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Chapter 29

Chapter 29. Electromagnetic Induction. Goals for Chapter 29. To examine experimental evidence that a changing magnetic field induces an emf To learn how Faraday’s law relates the induced emf to the change in flux To determine the direction of an induced emf. Goals for Chapter 29.

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Chapter 29

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  1. Chapter 29 Electromagnetic Induction

  2. Goals for Chapter 29 • To examine experimental evidence that a changing magnetic field induces an emf • To learn how Faraday’s law relates the induced emf to the change in flux • To determine the direction of an induced emf

  3. Goals for Chapter 29 • To calculate the emf induced by a moving conductor • To learn how a changing magnetic flux generates an electric field • To study Maxwell’s Equations – the four fundamental equations that describe electricity and magnetism

  4. Introduction • How is a credit card reader related to magnetism? • Energy conversion makes use of electromagnetic induction. • Faraday’s law and Lenz’s law tell us about induced currents.

  5. Induced current • A changing magnetic flux causes an induced current. No change => NO induced current!

  6. Induced current • A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current.

  7. Induced current • A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current.

  8. Induced current • A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current.

  9. Magnetic flux through an area element

  10. Faraday’s law • Flux depends on orientation of surface with respect to B field.

  11. Faraday’s law • Flux depends on orientation of surface with respect to B field.

  12. Faraday’s law • Flux depends on orientation of surface with respect to B field.

  13. Faraday’s law • Faraday’s law: Induced emf in a closed loop equals negativeof time rate of change of magnetic flux through the loop  = –dB/dt In this case, if the flux changed from maximum to minimum in some time t, and loop was conducting, an EMF would be generated!

  14. Faraday’s law • Faraday’s law: Induced emf in a closed loop equals negativeof time rate of change of magnetic flux through the loop  = –dB/dt [B ]= Tesla-m2 [d B/ dt] = Tesla-m2/sec and from F = qv x BTeslas = Newtons-sec/Coulomb-meters [N/C][sec/meters] [d B/ dt] = [N/C][sec/meter][m2/sec] = Nm/C = Joule/C = VOLT!

  15. Emf and the current induced in a loop • Example 29.1: What is induced EMF & Current?

  16. Emf and the current induced in a loop • Example 29.1: What is induced EMF & Current? df/dt = d(BA)/dt = (dB/dt) A = 0.020 T/s x 0.012 m2 = 0.24 mV I = E/R = 0.24 mV/5.0W = 0.048 mA

  17. Direction of the induced emf • Direction of induced current from EMF creates B field to KEEP original flux constant!

  18. Direction of the induced emf • Direction of induced current from EMF creates B field to KEEP original flux constant! Induced current generates B field flux opposing change

  19. Direction of the induced emf • Direction of induced current from EMF creates B field to KEEP original flux constant!

  20. Direction of the induced emf • Direction of induced current from EMF creates B field to KEEP original flux constant! Induced current generates B field flux opposing change

  21. Direction of the induced emf • Direction of induced current from EMF creates B field to KEEP original flux constant!

  22. Direction of the induced emf • Direction of induced current from EMF creates B field to KEEP original flux constant! Induced current generates B field flux opposing change

  23. Direction of the induced emf • Direction of induced current from EMF creates B field to KEEP original flux constant!

  24. Direction of the induced emf • Direction of induced current from EMF creates B field to KEEP original flux constant! Induced current generates B field flux opposing change

  25. Lenz’s law Lenz’s law: The direction of any magnetic induction effect is such as to oppose the cause of the effect.

  26. Magnitude and direction of an induced emf • Example 29.2 – 500 loop circular coil with radius 4.00 cm between poles of electromagnet. B field decreases at 0.200 T/second. What are magnitude and direction of induced EMF?

