Faraday s Law. Underpinning of Much Technology

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1 Module 21: Faraday s Law 1

2 Faraday s Law Fourth (Final) Maxwell s Equation Underpinning of Much Technology 2

3 Demonstration: Falling Magnet 3

4 Magnet Falling Through a Ring Link to movie Falling magnet slows as it approaches a copper ring which has been immersed in liquid nitrogen. 4

5 Demonstration: Jumping Rings 5

6 Jumping Ring An aluminum ring jumps into the air when the solenoid beneath it is energized 6

7 What is Going On? It looks as though the conducting loops have current in them (they behave like magnetic dipoles) even though they aren t hooked up 7

8 Demonstration: t Induction Link to movie 8

9 Electromagnetic Induction 9

10 Faraday s Law of Induction = dφ B dt A changing magnetic flux induces an EMF 10

11 What is EMF? G G = E d s Looks like potential. It s a driving force for current 11

12 Magnetic Flux Thru Wire Loop Analogous to Electric Flux (Gauss Law) (1) Uniform B Φ B = BA = BA cos θ = B G A G (2) Non-Uniform B G G Φ = B dd A = Φ B S 12

13 Faraday s Law of Induction G G d Φ = E d s = B dt A changing magnetic flux induces an EMF, a curling E field 13

14 Faraday s Law of Induction = dφ B dt A changing magnetic flux induces an EMF 14

15 Minus Sign? Lenz s Law Induced EMF is in direction that opposes the change in flux that caused it 15

16 Concept Question: Loop The magnetic field through a wire loop is pointed upwards and increasing with time. The induced current in the coil is 1. Clockwise as seen from the top 2. Counterclockwise 16

17 Concept Question: Loop The magnetic field through a wire loop is pointed upwards and decreasing with time. The induced current in the coil is 1. Clockwise as seen from the top 2. Counterclockwise 17

18 Ways to Induce EMF ε = d BAcosθ ( ) dt Quantities which can vary with time: Magnitude of B Area A enclosed by the loop Angle θ between B and loop normal 18

19 Ways to Induce EMF ε = d BAcosθ ( ) dt Quantities which can vary with time: Magnitude of B Area A enclosed by the loop Angle θ between B and loop normal 19

20 Magnet Falling Through h a Ring Link to movie Falling magnet slows as it approaches a copper ring which h has been immersed in liquid id nitrogen. 20

21 Concept Question: Loop in Uniform B out Field A rectangular wire loop is pulled thru a uniform B field penetrating its top half, as shown. The induced current and the force and torque on the loop are: 1. Current CW, Force Left, No Torque 2. Current CW, No Force, Torque Rotates CCW 3. Current CCW, Force Left, No Torque 4. Current CCW, No Force, Torque Rotates CCW 5. No current, force or torque 21 v

22 Concept Question: Faraday s Law: A coil moves up from underneath a magnet with its north pole pointing upward. The current ti in the coil and the force on the coil: Loop 1. Current clockwise; force up 2. Current counterclockwise; force up 3. Current clockwise; force down 4. Current counterclockwise; force down 22

23 Technology Many Applications of Faraday s Law 23

24 Electric Guitar 24

25 Metal Detector See Animation of how VLF metal detectors t work: Induction Stovetops t Ground Fault Interrupters t (GFI) 25

26 Experiment 5: Faraday s a Law of Induction 26

27 Example: Magnitude of B Magnet Falling Through h a Ring Falling magnet approaches a copper ring or Copper Ring approaches Magnet 27

28 Moving Towards Dipole Move ring down As ring approaches, what happens to flux? Flux up increases 28

29 Part 1: Current & Flux I > 0 BLACK RED Current? Flux? Φ = ( ) t () t = R I t ' dt ' 0 29

30 Concept Question Predictions: Flux & Current 30

31 Concept Q. : Flux Measurement (A) t (B) t (C) (D) t t Moving from above to below and back, you will measure a flux of: 1. A then A 5. B then B 2. C then C 6. D then D 3. A then C 7. B then D 4. C then A 8. D then B 31

