iclicker Quiz (1) I have completed at least 50% of the reading and studyguide assignments associated with the lecture, as indicated on the course schedule. a) True b) False
Note on Monday is fee late day for exam 4.
iclicker Quiz: 31:1&4 I have completed at least 50% of the reading and studyguide assignments associated with the lecture, as indicated on the course schedule. A. True B. False Today: use your Chapter Summaries. Review; 3 ; Hint: The exam runs Wednesday 2 Nov. 4 pm until Saturday 5 November plus Monday Nov. 7 all day is a fee late day. Faraday s Law of induction, Electric Field is nonconservative.
Induced Fields Magnetic fields may vary in time. Experiments conducted in 1831 showed that an emf can be induced in a circuit by a changing magnetic field. Experiments were done by Michael Faraday and Joseph Henry. The results of these experiments led to Faraday s Law of Induction. An induced current is produced by a changing magnetic field. There is an induced emf associated with the induced current. A current can be produced without a battery present in the circuit. Faraday s law of induction describes the induced emf. Introduction
Michael Faraday: 1791 1867 British physicist & chemist Great experimental scientist Contributions to early electricity include: Invention of motor, generator, & transformer Electromagnetic induction Laws of electrolysis Introduction
EMF Produced by a Changing Magnetic Field, 1 A loop of wire is connected to a sensitive ammeter. When a magnet is moved toward the loop, the ammeter deflects. The direction was arbitrarily chosen to be negative. Section 31.1
EMF Produced by a Changing Magnetic Field, 2 When the magnet is held stationary, there is no deflection of the ammeter. Therefore, there is no induced current. Even though the magnet is in the loop Section 31.1
EMF Produced by a Changing Magnetic Field, 3 The magnet is moved away from the loop. The ammeter deflects in the opposite direction. Section 31.1
Induced Current Experiment, Summary Section 31.1
EMF Produced by a Changing Magnetic Field, Summary The ammeter deflects when the magnet is moving toward or away from the loop. The ammeter also deflects when the loop is moved toward or away from the magnet. Therefore, the loop detects that the magnet is moving relative to it. We relate this detection to a change in the magnetic field. This is the induced current that is produced by an induced emf. Section 31.1
Faraday s Experiment Set Up A primary coil is connected to a switch and a battery. The wire is wrapped around an iron ring. A secondary coil is also wrapped around the iron ring. There is no battery present in the secondary coil. The secondary coil is not directly connected to the primary coil. Section 31.1
Faraday s Experiment Close the switch & observe the current readings given by the ammeter. Section 31.1
Faraday s Experiment Findings At the instant the switch is closed, the ammeter changes from zero in one direction and then returns to zero. When the switch is opened, the ammeter changes in the opposite direction and then returns to zero. The ammeter reads zero when there is a steady current or when there is no current in the primary circuit. Section 31.1
Faraday s Experiment Conclusions An electric current can be induced in a loop by a changing magnetic field. This would be the current in the secondary circuit of this experimental set-up. The induced current exists only while the magnetic field through the loop is changing. This is generally expressed as: an induced emf is produced in the loop by the changing magnetic field. The actual existence of the magnetic flux is not sufficient to produce the induced emf, the flux must be changing. Section 31.1
Faraday s Law: ε = dφ dt B ds ε Φ B E ds B da B(t) Michael Faraday E The electric circulation (emf) around a closed loop is proportional to the negative time derivative of the magnetic flux passing through the loop, where the positive directions of circulation and flux are related by the RHR.
I Q B E 0 0 0 µ ε = = Φ = Φ C Fundamental principles of E&M to date: = = = = Φ = Φ s B s E A B A E d d d d B E C ε 0 dt d B Φ = ε non-conservative! 0 = s E d ε
Faraday s Law of Induction Statements The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit. Mathematically, ε = dφ dt Remember F B is the magnetic flux through the circuit and is found by Φ B = B d A If the circuit consists of N loops, all of the same area, and if Φ B is the flux through one loop, an emf is induced in every loop and Faraday s law becomes dφ ε = N dt B B
Faraday (1821) www.wikipedia.org
www.wikipedia.org
Three obvious ways to change flux through a loop Φ B = B da = BAcos(θ ) 1)Change the field strength. 2)Change the shape of loop. 3)Reorient loop in the field. ε = (1) (2) (3) d Φ db da d B = Acos( θ ) B cos( θ ) + BAsin( θ ) θ dt dt dt dt
ε E B t) = µ ni sol ( t) = B cos( ω ) ( 0 max t Φ = B( t) da = B( t) A = Bmax Acos( ωt) B dφ B ε ( t) E( t) ds = = Bmax Aω sin( ωt) dt Circulating E-field: ε ( t) E( t) ds = 2π re( t) E= ε 2π r
Induced emf and Electric Fields An electric field is created in the conductor as a result of the changing magnetic flux. Even in the absence of a conducting loop, a changing magnetic field will generate an electric field in empty space. This induced electric field is nonconservative. Unlike the electric field produced by stationary charges The emf for any closed path can be expressed as the line integral of over the path. Faraday s law can be written in a general form: Section 31.4
