Faraday’s Law

1. Physics 102: Lecture 10 Faraday’s Law Changing Magnetic Fields create Electric Fields • Exam 1 tonight • Be sure to bring your ID and go to correct room • All you need is a #2 pencil and calculator • No cell phones • No I-pods, laptops, etc.

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. 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 7

4. A B f normal A Note: The flux can be negative (if field lines go thru loop in opposite direction) First a preliminary: Magnetic Flux • “Counts” number of field lines through loop. B Uniform magnetic field, B, passes through a plane surface of area A. Magnetic flux F=BA Magnetic flux FBA cos(f) f is angle between normal and B 22

5. Preflight 10.7 B n Compare the flux through loops a and b. 1) Fa>Fb 2) Fa< Fb n “more lines pass through its surface in that position.” b a FA = B A cos(0) = BA FB = B A cos(90) = 0 73% 27% 24

6. 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 SinceF= B A cos(f), 3 things can change F • Area of loop • Magnetic field B • Angle f between A and B 26

7. Lenz’s Law (EMF Direction) Induced emf opposes change in flux • If flux increases: • New EMF makes new field oppositeto original field • If flux decreases: • New EMF makes new field in samedirectionas original field EMF does NOT oppose B field, or flux! EMF opposes the CHANGE in flux 28 demo: 1093

8. ACT: Change Area 3 W 2 1 v L v v Which loop has the greatest induced EMF at the instant shown above? 1 moves right - gets 4 more field lines. 2 moves down - gets 0 more field lines. 3 moves down - only gets 2 more lines. 1 is gaining flux fastest! E3 = BvW E1 = BvL E2 = 0 35

9. vt W V Example: Change Area W V L I t=0 F0=BLW t Ft=BL(W+vt) F = B A cos(q) EMF Magnitude: EMF Direction: B is out of page and F is increasing so EMF creates B field (inside loop) going into page. 38

10. Motional EMF circuit Moving bar acts like battery e = vBL B • Direction of Current - + • Magnitude of current V I = e/R = vBL/R Clockwise (+ charges go down thru bar, up thru bulb) • Direction of force (F=ILB sin(q)) on bar due to magnetic field What changes if B points into page? To left, slows down DEMO: 371 15

11. Motional EMF circuit Moving bar acts like battery e = vBL B x x xx x x xx x x xx x x xx x • Direction of Current + - • Magnitude of current x x xx x x xx x x xx x x xx x V x x xx x x xx x x xx x x xx x I = e/R = vBL/R x x xx x x xx x x xx x x xx x x x xx x x xx x x xx x x xx x Counter-Clockwise (+ charges go up thru bar, down thru bulb) • Direction of force (F=ILB sin(q)) on bar due to magnetic field Still to left, slows down 18

12. Preflight 10.4 Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. • Increase • Stay the Same • Decrease To keep the bar moving at the same speed, the force supplied by the hand will have to: 28% 61% 10% F=ILB sin(q) B and v still perpendicular (q=90), so F=ILB just like before! 19

13. Preflight 10.5 Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. • True • False To keep the bar moving to the right, the hand will have to supply a force in the opposite direction. 53% 47% Current flows in the opposite direction, so force from the B field remains the same! 20

14. ACT: Change B SN As current is increasing in the solenoid, what direction will current be induced in ring? • Same as solenoid • Opposite of solenoid • No current •  Solenoid current (counter-clockwise) •  B-field (upwards) =>  Flux thru loop • EMF will create opposite B-field (downwards) • Induced loop current must be clockwise Demo 157 40

15. N S ACT: Change B II Which way is the magnet moving if it is inducing a current in the loop as shown? • Up • Down S N Field from magnet is down. Induced current creates field up - opposite original. So flux from magnet must be increasing. Magnet must be falling down Demo 371 42

16. B f n A Change f Example A flat coil of wire has A=0.2 m2 and R=10W. At time t=0, it is oriented so the normal makes an angle f0=0 w.r.t. a constant B field of 0.12 T. The loop is rotated to an angle of =30o in 0.5 seconds. Calculate the induced EMF. Fi = B A cos(0) Ff = B A cos(30) e = 6.43x10-3 Volts What direction is the current induced? B upwards and F decreasing. Induced B will be in same direction (opposes change). Current must be counter clockwise. Demo 68, 371 44

17. Magnetic Flux Examples Example A conducting loop is inside a solenoid (B=monI). What happens to the flux through the loop when you… Increase area of solenoid? Nothing Increase area of loop? Increases Increase current in solenoid? Increases FBA cos(f) Rotate loop slightly? Decreases 48

18. Magnetic Flux II Example A solenoid (B=monI) is inside a conducting loop. What happens to the flux through the loop when you… Increase area of solenoid Increases Increase area of loop Nothing Increase current in solenoid Increases FBA cos(f) 50

19. Demo: Change B As current is increasing in the solenoid, what direction will current be induced in ring? •  Solenoid current (counter-clockwise) •  B-field (upwards) =>  Flux thru loop • EMF will create opposite B-field (downwards) • Induced loop current must be clockwise Demo 157 40

20. Good Luck Tonight! 50

21. Velocity Velocity - v L - + + Motional EMF, Preflight 10.1 B Moving + charge feels forcedownwards: v F = q v B sin(q) + F B Moving + charge still feels forcedownwards: Potential Difference = F L/q EMF = q v B sin(q) L/q = v B L Only 22% got this correct on the preflight!! 10

22. Preflight 10.2 • Which bar has the larger motional emf? v a b v E = v B L sin(q) q is angle between v and B Case a: q = 0, so E = 0 Case b: q = 90, so E = v B L 62% got this correct. 12