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  • 1. Faradays Law Physics 102:Lecture 10 Changing Magnetic Fields create Electric Fields

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. Motional EMF

  • 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 baracts like a battery(i.e. generates EMF)!!

(Recall that e- actually move, opposite current) V F q + q I 4. Faradays 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

5. First a preliminary:Magnetic Flux

  • Counts number of field lines through loop.

Uniform magnetic field,B , passes through a plane surface of areaA . Magnetic flux = B A (Units Tm 2= Wb) Magnetic flux B Acos( ) is angle betweennormalandB B A B A normal Note: The flux can be negative (if field lines go thru loop in opposite direction) 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 A cos(0) = BA B= B A cos(90) = 0 more lines pass through its surface in that position. 7. Faradays Law of Induction:

  • induced EMF = rate of change of magnetic flux
  • Since = B A cos( ), 3 things can change
      • Area of loop
      • Magnetic field B
      • Anglebetween normal and B

8. ACT: Change Area1 v v 3 Which loop has the greatest induced EMF at the instant shown above? L W 2 v 9. Faraday: Change AreaV t=0 0 =BLW t t =BL(W+vt) L W EMF Magnitude: = B A cos( ) Example What about thesignof the EMF? V W vt 10. Lenzs Law (EMF direction) V

  • Flux is increasing
  • Induced current is clockwise
  • Current loop generatesinduced B field
    • from RHR2, into page, opposite external B field!

What happens if the velocity isreversed ? V I B ind 11. Lenzs Law (EMF direction) V

  • Flux is decreasing
  • Induced current iscounterclockwise
  • Current loop generates induced B field
    • from RHR2,out of the page , along external B field!

Induced EMFopposes changein fluxV I B ind 12. Lenzs Law(EMF Direction) Induced emfopposes changein fluxEMF does NOT oppose B field, or flux! EMF opposes theCHANGEin flux

  • If flux increases:
  • New EMF makes new fieldopposite tooriginal field
  • If flux decreases:
    • New EMF makes new fieldin same direction asoriginal field

13. Motional EMF circuit

  • Direction of Current
  • B field generates force on current-carrying bar

I = /R

  • Magnitude of current

Clockwise ( +charges godownthru bar,upthru bulb) F bar= ILB sin( ), t o left (RHR1) V F baropposes v! = vBL/R

  • Careful! There are two forces:

F bar= force on bar from induced current F q= force on + charges in bardrivinginduced current I F q + q F bar 14. Motional EMF circuit

  • Direction of Current

xxx xxxx xxxx xxxx xxxxx xxxx xxxx xxxx xxxxx xxxx xxxx xxxx xxxxx xxxx xxxx xxxx xxxxx xxxx xxxx xxxx xxI = /R= vBL/R Still to left, opposite v What happens if field isreversed ? (TRY IT AT HOME) V

  • Direction of force(F=ILB sin( ))on bar due to magnetic field
  • Magnitude of current

Counter-Clockwise ( +charges goupthru bar,downthru bulb) F always opposes v, bar slows down Must apply external force to keep bar moving 15. 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( ) 16. 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. 17. Faradays Law of Induction:

  • induced EMF = rate of change of magnetic flux
  • Since = B A cos( ), 3 things can change
      • Area of loop
      • Magnetic field B
      • Anglebetween normal and B

18. ACT: Induction cannon (Demo)

  • As current increases in the solenoid, what direction will induced current be in ring?
  • Same as solenoid
  • Opposite of solenoid
  • No current

A solenoid is driven by an increasing current. A loop of wire is placed around it B sol 19. 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

  • What happens when loop has less resistance?
  • What happens if the loop is broken?

20.

  • Which way is the magnet moving if it is inducing a current in the loop as shown?
  • Up
  • Down

ACT: Change B (Demo) Demo 371 21. ACT: Change B II (contd)

  • If I reduce the resistance in the wire, the magnet will fall
  • faster
  • slower
  • at the same speed

N S 22. 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 Acos( ) Increases Decreases Example 23. 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 Acos( ) Example 24. Faradays and Lenzs Law

  • Faraday: Induced emf = rate of change of magnetic flux
  • Since = B A cos( ), 3 things can change
      • Area of loop
      • Magnetic field B
      • Anglebetween normal and B

Next lecture Lenz: Induced emfopposes changein flux