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Chapter 20

Chapter 20. Induced Voltages and Inductance Induce emf and Magnetic flux Faraday’s law of induction Lenz’s law Motional emf Generators Self-Inductance RL circuits Energy stored in a magnetic field. Michael Faraday. 1791 – 1867 Great experimental scientist

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Chapter 20

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  1. Chapter 20 Induced Voltages and Inductance • Induce emf and Magnetic flux • Faraday’s law of induction • Lenz’s law • Motional emf • Generators • Self-Inductance • RL circuits • Energy stored in a magnetic field

  2. Michael Faraday • 1791 – 1867 • Great experimental scientist • Invented electric motor, generator and transformers • Discovered electromagnetic induction • Discovered laws of electrolysis

  3. Faraday’s Experiment – Set Up • What is induced emf? • How is it produced?

  4. Magnetic Flux • What is magnetic flux? • How do I calculate it? • What is the SI units? • Why the angle dependence? • Flux and B

  5. Electromagnetic Induction –An Experiment • What is electromagnetic induction? • What is induced current?

  6. Example • The quarter-circle loop shown in figure has an area of 15 cm2. A magnetic field, with B=0.16T exists in the +x direction. Find the flux through the loop in each orientation shown.

  7. Example B a) n plane normal 20º B 20º 70º B normal 20º plane b) c)

  8. Faraday’s Law and Electromagnetic Induction • What is Faraday’s law? • What is the formula? • What is the SI units? • How to change the flux? • What is Lenz’s law?

  9. Example • As shown a metal rod makes contact with a partial circuit. The circuit is perpendicular to the magnetic field. Find the induced emf if the rod moves with velocity of v=2m/s. Assume L=0.5m

  10. Lenz’ Law – Example

  11. Example • See figures

  12. Example • See figures

  13. Applications of Faraday’s Law – Ground Fault Interrupters

  14. Applications of Faraday’s Law – Apnea Monitor

  15. Application of Faraday’s Law – Motional emf • What is motional emf? • How is it produced? • The force on charges • The potential difference

  16. Motional emf in a Circuit • How do I calculate motional emf? • Motional emf and Battery • What is the resulting current?

  17. Example • As shown, a metal rod makes contact with a partial circuit and completes the circuit. The circuit area is perpendicular to the magnetic field with B=0.15T. If the resistance of the total circuit is 3 ohm, how large a force is needed to move the rod as indicated with a speed of 2 m/s.

  18. Lenz’ Law Revisited – Moving Bar Example • How do I calculate the direction of induced current? • One possibility

  19. Lenz’ Law, Bar Example • Another possibility • Conservation of energy

  20. Lenz’ Law – Moving Magnet Example • When applying Lenz’ Law, there are two magnetic fields to consider • The external changing magnetic field that induces the current in the loop • The magnetic field produced by the current in the loop

  21. AC Generators • What is a generator? • How does it work? • Emf of the loop

  22. DC Generators

  23. Motors • What is a Motor? • Motors an Back

  24. Joseph Henry • 1797 – 1878 • First director of the Smithsonian • First president of the Academy of Natural Science • First to produce an electric current with a magnetic field • Improved the design of the electro-magnetic and constructed a motor • Discovered self-inductance

  25. Self-inductance • What is self-inductance? • How do I calculate it? • What are it SI units? • What is inductance? • How do I calculate it?

  26. Example • A coiled telephone cord has 70 turns, a cross-sectional diameter of 1.3 cm, and an unstrectched length of 60 cm. Determine an approximate value for the self-inductance of the unstretched cord.

  27. Inductor and RL Circuit • What is an inductor? • How does it work in a circuit? • RL circuit • What is the time constant? • How do I find the current in the circuit? • What is the energy stored in the inductor?

  28. Example • For the circuit shown, determine • Time constant • Current after one time constant • Change in potential at t=0 and t=first time constant • The rate of change of current after first time constant

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