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Faraday’s Law

Physics 102: Lecture 10. Faraday’s Law. Changing Magnetic Fields create Electric Fields. Today’s lecture will cover Textbook Sections 20.1, 3-4. Faraday’s Law. Key to EVERYTHING in E+M Generating electricity Microphones, Speakers and Tape Decks Amplifiers

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Faraday’s Law

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  1. Physics 102: Lecture 10 Faraday’s Law Changing Magnetic Fields create Electric Fields • Today’s lecture will coverTextbook Sections 20.1, 3-4 Physics 102: Lecture 10, Slide 1

  2. Faraday’s Law • Key to EVERYTHING in E+M • Generating electricity • Microphones, Speakers and Tape Decks • Amplifiers • Computer disks and card readers • Ground Fault Interrupters • Changing B creates new E Physics 102: Lecture 10, Slide 2

  3. Motional EMF circuit Moving bar acts like battery E = vBL B x x xx x x xx x x xx x x xx x • Direction of Current + - • Magnitude of current x x xx x x xx x x xx x x xx x V x x xx x x xx x x xx x x xx x x x xx x x xx x x xx x x xx x x x xx x x xx x x xx x x xx x • Direction of force (F=ILB sin(q)) on bar due to magnetic field Physics 102: Lecture 10, Slide 3

  4. Motional EMF circuit Moving bar acts like battery E = vBL B • Direction of Current? • Magnitude of current V I = E /R = vBL/R • Direction of force (F=ILB sin(q)) on bar due to magnetic field? Physics 102: Lecture 10, Slide 4

  5. Motional EMF circuit Moving bar acts like battery E = vBL B • Direction of Current - + • Magnitude of current V I = E /R = vBL/R Clockwise (+ charges go down thru bar, up thru bulb) • Direction of force (F=ILB sin(q)) on bar due to magnetic field What changes if B points into page? To left, slows down Physics 102: Lecture 10, Slide 5

  6. v L Motional EMF, Preflight 10.1 B F = q v B sin(q) Which of the following statements is true? • positive charge accumulates at the top of the bar, negative at the bottom • since there is not a complete circuit, no charge accumulates at the bar's ends • negative charge accumulates at the top of the bar, positive at the bottom Physics 102: Lecture 10, Slide 6

  7. Velocity v L Motional EMF, Preflight 10.1 B Moving + charge feels force downwards: v F = q v B sin(q) + B Moving + Charge still feels force downwards: Potential Difference  F d/q EMF = q v B sin(q) L/q = Physics 102: Lecture 10, Slide 7

  8. Velocity Velocity - v L - + + Motional EMF, Preflight 10.1 B Moving + charge feels forcedownwards: v F = q v B sin(q) + B Moving + charge still feels forcedownwards: |ΔV|  |ΔU| =Fd EMF = q v B sin(q) L/q = v B L q q Physics 102: Lecture 10, Slide 8

  9. Preflight 10.2 • Which bar has the larger motional emf? v a b v E = v B L sin(q) q is angle between v and B Case a: Case b: Physics 102: Lecture 10, Slide 9

  10. Preflight 10.2 • Which bar has the larger motional emf? v a b v E = v B L sin(q) q is angle between v and B Case a: Case b: v perpendicular to B Physics 102: Lecture 10, Slide 10

  11. Preflight 10.4, 10.5 Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. Increase Stay the Same Decrease To keep the bar moving at the same speed, the force supplied by the hand will have to: To keep the bar moving to the right, the hand will have to supply a force in the opposite direction: True False Physics 102: Lecture 10, Slide 11

  12. Preflight 10.4 Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. • Increase • Stay the Same • Decrease To keep the bar moving at the same speed, the force supplied by the hand will have to: F = ILB sin(q) B and v still perpendicular (q=90), so F=ILB just like before! Physics 102: Lecture 10, Slide 12

  13. Preflight 10.5 Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. • True • False To keep the bar moving to the right, the hand will have to supply a force in the opposite direction. Current flows in the opposite direction, so force from the B field remains the same! Physics 102: Lecture 10, Slide 13

  14. A B f normal A Note: The flux can be negative (if field lines go thru loop in opposite direction) Magnetic Flux • Count number of field lines through loop. B Uniform magnetic field, B, passes through a plane surface of area A. Magnetic flux F=BA Magnetic flux FBA cos(f) f is angle between normal and B Physics 102: Lecture 10, Slide 14

  15. Preflight 10.7 B n Compare the flux through loops a and b. 1) Fa>Fb 2) Fa< Fb n b a FA = FB = Physics 102: Lecture 10, Slide 15

  16. Preflight 10.7 B n Compare the flux through loops a and b. 1) Fa>Fb 2) Fa< Fb n b a FA = B A cos(0) = BA FB = B A cos(90) = 0 Physics 102: Lecture 10, Slide 16

  17. Faraday’s Law (EMF Magnitude) Emf = Change in magnetic Flux/Time SinceF= B A cos(f), 3 things can change F 1. 2. 3. Physics 102: Lecture 10, Slide 17

  18. Faraday’s Law (EMF Magnitude) Emf = Change in magnetic Flux/Time SinceF= B A cos(f), 3 things can change F • Area of loop • Magnetic field B • Angle f between A and B Physics 102: Lecture 10, Slide 18

