Lecture 32: WED 01 APR Review Session : Midterm 3 Physics 2102 Jonathan Dowling

EXAM 03: 6PM THU 02 APR LOCKETT 5 EXAM 03 REVIEW: 6PM WED 01 APR NICHOLSON 130 The exam will cover: Ch.28 (second half) through Ch (displacement current, and Maxwell's equations). 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:

Highest Torque:  = ±90° sin  = ±1 Lowest Torque:  = 0° & 90° 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=?

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 charged, and the current is i=( E /R)(1  e –tR/L ). When the switch is opened, the inductors begins to discharge. The current in this case is then i= ( E /R) e –tR/L

E

LC Circuits

q max = EC q i i max =  EC T Frequency: f =  [Hertz] Angular Frequency:  =  f  [rad/s] Period: T = 1/f =  [sec]

r