1. Induction experiments(sec. 29.1) Faraday’s law (sec. 29.2) Lenz’s law(sec. 29.3) Motional electromotive force(sec. 29.4) Induced electric fields(sec. 29.5) Eddy currents(sec. 29.6) Displacement Current(sec. 29.7) Electromagnetic Induction Ch. 29 C 2012 J. F. Becker

2. Learning Goals - we will learn: ch 29 The experimental evidence that a changing magnetic field induces an emf ! How Faraday’s Law relates the induced emf in a loop to the change in magnetic flux through the loop. How a changing magnetic flux generates an electric field that is very different from that produced by an arrangement of charges. Four fundamental equations completely describe both electricity and magnetism.

3. Current induced in a coil.

5. When B is constant and the shape, location, and orientation of the coil does not change, the induced current is zero in the coil.

6. Conducting loop in increasing B field.

7. Magnetic flux through an area.

8. Lenz’s law Lenz’s Law The induced emf (or current) always tends to oppose or cancel the change that caused it. O O

10. Faraday’s Law of Induction How electric generators, credit card readers, and transformers work. A changing magnetic flux causes (induces) an emf in a conducting loop. C 2004 Pearson Education / Addison Wesley Eqn 29.3

11. Changing magnetic flux through a wire loop.

12. Alternator (AC generator)  = 90 o

13. DC generator  = 90 o

14. Slidewire generator

15. Magnetic force (F = IL x B) due to the induced current is toward the left, opposite to velocity v.

16. Lenz’s law Lenz’s Law The induced emf (or current) always tends to oppose or cancel the change that caused it. O O

17. Currents (I) induced in a wire loop.

18. Motional induced emf ( e ): e = v B L because the potential difference between a and b is e = D V = energy / charge = W/q e = D V = work / charge D V = F x distance / q D V = (q v B) L / q so e = v B L Length and velocity are perpendicular to B

19. Solenoid with increasing current I which induces an emf in the (yellow) wire. An induced current I’ is moved through the (yellow) wire by an induced electric field E in the wire.

20. Eddy currents formed by induced emf in a rotating metal disk.

21. Metal detector – an alternating magnetic field Bo induces eddy currents in a conducting object moved through the detector. The eddy currents in turn produce an alternating magnetic field B’ and this field induces a current in the detector’s receiver coil.

22. A capacitor being charged by a current i C has a “displacement current” between the plates equal to i C, with displacement current i D = e A dE/dt. This changing E field can be regarded as the source of the magnetic field between the plates. ( E _ B ) DISPLACEMENT CURRENT

23. A capacitor being charged by a current i C has a displacement current equal to i C between the plates, with displacement current i D = e A dE/dt From C = e A / d and D V = E d we can use q = C V to get q = ( e A / d ) (E d ) = e E A = e F E and from i C = dq / dt = e A dE / dt = e d F E / dt = i D We now see that a changing E field can produce a B field, and from Faraday’s Law, a changing B field can produce an E field or emf. C 2011 J. Becker

24. MAXWELL’S EQUATIONS C 2004 Pearson Educational / Addison Wesley The relationships between electric and magnetic fields and their sources can be stated compactly in four equations, called Maxwell’s equations. Together they form a complete basis for the relation of E and B fields to their sources.

25. Determine direction of induced current for a) increasing B b) decreasing B Lenz’s law (Exercise 29.16)

26. Lenz’s law (Exercise 29.17)

27. Lenz’s law (Exercise 29.18)

28. Motional emf and Lenz’s law (Exercise 29.21)

29. Motional emf and Lenz’s law (Exercise 29.26)

30. TRANSFORMERS can step-up AC voltages or step-down AC voltages.

31. Lenz’s law (Exercise 29.18)

32. Transformer: AC source is V 1 and secondary provides a voltage V 2 to a device with resistance R. TRANSFORMERS can step-up AC voltages or step- down AC voltages.  2 /  1 = N 2 /N 1 V 1 I 1 = V 2 I 1   =    e = -N d F B / dt

33. Figure 32.2b

34. Large step-down transformers at power stations are immersed in tanks of oil for insulation and cooling.

35. Figure 31.22

36. Figure 31.23

37. See www.physics.sjsu.edu/becker/physics51 Review C 2012 J. F. Becker