Physics 212 Lecture 17

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.

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.

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.

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

8. dB/dt Faraday’s Law In Words: 1)When the fluxFBthrough 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

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

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

12. Checkpoint 1a 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. zero B. clockwise C. counterclockwise

13. Checkpoint 1b A copper loop is placed in a uniform magnetic field as shown. You are looking from the right. Checkpoint 1b 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. clockwise C. counterclockwise

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 secondC. Changes direction twice per second

15. Checkpoint 2 B O X B A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet (copper is notferromagnetic) 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 > g B.a = g C. a < g

17. Calculation y A rectangular loop (height = a,length = b,resistance = R,mass = m) coasts with a constant velocity v0in + x direction as shown. At t =0, the loop enters a region of constantmagnetic field Bdirected 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? 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 b a v0 x Conceptual Analysis Strategic Analysis