1. Physics 212 Lecture 17, Slide 1 Physics 212 Lecture 17 Faraday’s Law

2. Main Point 1 First, we introduced the concept of the magnetic flux and found that the motional emfs produced in the three examples from the last prelecture could all be written simply as the time rate of change of the magnetic flux through the circuit. Physics 212 Lecture 17, Slide 2

3. Main Point 2 Second, we introduced Faraday’s Law, which states that whenever magnetic flux changes in time, not just in the case of a moving conductor, an emf will be produced. In particular, this induced emf will just be equal to minus the time rate of change of the magnetic flux. Physics 212 Lecture 17, Slide 3

4. Main Point 3 Finally, we observed that this induced emf is determined by integrating the electric field around the loop, so that Faraday’s law can be written more generally only in terms of the electric and magnetic fields. A changing magnetic flux creates an electric field. Faraday’s law represents the first important step in establishing the deep connections between electric and magnetic fields which ultimately will explain the existence of electromagnetic waves and the identification of light as an electromagnetic phenomenon. Physics 212 Lecture 17, Slide 4

5. Physics 212 Lecture 17, Slide 5 Faraday’s Law Looks scary but it’s not – its amazing and beautiful ! A changing magnetic flux produces an electric field. Electricity and magnetism are on intimate terms

6. Physics 212 Lecture 17, Slide 6 In Practical Words: 1) When the flux  B through a loop changes, an emf is induced in the loop. There are many ways to change this… Faraday’s Law: where B A Think of  B as the number of field lines passing through the surface Flux Show Projection

7. Physics 212 Lecture 17, Slide 7

8. Physics 212 Lecture 17, Slide 8 Faraday’s Law In Words: 1) When the flux  B through a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery). 3) The current that flows induces a new magnetic field. 4) The new magnetic field opposes the change in the original magnetic field. B dB/dt

9. Physics 212 Lecture 17, Slide 9 The Ways Flux Can Change Change Area Change magnetic field Change orientation ALL THESE CHANGES CAN BE UNDERSTOOD FROM MOTIONAL EMF WHAT’S NEW WITH FARADAY? Flux can change WITHOUT moving any conductor !! e.g., change current that produces magnetic field e.g., change current that produces magnetic field

10. Physics 212 Lecture 17, Slide 10 Faraday’s Law Executive Summary: emf → current → field a) induced only when flux is changing b) opposes the change b) opposes the change

11. Physics 212 Lecture 17, Slide 11

12. Checkpoint 1a Physics 212 Lecture 17, Slide 12 A copper loop is placed in a uniform magnetic field as shown. You are looking from the right. Suppose the loop is moving to the right. The current induced in the loop is: A. zeroB. clockwiseC. counterclockwise

13. Physics 212 Lecture 17, Slide 13 Checkpoint 1b A copper loop is placed in a uniform magnetic field as shown. You are looking from the right. Now suppose the that loop is stationary and that the magnetic field is decreasing in time. The current induced in the loop is: A. zero B. clockwiseC. counterclockwise

14. Physics 212 Lecture 17, Slide 14 Checkpoint 1c Now suppose that the loop is spun around a vertical axis as shown, and that it makes one complete revolution every second. The current induced in the loop: A. Is zero B. Changes direction once per second C. Changes direction twice per second

15. Physics 212 Lecture 17, Slide 15 (copper is not ferromagnetic) X O B B Checkpoint 2 A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet Will the acceleration a of the falling ring in the presence of the magnet be any different than it would have been under the influence of just gravity (i.e. g)? A. a > gB. a = gC. a < g

16. Physics 212 Lecture 17, Slide 16

17. Calculation Physics 212 Lecture 17, Slide 17 Conceptual Analysis Strategic Analysis y x v0v0 a b 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 B A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v 0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. What is the direction and the magnitude of the force on the loop when half of it is in the field?

18. Physics 212 Lecture 17, Slide 18

19. Physics 212 Lecture 17, Slide 19

20. Physics 212 Lecture 17, Slide 20