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Physics 212 Lecture 16

Conductors moving in B field. Induced emf !!. Physics 212 Lecture 16. Motional EMF. The Big Idea. F. F. E. +. +. +. +. +. -. -. -. -. F B. E. F E. B. When a conductor moves through a region containg a magnetic field:

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Physics 212 Lecture 16

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  1. Conductors moving in B field Induced emf !! Physics 212 Lecture 16 Motional EMF

  2. The Big Idea F F E + + + + + - - - - FB E FE B When a conductor moves through a region containg a magnetic field: • Magnetic forces may be exerted on the charge carriers in the conductor X X X X X X X X X L v X X X X X X X X X • These forces produce a charge separation in the conductor • This charge distribution creates an electric field in the conductor • The equilibrium distribution is reached when the forces from the electric and magnetic fields cancel • The equilibrium electric field produces a potential difference (emf) in the conductor 05

  3. Rotate picture by 90o (top view) X XXXXXXXX a b + + - - F v B X v F X XXXXXXXX Fb = qvB Fa = 0 Two identical conducting bars (shown in end view) are moving through a vertical magnetic field. Bar (a) is moving vertically and bar (b) is moving horizontally. Checkpoint 1 B Which of the following is true? A. A motional emf exists in the bar for case (a), but not (b)B. A motional emf exists in the bar for case (b), but not (a)C. A motional emf exists in the bar for both cases (a) and (b)D. A motional emf exists in the bar for neither case (a) nor case (b) A B C D Bar a No force on charges No charge separation No E field No emf Bar b Opposite forces on charges Charge separation E = vB emf = EL = vBL :22

  4. A conducting bar (green) rests on two frictionless wires connected by a resistor as shown. Equivalent circuit V I R + - F X X X X X X X X X F B v0 X X X X X X X X X Fb = qv0B Checkpoint 2a Changing Area A B The entire apparatus is placed in a uniform magnetic field pointing into the screen, and the bar is given an initial velocity to the right. The motion of the green bar creates a current through the bar A. going upB. going down C D Rotate picture by 90o A B Bar Opposite forces on charges Charge separation E = v0B emf = EL = v0BL :22

  5. A conducting bar (green) rests on two frictionless wires connected by a resistor as shown. F I F points to left Checkpoint 2b Energy External agent must exert force F to the right to maintain constant v0 This energy is dissipated in the resistor! Changing Area A B The entire apparatus is placed in a uniform magnetic field pointing into the screen, and the bar is given an initial velocity to the right. The current through this bar results in a force on the bar A. downB. upC. rightD. left E. into the screen C D A Preflight 5 B C D E Counterclockwise Current :22

  6. A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? Checkpoint 5 B = 0 B = 5 T Out of Screen v Let’s step through this one 20

  7. - E t + t - - L E v E + + t - L E v + L v Only leading side has charge separation emf = BLv (cw current) Leading and trailing sides have charge separation emf = BLv – BLv = 0 (no current) Only trailing side has charge separation emf = BLv (ccw current) 20

  8. A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? Checkpoint 5 B = 0 B = 5 T Out of Screen v 20

  9. Checkpoint 3 - + B B     B B       - + v I Changing B field A conducting rectangular loop moves with velocity v toward an infinite straight wire carrying current as shown. What is the direction of the induced current in the loop? A. clockwiseB. counter-clockwiseC. there is no induced current in the loop 20

  10. Generator: Changing Orientation Perpendicular to front and back legs On which legs of the loop is charge separated? • Top and Bottom legs only • Front and Back legs only • All legs • None of the legs parallel to top and bottom legs 22

  11. Generator: Changing Orientation Largest for q = 0 (v perp to B) = v L w At what angle q is emf the largest? • (A) q = 0 • (B) q = 45o • (C) q = 90o • (D) emf is same at all angles 22

  12. Generator: Changing Orientation  + - I X A rectangular loop rotates in a region containing a constant magnetic field as shown. The side view of the loop is shown at a particular time during the rotation. At this time, what is the direction of the induced (positive) current in segment ab? A. from b to aB. from a to bC. there is no induced current in the loop at this time Checkpoint 4 v B v 20

  13. Putting it together Change Area of loop Change magnetic fieldthrough loop Change orientation of looprelative to B Faraday’s Law We will study this law in detail next time !

  14. Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? v I h x L • Conceptual Analysis: • Long straight current creates magnetic field in region of the loop. • Vertical sides develop emf due to motion through B field • Net emf produces current • Strategic Analysis: • Calculate B field due to wire. • Calculate motional emf for each segment • Use net emf and Ohm’s law to get current

  15. Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? v I h x L • What is the direction of the B field produced by the wire in the region of the loop? • Into the page • Out of the page • Left • Right • Up

  16. Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? B into page v I h x L • What is the emf induced on the left segment? • Top is positive • Top is negative • Zero

  17. Example Problem perpendicular to wire A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? B into page v I h x L • What is the emf induced on the top segment? • left is positive • left is negative • Zero

  18. Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? B into page v I h x L • What is the emf induced on the right segment? • top is positive • top is negative • Zero

  19. Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? B into page v I h x L Which expression represents the emf induced in the left wire (A) (B) (C)

  20. Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? B into page v I h x L Which expression represents the emf induced in the right wire (A) (B) (C)

  21. Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? B into page v I h x L Which expression represents the total emf in the loop? (A) (B) (C)

  22. Follow-Up + + I - - eLeft > eRight Clockwise current A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. B into page v I h x L What is the direction of the induced current? Clockwise (A) (B) Counterclockwise

  23. Follow-Up B into page I Total force from B Points to the left !! A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. B into page v I I h What is the direction of the force exerted by the magnetic field on the loop? x L UP (A) DOWN (B) LEFT (C) RIGHT (B) F = 0 (B)

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