1. Changing Magnetic Fields create Electric Fields
Physics 102: Lecture 10
Faraday’s Law
Changing Magnetic Fields create Electric Fields 1

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 I V + q Fq
Moving + charges in bar experience force down (RHR1)
Electrical current driven clockwise!
Moving bar acts like a battery (i.e. generates EMF)!!
(Recall that e- actually move, opposite current)

4. 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
Demo 371: Helmholz coil and bar magnet

5. 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. A
Magnetic flux F = B A
(Units Tm2 = Wb) B A f
normal
Magnetic flux F  B A cos(f)
f is angle between normal and B
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.
“more lines pass through its surface in that position.” b a
FA = B A cos(0) = BA
FB = B A cos(90) = 0
Compare the flux through loops a and b.
1) Fa>Fb ) Fa< Fb

7. Faraday’s Law of Induction:
“induced EMF” = rate of change of magnetic flux
Demo 371: Helmholz coil and bar magnet
Since F= B A cos(f), 3 things can change F
Area of loop
Magnetic field B
Angle f between normal and B

8. ACT: Change Area 3 W 2 1 v L v v
Which loop has the greatest induced EMF at the instant shown above?

9. Faraday: Change Area Example F = B A cos(q) W V W vt V L t=0 F0=BLW t
Ft=BL(W+vt)
F = B A cos(q)
EMF Magnitude:
What about the sign of the EMF?

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

11. Lenz’s Law (EMF direction)V I V
Bind
Flux is decreasing
Induced current is counterclockwise
Current loop generates induced B field
– from RHR2, out of the page, along external B field!
Induced EMF opposes change in flux

12. Lenz’s Law (EMF Direction)
Induced emf opposes 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
Demo 193: copper pipe and cow magnet. Current induced in pipe opposes movement of magnet.
EMF does NOT oppose B field, or flux!
EMF opposes the CHANGE in flux

13. Motional EMF circuit Magnitude of current Direction of Current+ q V
I = e/R
= vBL/R Fq
Fbar
Direction of Current
Clockwise (+ charges go down thru bar, up thru bulb)
B field generates force on current-carrying bar
Demo: Helmholtz coil and bar magnet
Fbar = ILB sin(q), to left (RHR1)
Fbar opposes v!
Careful! There are two forces:
Fbar = force on bar from induced current
Fq = force on + charges in bar driving induced current

14. Motional EMF circuit Magnitude of current Direction of Current
What happens if field is reversed? (TRY IT AT HOME)
x x x x x x x x x x x x x x x x x
Magnitude of current
x x x x x x x x x x x x x x x x x V
I = e/R = vBL/R
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
Direction of Current
x x x x x x x x x x x x x x x x x
Counter-Clockwise (+ charges go up thru bar, down thru bulb)
Direction of force (F=ILB sin(q)) on bar due to magnetic field
F always opposes v, bar slows down Must apply external force to keep bar moving
Still to left, opposite v

15. Preflight 10.4 Increase Stay the Same Decrease F=ILB sin(q)
To keep the bar moving at the same speed, the force supplied by the hand will have to:
Increase
Stay the Same
Decrease
F=ILB sin(q)

16. Faraday’s Law of Induction:
“induced EMF” = rate of change of magnetic flux
Demo 371: Helmholz coil and bar magnet
Since F= B A cos(f), 3 things can change F
Area of loop
Magnetic field B
Angle f between normal and B 

17. ACT: Induction cannon (Demo)
A solenoid is driven by an increasing current. A loop of wire is placed around it
Bsol
As current increases in the solenoid, what direction will induced current be in ring?
Same as solenoid
Opposite of solenoid
No current
Demo: EM cannon; soleoid S-N N-S loop…they repel each other

18. Induction cannon (Demo)
A solenoid is driven by an increasing current. A loop of wire is placed around it
Recall: current loop behaves like bar magnet
Opposite currents => opposite polarities
Like poles repel! Loop shoots up N S
Demo: EM cannon; soleoid S-N N-S loop…they repel each other N S
What happens when loop has less resistance?
What happens if the loop is broken?

19. ACT: Change B (Demo)
Which way is the magnet moving if it is inducing a current in the loop as shown? Up
Down N S
Demo: Helmholtz coil and bar magnet
Demo: copper pipe and cow magnet
Demo 371

20. ACT: Change B II (cont’d)
If I reduce the resistance in the wire, the magnet will fall
faster
slower
at the same speed N S N S

21. Faraday’s and Lenz’s Law
Faraday: Induced emf = rate of change of magnetic flux
Lenz: Induced emf opposes change in flux
Demo 371: Helmholz coil and bar magnet
Since F= B A cos(f), 3 things can change F
Area of loop
Magnetic field B
Angle f between normal and B  
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