1. Physics 102: Lecture 10, Slide 1 Faraday’s Law Physics 102: Lecture 10 Changing Magnetic Fields create Electric Fields Last Two Lectures Magnetic fields Forces on moving charges and currents Torques on current loops Magnetic field due to –Long straight wire –Solenoid

2. Physics 102: Lecture 10, Slide 2 Last Two Lectures Magnetic fields Forces on moving charges and currents Torques on current loops Magnetic field due to –Long straight wire –Solenoid

3. Physics 102: Lecture 10, Slide 3 Today: Faraday’s Law The principle that unifies electricity and magnetism Key to many things in E&M –Generating electricity –Microphones, speakers and tape decks –Amplifiers –Computer disks and card readers

4. Physics 102: Lecture 10, Slide 4

5. Physics 102: Lecture 10, Slide 5 First a preliminary: Magnetic Flux “Counts” number of field lines through loop. Uniform magnetic field, B, passes through a plane surface of area A. A Magnetic flux  = B A Magnetic flux   B A cos(  )  is angle between normal and B B A  normal B Note: The flux can be negative (if field lines go thru loop in opposite direction)

6. Physics 102: Lecture 10, Slide 6 Preflight 10.7 Compare the flux through loops a and b. 1)  a >  b 2)  a <  b a b n n B  A =  B = “more lines pass through its surface in that position.”

7. Physics 102: Lecture 10, Slide 7 Faraday’s Law of Induction: This is new physics and not simply an application of stuff you already know “induced emf” = rate of change of magnetic flux Since  = B A cos(  3 things can change  1.Area of loop 2.Magnetic field B 3.Angle  between A and B

8. Physics 102: Lecture 10, Slide 8

9. Physics 102: Lecture 10, Slide 9 Lenz’s Law (EMF Direction) Induced emf opposes change in flux EMF does NOT oppose B field, or flux! EMF opposes the CHANGE in flux If flux increases: New EMF makes new field opposite to original field If flux decreases: New EMF makes new field in same direction as original field

10. Physics 102: Lecture 10, Slide 10 ACT: Change Area 1 v v 3 Which loop has the greatest induced EMF at the instant shown above? L W 2 v

11. Physics 102: Lecture 10, Slide 11 Example: Change Area V t=0  0 =BLW t  t =BL(W+vt) L W V W vt EMF Direction: B is out of page and  is increasing so EMF creates B field (inside loop) going into page. I EMF Magnitude:  = B A cos(  )

12. Physics 102: Lecture 10, Slide 12

13. Physics 102: Lecture 10, Slide 13 Motional EMF circuit Direction of Current Direction of force (F=ILB sin(  )) on bar due to magnetic field I =  /R Magnitude of current Clockwise (+ charges go down thru bar, up thru bulb) To left, slows down Moving bar acts like battery  = vBL B -+-+ V What changes if B points into page? = vBL/R

14. Physics 102: Lecture 10, Slide 14 Motional EMF circuit I =  /R = vBL/R Still to left, slows down Moving bar acts like battery  = vBL B + - V x x x x x x x x x x x x x x x x x Direction of Current Direction of force (F=ILB sin(  )) on bar due to magnetic field Magnitude of current Counter-Clockwise (+ charges go up thru bar, down thru bulb) 18

15. Physics 102: Lecture 10, Slide 15 Preflight 10.4 Increase Stay the Same Decrease Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. To keep the bar moving at the same speed, the force supplied by the hand will have to: 19

16. Physics 102: Lecture 10, Slide 16

17. Physics 102: Lecture 10, Slide 17 Preflight 10.5 True False Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. To keep the bar moving to the right, the hand will have to supply a force in the opposite direction.

18. Physics 102: Lecture 10, Slide 18 ACT: Change B As current is increasing in the solenoid, what direction will current be induced in ring? 1)Same as solenoid 2)Opposite of solenoid 3)No current SNSN

19. Physics 102: Lecture 10, Slide 19 ACT: Change B II SNSN N S Which way is the magnet moving if it is inducing a current in the loop as shown? 1)Up 2)Down

20. Physics 102: Lecture 10, Slide 20

21. Physics 102: Lecture 10, Slide 21 ACT: Change B II (cont’d) If I reduce the resistance in the wire, the magnet will fall 1)faster 2)slower 3)at the same speed SNSN N S

22. Physics 102: Lecture 10, Slide 22 Change  A flat coil of wire has A=0.2 m 2 and R=10 . At time t=0, it is oriented so the normal makes an angle  0 =0 w.r.t. a constant B field of 0.12 T. The loop is rotated to an angle of  =30 o in 0.5 seconds. Calculate the induced EMF. n B A   i = B A cos(0)  f = B A cos(30)  = 6.43x10 -3 Volts What direction is the current induced?

23. Physics 102: Lecture 10, Slide 23 Magnetic Flux Examples A conducting loop is inside a solenoid (B=  o nI). What happens to the flux through the loop when you… Increase area of solenoid? Increase area of loop? Increase current in solenoid? Rotate loop slightly?   B A cos(  )

24. Physics 102: Lecture 10, Slide 24

25. Physics 102: Lecture 10, Slide 25 Magnetic Flux II Increase area of solenoid Increase area of loop Increase current in solenoid A solenoid (B=  o nI) is inside a conducting loop. What happens to the flux through the loop when you…   B A cos(  )

26. Physics 102: Lecture 10, Slide 26 Motional EMF, Preflight 10.1 F = q v B sin(  ) + v + - - + Potential Difference = F L/q EMF = q v B sin(  ) L/q = B L v Velocity Moving + charge feels force downwards: Moving + charge still feels force downwards: B F

27. Physics 102: Lecture 10, Slide 27 Preflight 10.2 Which bar has the larger motional emf? a b v v E = v B L sin(  )  is angle between v and B Case a:  = 0, so E = 0 Case b:  = 90, so E = v B L

28. Physics 102: Lecture 10, Slide 28