  19. Lenz’s Law (EMF Direction) Emf opposes change in flux • If flux increases: • New EMF makes new field _________ original field • If flux decreases: • New EMF makes new field _________ original field Physics 102: Lecture 10, Slide 19

  20. Lenz’s Law (EMF Direction) Emf opposes change in flux • If flux increases: • New EMF makes new field opposite to the original field (to oppose the increase) • If flux decreases: • New EMF makes new field in the same direction as the original field (to oppose the decrease) Physics 102: Lecture 10, Slide 20

  21. B B n n a a Preflight 10.9 The magnetic field strength through the loop is cut in half (decreasing the flux). If you wanted to create a second magnetic field to oppose the change in flux, what would be its direction? Left Right Physics 102: Lecture 10, Slide 21

  22. B B n n a a Preflight 10.9 The magnetic field strength through the loop is cut in half (decreasing the flux). If you wanted to create a second magnetic field to oppose the change in flux, what would be its direction? Left Right The original flux is to the right and decreasing. To oppose the change and keep the total field strength the same, add another field in the same direction. Physics 102: Lecture 10, Slide 22

  23. ACT: Change Area 3 W 2 1 v L v v Which loop has the greatest induced EMF at the instant shown above? Loop 1 Loop 2 Loop 3 Physics 102: Lecture 10, Slide 23

  24. ACT: Change Area 3 W 2 1 v L v v Which loop has the greatest induced EMF at the instant shown above? 1 moves right - gets 4 more field lines. 2 moves down - gets 0 more field lines. 3 moves down - only gets 2 more lines. 1 is gaining flux fastest! E3 = vBW E 1 = vBL E2 = 0 Physics 102: Lecture 10, Slide 24

  25. vt W V Change Area II W V L I t=0 F0=BLW t Ft=BL(W+vt) F = B A cos(f) ?? EMF Magnitude: = = EMF Direction: B is out of page and F is increasing so EMF creates B field (inside loop) going ________. Physics 102: Lecture 10, Slide 25

  26. vt W V Change Area II W V L I t=0 F0=BLW t Ft=BL(W+vt) F = B A cos(f) EMF Magnitude: EMF Direction: B is out of page and F is increasing so EMF creates B field (inside loop) going into page. Physics 102: Lecture 10, Slide 26

  27. ACT: Change B N As current is increasing in the solenoid, what direction will current be induced in ring? • Same as solenoid • Opposite of solenoid • No current S Physics 102: Lecture 10, Slide 27

  28. ACT: Change B SN As current is increasing in the solenoid, what direction will current be induced in ring? • Same as solenoid • Opposite of solenoid • No current •  Solenoid current (counter-clockwise) •  B-field (upwards) =>  Flux thru loop • EMF will create opposite B-field (downwards) • Induced loop current must be clockwise Physics 102: Lecture 10, Slide 28

  29. N S ACT: Change B II Which way is the magnet moving if it is inducing a current in the loop as shown? • Up • Down S N If I reduce the resistance in the wire, the magnet will fall Faster slower at the same speed Physics 102: Lecture 10, Slide 29

  30. N S ACT: Change B II Which way is the magnet moving if it is inducing a current in the loop as shown? • Up • Down S N If I reduce the resistance in the wire, the magnet will fall Faster slower at the same speed larger induced current, stronger magnetic field Physics 102: Lecture 10, Slide 30

  31. B f n A Change f Example A flat coil of wire has A=0.2 m2 and R=10W. At time t=0, it is oriented so the normal makes an angle f0=0 w.r.t. a constant B field of 0.12 T. The loop is rotated to an angle of =30o in 0.5 seconds. Calculate the induced EMF. What direction is the current induced? Physics 102: Lecture 10, Slide 31

  32. B f n A Change f Example A flat coil of wire has A=0.2 m2 and R=10W. At time t=0, it is oriented so the normal makes an angle f0=0 w.r.t. a constant B field of 0.12 T. The loop is rotated to an angle of =30o in 0.5 seconds. Calculate the induced EMF. Fi = B A cos(0) Ff = B A cos(30) e = 6.43x10-3 Volts What direction is the current induced? F upwards and decreasing. New field will be in same direction (opposes change). Current must be counter clockwise. Physics 102: Lecture 10, Slide 32

  33. Magnetic Flux Examples Example A conducting loop is inside a solenoid (B=monI). What happens to the flux through the loop when you… Increase area of solenoid? Increase area of loop? Increase current in solenoid? FBA cos(f) Rotate loop slightly? Physics 102: Lecture 10, Slide 33

  34. Magnetic Flux Examples Example A conducting loop is inside a solenoid (B=monI). What happens to the flux through the loop when you… Increase area of solenoid? No change Increase area of loop? Increases Increase current in solenoid? Increases FBA cos(f) Rotate loop slightly? Decreases Physics 102: Lecture 10, Slide 34

  35. Magnetic Flux II Example A solenoid (B=monI) is inside a conducting loop. What happens to the flux through the loop when you… Increase area of solenoid Increases Increase area of loop No change Increase current in solenoid Increases FBA cos(f) Physics 102: Lecture 10, Slide 35

  36. See you later! • Read Sections 20.2, 6 Physics 102: Lecture 10, Slide 36

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