  27. Magnitude and direction of an induced emf • Example 29.2 – 500 loop circular coil with radius 4.00 cm between poles of electromagnet. B field decreases at 0.200 T/second. What are magnitude and direction of induced EMF? Careful with flux ANGLE!f between A and B!  = –N dB/dt = [NdB/dt] x [A cos f] Direction? Since B decreases, EMF resists change…

  28. A simple alternator – Example 29.3 • An alternator creates alternatingpositive and negative currents (AC) as a loop is rotated by an external torque while in a fixed magnetic field (or vice-versa!) Note – w comes from an external rotating force! • Water turning a turbine (hydroelectric) • Gasoline Motor turning a shaft (AC generator)

  29. A simple alternator – Example 29.3 • An alternator creates alternatingpositive and negative currents (AC) as a loop rotates in a fixed magnetic field (or vice-versa!) Note – NO commutator to reverse current direction in the loop – so you will get ALTERNATING current

  30. A simple alternator – Example 29.3 • An alternator creates alternatingpositive and negative currents (AC) as a loop rotates in a fixed magnetic field (or vice-versa!) For simple alternator rotating at angular rate of w, what is the induced EMF?

  31. A simple alternator • Example 29.3: For simple alternator rotating at angular rate of w, what is induced EMF? • B is constant; A is constant • Flux B is NOT constant! • B = BAcos f • Angle f varies in time: f = wt • EMF = - d [B ]/dt = -d/dt [BAcos(wt)] • So EMF = wBAsin(wt)

  32. A simple alternator • EMF = wBAsin(wt)

  33. DC generator and back emf in a motor • Example 29.4: A DC generator creates ONLY one-directional (positive) current flow with EMF always the same “sign.” Slip rings DC generator AC alternator

  34. DC generator and back emf in a motor • Example 29.4: A DC generator creates ONLY one-directional (positive) current flow with EMF always the same “sign.” Commutator AC alternator DC generator

  35. DC generator and back emf in a motor • Commutator results in ONLY unidirectional (“direct”) current flow: EMF(DC gen) = | wBAsin(wt) |

  36. DC generator and back emf in a motor • Example 29.4: A DC generator creates ONLY one-directional (positive) current flow with EMF always the same “sign.” “Back EMF” Generated from changing flux through the loop DC generator

  37. DC generator and back emf in a motor • Average EMF generated = AVG( | wBAsin(wt) | )over Period T where T = 1/f = 2p/w

  38. DC generator and back emf in a motor

  39. DC generator and back emf in a motor • Example 29.4: 500 turn coil, with sides 10 cm long, rotating in B field of 0.200 T generates 112 V. What is w?

  40. Lenz’s law and the direction of induced current

  41. Lenz’s law and the direction of induced current

  42. Slidewire generator – Example 29.5 • What is magnitude and direction of induced emf? Area A vector chosen to be into page

  43. Slidewire generator – Example 29.5 • B is constant; A is INCREASING => flux increases!

  44. Slidewire generator – Example 29.5 • Area A = Lx so dA/dt = L dx/dt = Lv Width x

  45. Slidewire generator • EMF = - d [B ]/dt = -BdA/dt = -BLv Induced current creates B OUT of page

  46. Work and power in the slidewire generator • Let resistance of wires be “R” • What is rate of energy dissipation in circuit and rate of work done to move the bar?

  47. Work and power in the slidewire generator • EMF = -BLv • I = EMF/R = -BLv/R • Power = I2R = B2L2v2/R

  48. Work and power in the slidewire generator • Work done = Force x Distance • Power applied = Work/Time = Force x velocity • Power = Fv = iLBv and I = EMF/R • Power = (BLv/R)LBv = B2L2v2/R

  49. Motional electromotive force • The motional electromotive force across the ends of a rod moving perpendicular to a magnetic field is = vBL.

  50. Motional electromotive force • The motional electromotive force across the ends of a rod moving perpendicular to a magnetic field is = vBL. • Across entire (stationary) conductor, E field will push current!

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