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

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

Physics 102: Lecture 10, Slide 3 Summary of Right-Hand Rules B I B I r RHR 1RHR 2 Alternate Force on moving q B field from current I Straight wire Solenoid I

Physics 102: Lecture 10, Slide 4 Motional EMF V A metal bar slides with velocity v on a track in a uniform B field Moving + charges in bar experience force down (RHR1) Electrical current driven clockwise! Moving bar acts like a battery (i.e. generates EMF)!! FqFq (Recall that e- actually move, opposite current) + q I

Physics 102: Lecture 10, Slide 5 Faraday’s Law of Induction: “induced EMF” = rate of change of magnetic flux The principle that unifies electricity and magnetism Key to many things in E&M –Generating electricity –Microphones, speakers, guitar pickups –Amplifiers –Computer disks and card readers

Physics 102: Lecture 10, Slide 6 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 (Units Tm 2 = Wb) 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)

Physics 102: Lecture 10, Slide 7 Preflight 10.7 Compare the flux through loops a and b. 1)  a >  b 2)  a <  b a b n nB  A = B A cos(0) = BA  B = B A cos(90) = 0 68% 32% “more lines pass through its surface in that position.”

Physics 102: Lecture 10, Slide 8 Faraday’s Law of Induction: “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 normal and B

Physics 102: Lecture 10, Slide 9 ACT: Change Area 1 v v 3 Which loop has the greatest induced EMF at the instant shown above? L W 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

Physics 102: Lecture 10, Slide 10 Faraday: Change Area V t=0  i = BLW t  f = BL(W+vt) L W V W vt EMF Magnitude:  = B A cos(  ) What about the sign of the EMF?

Physics 102: Lecture 10, Slide 11 Lenz’s Law (EMF direction) V V Flux is increasing Induced current is clockwise Current loop generates induced B field – from RHR2, into page, opposite external B field! I B ind What happens if the velocity is reversed?

Physics 102: Lecture 10, Slide 12 Lenz’s Law (EMF direction) V V Flux is decreasing Induced current is counterclockwise Current loop generates induced B field – from RHR2, out of the page, along external B field! I Induced EMF opposes change in flux B ind

Physics 102: Lecture 10, Slide 13 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

Physics 102: Lecture 10, Slide 14 Motional EMF circuit Direction of Current B field generates force on current-carrying bar I =  /R Magnitude of current Clockwise (+ charges go down thru bar, up thru bulb) F bar = ILB sin(  ), to left (RHR1) V F bar opposes v! = vBL/R I FqFq + q F bar Careful! There are two forces: F bar = force on bar from induced current F q = force on + charges in bar driving induced current

Physics 102: Lecture 10, Slide 15 x x x x x x x x x x x x x x x x x Motional EMF circuit I =  /R = vBL/R Still to left, opposite v What happens if field is reversed? (TRY IT AT HOME) V 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) F always opposes v, bar slows down Must apply external force to keep bar moving

Physics 102: Lecture 10, Slide 16 Preflight 10.4 Increase Stay the Same Decrease 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! 25% 63% 12%

Physics 102: Lecture 10, Slide 17 Preflight 10.5 True False 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! 47% 53%

Physics 102: Lecture 10, Slide 18 Faraday’s Law of Induction: “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 normal and B 

Physics 102: Lecture 10, Slide 19 ACT: Induction cannon (Demo) As current increases in the solenoid, what direction will induced current be 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 1)Same as solenoid 2)Opposite of solenoid 3)No current B sol B ind A solenoid is driven by an increasing current. A loop of wire is placed around it

Physics 102: Lecture 10, Slide 20 Induction cannon (Demo) Recall: current loop behaves like bar magnet Opposite currents => opposite polarities Like poles repel! Loop shoots up A solenoid is driven by an increasing current. A loop of wire is placed around it NSNS What happens when loop has less resistance? What happens if the loop is broken?

Physics 102: Lecture 10, Slide 21 Which way is the magnet moving if it is inducing a current in the loop as shown? 1)Up 2)Down ACT: Change B (Demo) Field from magnet is down. Induced current creates field up - opposite original. So flux from magnet must be increasing. Magnet must be falling down N S Demo 371 NS

Physics 102: Lecture 10, Slide 22 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 Decreasing R, increases I. Increases opposing field, which makes magnet fall slower. N S NS

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

Physics 102: Lecture 10, Slide 24 Magnetic Flux II Increase area of solenoid Increase area of loop Increase current in solenoid Increases Nothing Increases A solenoid (B=  o nI) is inside a conducting loop. What happens to the flux through the loop when you…   B A cos(  )

Physics 102: Lecture 10, Slide 25 Faraday’s and Lenz’s Law Faraday: 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 normal and B   Next lecture Lenz: Induced emf opposes change in flux