Lecture 31: MON 10 NOV Review Session : Midterm 3

1. Physics 2113 Jonathan Dowling Lecture 31: MON 10 NOV Review Session : Midterm 3

2. EXAM 03: 6PM TUE 11 NOV in Cox Auditorium The exam will cover: Ch.27 through Ch.30 The exam will be based on: HW08 – HW11. The formula sheet for the exam can be found here: http://www.phys.lsu.edu/classes/fall2014/phys2113/downloads/FormulaSheetTest3.pdf You can see examples of old exam IIIs here: http://www.phys.lsu.edu/faculty/gonzalez/Teaching/Phys2102/Phys2102OldTests/

3. Circuits i = dq/dt Junction rule

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

5. 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

6. 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?

8. Circuits: Checkpoints, Questions

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.

11. 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?

13. v F L Magnetic Forces and Torques

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

15. (28-14)

16. Ch 28: Checkpoints and Questions

17. 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).

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

20. 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?

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

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

28. Force on each wire due to currents in the other wires? Magnetic field? Checkpoints/Questions Ampere’s Law: Find Magnitude of ∫B∙ds?

29. Right Hand Rule: Given Current i Find Magnetic Field B  The current in wires A,B,D is out of the page, current in C is into the page. Each wire produces a circular field line going through P, and the direction of the magnetic field for each is given by the right hand rule. So, the circles centers in A,B,D are counterclockwise, the circle centered at C is clockwise. When you draw the arrows at the point P, the fields from B and C are pointing in the same direction (up and left).

30. Right Hand Rule & Biot-Savart: Given i Find B  • A length of wire is formed into a closed circuit with radii a and b, as shown in the Figure, and carries a current i. • (a) What are the magnitude and direction of B at point P? • (b) Find the magnetic dipole moment of the circuit. μ=NiA

33. Lenz’s Law

34. i Induction and Inductance • Faraday’s law: or • Inductance: L=NΦ/i • For a solenoid: L=μ0n2Al=μ0N2A/l • Inductor EMF: EL= -L di/dt • RL circuits: i(t)=(E/R)(1–e–tR/L) or i(t)=i0e–tR/L • RL Time Constant: τ = L/R Units: [s] • Magnetic energy: U=Li2/2 Units: [J] • Magnetic energy density: u=B2/2m0 Units: [J/m3]

35. Changing B-Flux Induces EMF

36. Flux Up RL Circuits Flux Down

37. RL Circuits E/2 t=? Make or Break? At t=0 all L’s make breaks so throw out all loops with a break and solve circuit. At t=∞ all L’s make solid wires so replace L’s with wire and solve circuit.

38. Largest L? R,L or 2R,L or R, 2L or 2R,2L? Magnitude/direction of induced current?Magnitude/direction of magnetic field inducing current? Checkpoints/Questions Magnitude of induced emf/current? Given |∫E∙ds| , direction of magnetic field? Given B, dB/dt, magnitude of electric field? Current inducing EL? Current through the battery? Time for current to rise 50% of max value? Largest current?

39. When the switch is closed, the inductor begins to get fluxed up, and the current is i=(E/R)(1-e–t/τ). When the switch is opened, the inductors begins to deflux. The current in this case is then i= (E/R) e–t/τ