Faraday’s Law Physics 102: Lecture 10 Changing Magnetic Fields create Electric Fields Exam II Exam 1 tonight Be sure to bring your ID and go to correct roomcorrect room All you need is pencil/pen and calculator –No cell phones –No IPods, etc.

Last Two Lectures Magnetic fields Forces on moving charges and currents Magnetic field due to –Long straight wire –Solenoid

Today: Faraday’s Law Key to EVERYTHING in E+M –Generating electricity –Microphones, Speakers and Tape Decks –Amplifiers –Computer disks and card readers –Ground Fault Interrupters 7

Motional EMF, Preflight 10.1 F = q v B sin(  ) + v Potential Difference  = F d/q EMF = q v B sin(  ) L/q = v B L B L v Only 22% got this correct on the preflight!! Velocity Moving + charge feels force downwards: Moving + charge still feels force downwards: B 10 F

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 52% got this correct. 12 “A is parallel, b is perpendicular”

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 15 DEMO: 371

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

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: F=ILB sin(  )) B and v still perpendicular (  =90), so F=ILB just like before! 32% 52% 16% 19

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. Current flows in the opposite direction, so force from the B field remains the same! 51% 49% 20

Magnetic Flux Count 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 22 B A  normal B Note: The flux can be negative (if field lines go thru loop in opposite direction)

Preflight 10.7 Compare the flux through loops a and b. 1)  a >  b 2)  a <  b a b n n B  A = B A cos(0) = BA  B = B A cos(90) = 0 68% 32% 24 “more lines pass through its surface in that position.”

Faraday’s Law (EMF Magnitude) Emf = Change in magnetic Flux/Time Since  = B A cos(  3 things can change  1.Area of loop 2.Magnetic field B 3.Angle  between A and B 26

28 Lenz’s Law (EMF Direction) 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 original field If flux decreases: New EMF makes new field same as original field demo: 1093

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

Change Area II 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 38 EMF Magnitude:  = B A cos(  )

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 40 SNSN  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

ACT: Change B II SNSN Flux from magnet is down. Induced current creates flux up - opposite original. So flux from magnet must be increasing. Magnet must be falling down N S 42 Which way is the magnet moving if it is inducing a current in the loop as shown? 1)Up 2)Down Demo 371

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 Decreasing R, increases I. Increases opposing field, which makes magnet fall slower. 42

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 44 What direction is the current induced?  upwards and decreasing. New field will be in same direction (opposes change). Current must be counter clockwise. Demo 68, 371

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? Nothing Increases   B A cos(  ) Increases Decreases 48

Magnetic Flux II Increase area of solenoid Increase area of loop Increase current in solenoid Increases Nothing Increases 50 A solenoid (B=  o nI) is inside a conducting loop. What happens to the flux through the loop when you…   B A cos(  )

Good Luck Tonight! 50