PHYS 2415 No Open Laptops!!

1. PHYS 2415No Open Laptops!! Professor Stephen Thornton October 15, 2012

2. Reading Quiz:Which of the following situations has a changing magnetic flux? B is constant everywhere.The ring is conducting. A) Only 1 B) Only 2 C) Only 3 D) 1 and 2 E) 1 and 3 rotates up and down swings

3. Reading Quiz: Which of the following situations has a changing magnetic flux? B is constant everywhere.The ring is conducting. Situation 2 is the only one in which the magnetic flux changes. A current will be induced in the ring as a result of the ring rotating in the magnetic field. A) Only 1 B) Only 2 C) Only 3 D) 1 and 2 E) 1 and 3 rotates up and down swings

4. Today Changing magnetic fields can produce a current! Called magnetic induction. It is actually change in magnetic flux that causes induced currents. Lots of applications! Lenz’s law helps us determine direction of current. Motional emf Electric motors and generators depend on it!

5. Induced EMF Almost 200 years ago, Michael Faraday looked for evidence that a magnetic field would induce an electric current with this apparatus:

6. Do demos about induced currents. Push and pull magnet in and out of coils of wire to show current production.

7. Induced Current Produced by a Moving Magnet

8. Induced EMF Therefore, a changing magnetic field induces an emf/current. Faraday’s experiment used a magnetic field that was changing because the current producing it was changing; the previous graphic shows a magnetic field that is changing because the magnet is moving.

9. Magnetic Induction B linked by iron bar.

10. We conclude that it is the change in magnetic flux that causes induced current.

11. Faraday’s Discovery and the Law of Induction • There are many ways to change the magnetic flux through a surface: • Move the magnet • Turning current on or off in one loop induces current in another • Move the loop • Change the shape (and the area) of the loop

12. The Magnetic Flux Through a Loop

13. The induced emf in a wire loop is proportional to the rate of change of magnetic flux through the loop. Magnetic flux: Unit of magnetic flux: weber, Wb: 1 Wb = 1 T·m2.

14. Look at the mathematics.This is called Faraday’s Law of Induction after Michael Faraday.

15. Do some more demos.1) Magnet through coil again.2) Flash bulb3) LED coil

16. The induced current will always be in the direction to oppose the change that produced it. Lenz’s Law

17. Applying Lenz’s Law to a Magnet Moving Toward and Away From a Current Loop Induced current

18. Conceptual Quiz: A long, straight wire carries a steady current I. A rectangular conducting loop lies in the same plane as the wire, with two sides parallel to the wire and two sides perpendicular. Suppose the loop is pushed toward the wire as shown. Given the direction of I, the induced current in the loop is A) clockwise.B) counterclockwise C) need more information

19. Answer: B The loop has an increasing flux into the screen. A current will be induced to create a magnetic field coming out of the screen. The current will be counterclockwise to do this. Iind

20. Lenz’s Law Applied to a Decreasing Magnetic Field

21. Changing area. What happens to magnetic flux?What is direction of induced current?

22. Faraday’s Law of Induction; Lenz’s Law • Problem Solving: Lenz’s Law • Determine whether the magnetic flux is increasing, decreasing, or unchanged. • The magnetic field due to the induced current points in the opposite direction to the original field if the flux is increasing; in the same direction if it is decreasing; and is zero if the flux is not changing. • Use the right-hand rule to determine the direction of the induced current. • Remember that the external magnetic field and the magnetic field due to the induced current are different.

23. Conceptual Quiz A) clockwise B) counterclockwise C) no induced current If a North pole moves toward the loop from above the page, in what direction is the induced current?

24. Conceptual Quiz A) clockwise B) counterclockwise C) no induced current If a North pole moves toward the loop from above the page, in what direction is the induced current? The magnetic field of the moving bar magnet is pointing into the page and getting larger as the magnet moves closer to the loop. Thus the induced magnetic field has to point out of the page. A counterclockwise induced current will give just such an induced magnetic field. Follow-up: What happens if the magnet is stationary but the loop moves?

