

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. Capacitors in parallel and series • ΔV1 = ΔV2 = ΔV • Qtotal = Q1 + Q2 Q1=Q2 =Q ΔV = ΔV1+ΔV2 1/Ceq = 1/C1 + 1/C2 Ceq = C1 + C2 Series Parallel

25. Example: Equivalent Capacitance C1 C2 C3 V C4 C1 = 30 μF C2 = 15 μF C3 = 15 μF C4 = 30 μF in series Parallel combinationCeq=C1||C2

26. R R RC Circuits C C ε Charge Discharge Time constant Start w/uncharged CClose switch at t=0 Start w/charged CClose switch at t=0

27. Question R1=100Ω 10V C=1µF R2=100Ω What is the current through R1 Immediately after the switch is closed? A. 10A B. 1 A C. 0.1A D. 0.05A E. 0.01A

28. Question R1=100Ω 10V C=1µF R2=100Ω What is the current through R1 a long time after the switch is closed? A. 10A B. 1 A C. 0.1A D. 0.05A E. 0.01A

29. Question R1=100Ω 10V C=1µF R2=100Ω 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

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. FB on a Charge Moving in a Magnetic Field, Formula FB = q v x B • FB 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 = 104 G (Earth surface 0.5 G)

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

33. dB r ds r = distance from current element = permeability of free space Law of Biot-Savart B out of page • Each short length of current produces contribution to magnetic field. r  I in plane of page ds Field from very short section of current Physics 208 Lecture 15

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

35. y x z Magnetic field from loop Bz A. z Which of these graphs best represents the magnetic field on the axis of the loop? Bz B. z I Bz C. z Bz D. z Physics 208 Lecture 15