Chapter 27 Electromagnetic Induction and Faraday’s Law

1. Chapter 27 Electromagnetic Induction and Faraday’s Law

2. Induced EMF (1) Electric current magnetic field Faraday’s experiments (1820-1821) Changing magnetic field can produce a current 2

3. Induced EMF (2) Phenomenon of electromagnetic induction An induced EMF (electromotive force in P566) is produced by a changing magnetic field. 3

4. Faraday’s law of induction The EMF induced in a circuit is equal to the changing rate of magnetic flux through the circuit. Faraday’s law of induction 1) EMF is produced even if no current can flow (as when the circuit is not complete) 2) N loops coil: 3) Induction current in circuit: 4

5. Lenz’s law An induced EMF is always in a direction that opposes the original change in flux that caused it. This is known as Lenz’s law 1) Conservation of energy 2) Three ways to create EMF 5

6. Rotating coil Example1: A circular coil is rotating in uniform magnetic field. Determine the EMF. Solution: The magnetic flux: If the magnetic field is changing: 6

7. Induced charges Thinking:A small coil moves far away from the position in figure. How to determine the total induced charge going through the coil? 7

8. ++ : non-electrostatic field - -- EMF induced in moving conductor Conductor moves in B → motional EMF Caused by Lorentz force: Motional EMF: All ⊥ case: Direction? 8

9. moves with velocity Derived by Faraday’ law The result can also be derived by Faraday’ law It sweeps out an area dS Magnetic flux: EMF: 9

10. v (b) v l B Motion in uniform field Example2: Determine the EMF induced in the conductor in a uniform magnetic field. (a) EMF: → straight wire: Force: Power: 10

11. Rotates in uniform field Example3:A conductor rod rotates about axis o. Determine the induced EMF. (B, L, ω) Solution: For an infinitesimal: Total EMF in the conductor: Faraday’s law: 11

12. I o L L Rotates in nonuniform field Question:A conductor rod rotates about axis o. Determine the induced EMF when the two wires are perpendicular to each other. 12

13. Motion on rails Example4:Conducting rod rests on frictionless parallel rails with an EMF source. Determine the speed of rod if the source puts out (a) constant I; (b) constant EMF. (c) What is the terminal speed? Solution: (a) m, R 13

14. m, R (b) source puts outconstant EMF: (c) Terminal speed 14

15. Changing B produces E Conductor stays at rest, magnetic fieldchanges → Induced EMF → induced current Forces on static charges? Maxwell: It’s caused by electric field Induced (vortex) electric field:produced by changing magnetic field, and acts on electric charges. 15

16. where is the induced electric field Faraday’s law → general form Generalize the definition of V : For induced EMF in a closed circuit: General form of Faraday’s law 16

17. Induced electric field 1) Eiis produced by changing B, not by charges 2) Even if there is no conductor, Ei stillexists 3) Induced electric field is nonconservative 4) Minus sign shows the direction of Ei 17

18. I Comparison of fields Electrostatic / induced electric / magnetic field Field lines: vortex 18

19. R Vortex electric field Example5:Uniform magnetic field in cylindrical space changes as dB/dt=C>0. Determine the induced electric field. Solution: Analyze the symmetry 19

20. R 2R EMF in a wire Example6:Magnetic field in a solenoid changes as dB/dt=C>0. A straight wire lies tangent to the solenoid at its center. What is the EMF in wire? Solution: Induced electric field: 20

21. 1 2 R 2R a b Another Solution: Imagine a closed circuit Discussion: 21

22. Self inductance Thinking:If a solenoid with current I is cut off from the battery, will I drop abruptly to 0? How does I change over time? 22

23. *Applications of induction Sound systems / microphones: Transformers: Recording tape / computer memory 23

24. *Vortex current Vortex electric field → vortex current Heating effect → induction cooker Electromagnetic damping 24