# lect10 handout

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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

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