Lecture 32 Review Session A : Midterm 3

1. Physics 2113 Jonathan Dowling Lecture 32 Review Session A : Midterm 3

2. EXAM 03: 6PM WED 08 NOV in Cox Auditorium The exam will cover: Ch.27 through Ch.29 The exam will be based on: HW07–09 The formula sheet and practice exams are here: http://www.phys.lsu.edu/~jdowling/PHYS21133-FA15/lectures/index.html Note this link also includes tutorial videos on the various right hand rules. You can see examples of even older exam IIIs here: http://www.phys.lsu.edu/faculty/gonzalez/Teaching/Phys2102/Phys2102OldTests/

3. Multiloop Single loop DC Circuits Loop rule V = iR P = iV

4. Resistors vs Capacitors ResistorsCapacitors Key formula: V=iR Q=CV In series: same current same charge Req=∑Rj 1/Ceq=∑1/Cj In parallel: same voltage same voltage 1/Req=∑1/Rj Ceq=∑Cj

5. Resistorsin Series and in Parallel • What’s the equivalent resistance? • What’s the current in each resistor? • What’s the potential across each resistor? • What’s the current delivered by the battery? • What’s the power dissipated by each resisitor?

6. Series and Parallel

7. Series and Parallel

8. Series and Parallel

9. Problem: 27.P.018. [406649] Figure 27-33 shows five 5.00 resistors. (Hint: For each pair of points, imagine that a battery is connected across the pair.) Fig. 27-33 (a) Find the equivalent resistance between points F and H. (b) Find the equivalent resistance between points F and G. Slide Rules: You may bend the wires but not break them. You may slide any circuit element along a wire so long as you don’t slide it past a three (or more) point junction or another circuit element.

12. Too Many Batteries!

13. Circuits: Checkpoints, Questions

14. +E -iR (a) Rightward (EMF is in direction of current) (b) All tie (no junctions so current is conserved) (c) b, then a and c tie (Voltage is highest near battery +) (d) b, then a and c tie (U=qV and assume q is +)

15. (a) all tie (current is the same in series) The voltage drop is –iR proportional to R since i is same.

16. (a) Vbatt < 12V (walking with current voltage drop –ir (b) Vbatt > 12V (walking against current voltage increase +ir (c) Vbatt = 12V (no current and so ir=0)

17. Problem: 27.P.046. [406629] In an RC series circuit, E = 17.0 V, R = 1.50 MΩ, and C = 1.80 µF. (a) Calculate the time constant. (b) Find the maximum charge that will appear on the capacitor during charging. (c) How long does it take for the charge to build up to 16.0 µC?

19. v F L Magnetic Forces and Torques

20. Side view Top view C C (28-13)

21. (28-14)

22. Ch 28: Checkpoints and Questions

23. 28.3: Finding the Magnetic Force on a Particle: Always assume particle is POSITIVELY charged to work Out direction then flip your thumb over if it is NEGATIVE.

26. ICPP The left face is at a lower electric potential (minus charges) and the right face is at a higher electric potential (plus charges).

27. v F B into blackboard. Circular Motion: Since magnetic force is perpendicular to motion, the movement of charges is circular. r In general, path is a helix (component of v parallel to field is unchanged).

28. . electron Radius of Circlcular Orbit . C r Angular Frequency: Independent of v Period of Orbit: Independent of v Orbital Frequency: Independent of v

30. v F r Which has the longer period T? B into blackboard. Since v is the same and rp >> rethe proton has the longer period T. It has to travel around a bigger circle but at the same speed.

31. A B v v ICPP Two charged ions A and B traveling with a constant velocity venter a box in which there is a uniform magnetic field directed out of the page. The subsequent paths are as shown. What can you conclude? • (a) Both ions are negatively charged. • (b) Ion A has a larger mass than B. • (c) Ion A has a larger charge than B. • (d) None of the above. RHR says (a) is false. Same charge q, speed v, and same B for both masses. So: ion with larger mass/charge ratio (m/q) moves in circle of larger radius. But that’s all we know! Don’t know m or q separately.

32. Problem: 28.P.024. [566302] In the figure below, a charged particle moves into a region of uniform magnetic field , goes through half a circle, and then exits that region. The particle is either a proton or an electron (you must decide which). It spends 160 ns in the region. (a) What is the magnitude of B? (b) If the particle is sent back through the magnetic field (along the same initial path) but with 3.00 times its previous kinetic energy, how much time does it spend in the field during this trip?

36. L Magnetic Force on a Wire.

38. 28.8.2. A portion of a loop of wire passes between the poles of a magnet as shown. We are viewing the circuit from above. When the switch is closed and a current passes through the circuit, what is the movement, if any, of the wire between the poles of the magnet? a) The wire moves toward the north pole of the magnet. b) The wire moves toward the south pole of the magnet. c) The wire moves upward (toward us). d) The wire moves downward (away from us into board). e) The wire doesn’t move. i

39. L R R L Example Wire with current i. Magnetic field out of page. What is net force on wire? By symmetry, F2will only have a vertical component, Notice that the force is the same as that for a straight wire of length R, and this would be true no matter what the shape of the central segment!.

40. i

41. SP28-06 ICPP: Find Direction of B i

42. L B I Example 4: The Rail Gun rails • Conducting projectile of length 2cm, mass 10g carries constant current 100A between two rails. • Magnetic field B = 100T points outward. • Assuming the projectile starts from rest at t = 0, what is its speed after a time t = 1s? projectile • Force on projectile: F= iLB (from F = iL x B) • Acceleration: a = F/m = iLB/m (from F = ma) • v = at = iLBt/m (from v = v0 + at) • = (100A)(0.02m)(100T)(1s)/(0.01kg) = 2000m/s • = 4,473mph = MACH 8!

43. Highest Torque: θ = ±90° sinθ = ±1 θ = 0° –cosθ = –1 θ = 180° –cosθ = +1 B Lowest Torque: θ= 0° & 180° sinθ = 0

44. Torque on a Current Loop: Principle behind electric motors. Rectangular coil: A=ab, current = i Net force on current loop = 0 But: Net torque is NOT zero! For a coil with N turns, τ = N I A B sinθ, where A is the area of coil

45. Right hand rule: curl fingers in direction of current; thumb points along μ Define: magnetic dipole moment m Magnetic Dipole Moment We just showed: τ = NiABsinθ N = number of turns in coil A = area of coil. As in the case of electric dipoles, magnetic dipoles tend to align with the magnetic field.

46. +Q p=Qa -Q QE q QE Electric vs. Magnetic Dipoles

47. 1 and 3 are “downhill”. 2 and 4 are “uphill”. U1 = U4 > U2 = U3 τ is biggest when B is at right angles to μ

50. Right Hand Rule: Given Current i Find Magnetic Field B