Induced emf and Electric Fields, cont. The induced electric field is a nonconservative field that is generated by a E ds changing magnetic field. The field cannot be an electrostatic field because if the field were electrostatic, and hence conservative, the line integral of over a closed loop would be zero and it isn t. Section 31.4
Air-filled solenoid, and a single pickup loop ε bulb = BA ω = µ ni 0 sol sol A sol ω ε ε Magnetic solenoid core, multiple pickup loops bulb = ω = ( 1+ χ) µ ni NbulbB Asol Nbulb 0 sol A sol ω I Bulb current and power ε bulb ε = Pbulb = R R bulb bulb 2 bulb bulb
0.185
24-1 A uniform magnetic field oscillates in time as B = B 0 cos(ωt), where B 0 = [01] T, within a circular region of radius a = 2.50 cm. A loop of wire containing a single 1.20 V light bulb surrounds the field-containing region. Determine the oscillation frequency needed to light the bulb (i.e. to match the emf amplitude with the light bulb voltage specification). Note: do NOT use the more appropriate rms quantities if you know about them. [400; 990 Hz]
Applications of Faraday s Law GFCI A GFCI (ground fault circuit interrupter) protects users of electrical appliances against electric shock. When the currents in the wires are in opposite directions, the flux is zero. When the return current in wire 2 changes, the flux is no longer zero. The resulting induced emf can be used to trigger a circuit breaker. Section 31.1
2.42 Brainstorming quiz. What eqns from Chap Summ. or text should we use? Quiz: All of the equ
1.82
AC Generators A = ω t B Φ = B da B = BAcos( ωt) dφ B ε = N = NBAω sin( ωt) dt ε ε min max = 0 at θ = = NBAω at 0 or 180 θ = 90 or 270 N = 265 B = 1T A = 10 cm 2 = 10 4 m 2 ω = 2π (60 Hz) = 377 s 1 ε = NBAω = (265)(1)(0.0001)(377) = 10 V
AC Generators A = ω t B ε max NBAω ε max = NBAω I max = = R R Magnetic moment : µ = NIA Torque : τ = µ Bsin( ωt) 2 Pmax = ( τ maxω or ε max / R) = N 2 2 2 2 B A ω R N = 265 B = 1T A = 10 cm 2 = 10 4 m 2 ω = 2π (60 Hz) = 377 s 1 R = 100Ω ε = NBAω = 10 V P = 2 ε R = 2 10 100 = 1A P τ = = ω 100 377 = 0.265 N m Power is the mechanical work/time converted to heat in the resistive load.
AC Generator
DC Generator
DC Motor A = ω t B I = V R τ = µ B and µ = NIA = NBA I sin( ωt) P max = τ max ω = NBA Iω ω = Pmax / I NBA = V NBA
Note on Monday is fee late day for exam 4.
iclicker Quiz: 31:2&3 I have completed at least 50% of the reading and studyguide assignments associated with the lecture, as indicated on the course schedule. A. True B. False Today: generators as a review. Hint: Faraday s Law of induction, Lenz Law is common sense when you think about it.
Lenz s Law µ µ Change in Φ B ε I µ Φ B opposing initial change.
Lenz s Law
The House that Jack Built This is the farmer sowing the corn, That kept the the cock that crowed in the morn, That waked the priest all shaven and shorn, That married the man all tattered and torn, That kissed the maiden all forlorn, That milked the cow with the crumpled horn, That tossed the dog, That worried the cat, That killed the rat, That ate the malt That lay in the house that Jack built. The Flux that Jack Made (Lenz s Law) This is the change in magnetic flux, That generated the electromotive force, That drove the current around the loop, That generated the magnetic moment, That produced more magnetic flux, That opposed the original change that Jack made.
Lenz s Law Quiz I µ µ I Which way will the needle deflect when the switch is closed? (A) left (B) right (C) zero deflection
Lenz s Law Quiz Let s do #4. Which way will current in the loop flow at each point? (A) clockwise (B) counterclockwise (C) zero current
Note on Lab 9 is due Friday evening.
iclicker Quiz: 31:5 & 6 I have completed at least 50% of the reading and studyguide assignments associated with the lecture, as indicated on the course schedule. A. True B. False Today: Lenz law & lab 9 as a review; motional emf. Motors, eddy currents. Hint: Formulas for chapter summaries.
Imagine throwing a magnetic object through the loop shown, and observing a time dependent current. Define clockwise to be the positive direction. Characterize each graph as one of the following. a) Dipole with north pole head first b) Dipole with south pole entering first c) Positive monopole d) Negative monopole Let s do #1. ε ε (1) (2) x x (3) (4) ε ε x x
Due Friday night
Motional EMF + When the bar moves, the carriers in the bar experience a magnetic Lorentz force. Which side of the bar (top, bottom) will have a positive electric potential? A. Top B. Bottom. C. Neither This result is independent of the sign of the carrier charge?
Motional EMF + F B = F ε = E B v F B = qvb F E = qe = ε q B = 1T l = 0.1m v = 100 m/s ε = B v = 10 V
Example: helicopter blade d ε = d( B v) = B( dr) v ω t = B( dr) rω = ωb rdr
Lenz s Law and Motional EMF I I F B v v F B I I There must needs be opposition in all things. (2 nd Nephi 2:11)
ε = B v = IR I = B v R 2 B v F B = I B = R 2 F B increases with v until it balances F app FappR v = when the bar achieves its terminal velocity. 2 B 2 Power = ( Fv or I 2 R) = B 2 2 v R 2
Falling loop with mass m, horizontal width l and resistance R. I F B v F g ε = B v = IR B v I = R F B = I B = F g B = mg 2 2 R v F B = F g terminal velocity v = mgr B 2 2
Which shape falls fastest through the field? A. Solid B. Ring C. same Which shape falls fastest through the field? A. Solid B. Slotted C. Same
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