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

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: You can see examples of old exam IIIs here:

Circuits i = dq/dt Junction rule

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

Resistors vs Capacitors Resistors Capacitors Key formula: V=iR Q=CV In series: same current same charge R eq =∑R j 1/C eq = ∑1/C j In parallel: same voltage same voltage 1/R eq = ∑1/R j C eq =∑C j

Resistors in 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?

Circuits: Checkpoints, Questions

Problem: 27.P.018. [406649] Figure shows five 5.00 resistors. (Hint: For each pair of points, imagine that a battery is connected across the pair.) Fig (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.

Problem: 27.P.046. [406629] In an RC series circuit, E = 17.0 V, R = 1.50 M, 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?

Magnetic Forces and Torques L v F

C C Top view Side view (28-13)

(28-14)

Ch 28: Checkpoints and Questions

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

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

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?

Highest Torque:  = ±90° sin  = ±1 Lowest Torque:  = 0° & 180° sin  = 0 B  = 180° –cos  = +1  = 0° –cos  = –1

Right Hand Rule: Given Current i Find Magnetic Field B

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

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). Right Hand Rule: Given Current i Find Magnetic Field 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.  =NiA Right Hand Rule & Biot-Savart: Given i Find B

Lenz’s Law

Induction and Inductance Faraday ’ s law: or Inductance: L=N  /i –For a solenoid: L=  0 n 2 Al=  0 N 2 A/l Inductor EMF: E L =  L di/dt RL circuits: i(t)=( E /R)(1–e –tR/L ) or i(t)=i 0 e –tR/L RL Time Constant:  = L/R Units: [s] Magnetic energy: U=Li 2 /2Units: [J] Magnetic energy density: u=B 2 /2  0 Units: [J/m 3 ] i

Changing B-Flux Induces EMF

Flux Up Flux DownRL 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.

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

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