25. Conceptual Quiz A) clockwise B) counterclockwise C) no induced current If a coil is shrinking in a magnetic field pointing into the page, in what direction is the induced current?

26. Conceptual Quiz A) clockwise B) counterclockwise C) no induced current If a coil is shrinking in a magnetic field pointing into the page, in what direction is the induced current? The magnetic flux through the loop is decreasing, so the induced B field must try to reinforce it and therefore points in the same direction — into the page. According to the right-hand rule, an induced clockwise current will generate a magnetic field into the page. Follow-up: What if the B field is oriented at 90° to its present direction?

27. Motional emf What happens when we push rod down?

28. Determining the Direction of an Induced Current We exert force to push bar down.

29. Force and Induced Current A different situation. Rod goes out. Induced current to oppose change

30. Motional emf • Created by a conductor moving in a magnetic field • “Loop” is imaginary but real emf is induced in conductor

31. Find force and energy They are equal!

32. Conceptual Quiz A) clockwise B) counterclockwise C) no induced current If a coil is rotated as shown, in a magnetic field pointing to the left, in what direction is the induced current?

33. Conceptual Quiz A) clockwise B) counterclockwise C) no induced current If a coil is rotated as shown, in a magnetic field pointing to the left, in what direction is the induced current? As the coil is rotated into the B field, the magnetic flux through it increases. According to Lenz’s law, the induced B field has to oppose this increase, thus the new B field points to the right. An induced counterclockwise current produces just such a B field.

34. I Conceptual Quiz A) clockwise B) counterclockwise C) no induced current A wire loop is being pulled away from a current-carrying wire. What is the direction of the induced current in the loop?

35. I Conceptual Quiz A) clockwise B) counterclockwise C) no induced current A wire loop is being pulled away from a current-carrying wire. What is the direction of the induced current in the loop? The magnetic flux is into the page on the right side of the wire and decreasing due to the fact that the loop is being pulled away. By Lenz’s law, the induced B field will oppose this decrease. Thus, the new B field points into the page, which requires an induced clockwise current to produce such a B field.

36. I Conceptual Quiz A) clockwise B) counterclockwise C) no induced current What is the induced current if the wire loop moves in the direction of the yellow arrow?

37. I Conceptual Quiz A) clockwise B) counterclockwise C) no induced current What is the induced current if the wire loop moves in the direction of the yellow arrow? The magnetic flux through the loop is not changing as it moves parallel to the wire. Therefore, there is no induced current.

38. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Conceputal Quiz A) clockwise B) counterclockwise C) no induced current A wire loop is being pulled through a uniform magnetic field. What is the direction of the induced current?

39. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Conceptual Quiz A) clockwise B) counterclockwise C) no induced current A wire loop is being pulled through a uniform magnetic field. What is the direction of the induced current? Since the magnetic field is uniform, the magnetic flux through the loop is not changing. Thus no current is induced. Follow-up: What happens if the loop moves out of the page?

40. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Conceptual Quiz A) clockwise B) counterclockwise C) no induced current A wire loop is being pulled through a uniform magnetic field that suddenly ends. What is the direction of the induced current?

41. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Conceptual Quiz A) clockwise B) counterclockwise C) no induced current A wire loop is being pulled through a uniform magnetic field that suddenly ends. What is the direction of the induced current? The B field into the page is disappearing in the loop, so it must be compensated by an induced flux also into the page. This can be accomplished by an induced current in the clockwisedirection in the wire loop. Follow-up: What happens when the loop is completely out of the field?

42. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x v Conceptual Quiz A) clockwise B) counterclockwise C) no induced current A conducting rod slides on a conducting track in a constant B field directed into the page. What is the direction of the induced current?

43. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x v Conceptual Quiz A) clockwise B) counterclockwise C) no induced current A conducting rod slides on a conducting track in a constant B field directed into the page. What is the direction of the induced current? The B field points into the page. The flux is increasing since the area is increasing. The induced B field opposes this change and therefore points out of the page. Thus, the induced current runs counterclockwise, according to the right-hand rule. Follow-up: What direction is the magnetic force on the rod as it moves?