32 Concept Q.: Current Measurement (A) t (B) t (C) t NOTE: CCW is positive! (D) Moving from above to below and back, you will measure a current of: 1. A then A 5. B then B 2. C then C 6. D then D 3. Ath then C 7. B then D 4. C then A 8. D then B t 32

33 Part 2: Force Direction Force when Move Down? Move Up? Test with aluminum sleeve 33

34 Concept Question: Flux Behavior (1) t (2) t (3) (4) t NOTE: Magnet Upside Down t Moving from below to above, you would measure a flux best represented by which plot above (taking upward flux as positive)? 34

35 Concept Q.: Current Behavior (1) t (2) t (3) (4) t NOTE: Magnet Upside Down t Moving from above to below, you would measure a current best represented by which plot above (taking counterclockwise current as positive)? 35

36 Concept Question Confirming Predictions? Flux & Current 36

37 Concept Question Question: Wrap-Up Faraday s Law 37

38 Concept Q.: Loop Below Magnet A conducting loop is below a magnet and moving downwards. d This induces a current as pictured. The I ds x B force on the coil is 0% 1. Up 0% 2. Down 0% 3. Zero 38

39 Ways to Induce EMF ε = d BAcosθ ( ) dt Quantities which can vary with time: Magnitude of B Area A enclosed by the loop Angle θ between B and loop normal 39

40 The last of the Maxwell s Equations (Kind of) 40

41 Maxwell s Equations Creating Electric Fields G G Q E d A = in w S G G v E d s = v C ε 0 dφ dt B (Gauss's Law) (Faraday'sLaw) Creating G G Magnetic Fields w B da = 0 (Magnetic Gauss's Law) S G G B d s = μ I (Ampere's Law) 0 enc v v C 42

42 Faraday s Law of Induction = dφ B dt Changing magnetic flux induces an EMF Lenz: Induction opposes change 43

43 Faraday s Law Problem Solving Session 43

44 Ways to Induce EMF ε = d BAcosθ ( ) dt Quantities which can vary with time: Magnitude of B e.g. Falling Magnet Area A enclosed by the loop Angle θ between B and loop normal 44

45 Problem: Changing g Area Conducting rod pulled along two conducting rails in a uniform magnetic field B at constant velocity v l 1. Direction of induced current? 2. Direction of resultant force? 3. Magnitude of EMF? 4. Magnitude of current? 5. Power externally supplied to move at constant v? 45

46 Ways to Induce EMF ε = d ( dt BAcosθ) Quantities which can vary with time: Magnitude of B Area A enclosed e.g. Moving Coil & Dipole e.g. Sliding bar Angle θ between B and loop normal 46

47 Changing g Angle r r r Φ = B A= BA Φ = B A= 0 B B r 47

48 Motors & Generators 48

49 Concept Question Question: Generator 49

50 Concept Question: Generator A square coil rotates in a magnetic field directed d to the right. At the time shown, the current in the square, when looking down from the top of the square loop, will be 1. Clockwise 2. Counterclockwise 3. Neither, the current is zero 4. Id don t know 50

51 Problem: Generator Square loop (side L) spins with angular frequency ω in a field of strength B. It is hooked to a load R. 1) Write an expression for current I(t) ( assuming the loop is vertical at time t = 0. 2) How much work from generator per revolution? 3) To make it twice as hard to turn, what do you do to R? 51

52 Concept Question Question: Wrap-Up Faraday s Law 52

53 Concept Question: Circuit A circuit in the form of a rectangular piece of wire is pulled away from a long wire carrying current I in the direction shown in the sketch. The induced current in the rectangular circuit is 1. Clockwise 2. Counterclockwise 3. Neither, the current is zero 53

54 MIT OpenCourseWare SC Physics II: Electricity and Magnetism Fall 2010 For information about citing these materials or our Terms of Use, visit:

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