1. Changing Magnetic Fields create Electric Fields
Physics 102: Lecture 10
Faraday’s Law
Changing Magnetic Fields create Electric Fields
Today’s lecture will cover Textbook Sections 20.1, 3-4
Include java applet for generator here.
Physics 102: Lecture 10, Slide 1 1

2. Faraday’s Law Key to EVERYTHING in E+M Changing B creates new E
Generating electricity
Microphones, Speakers and Tape Decks
Amplifiers
Computer disks and card readers
Ground Fault Interrupters
Changing B creates new E
Physics 102: Lecture 10, Slide 2

3. Motional EMF circuit Magnitude of current Direction of Current
Moving bar acts like battery E = vBL B
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
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
Direction of force (F=ILB sin(q)) on bar due to magnetic field
Physics 102: Lecture 10, Slide 3

4. Motional EMF circuit Magnitude of current Direction of Current?
Moving bar acts like battery E = vBL B
Magnitude of current V
I = E /R
= vBL/R
Direction of Current?
Direction of force (F=ILB sin(q)) on bar due to magnetic field?
Physics 102: Lecture 10, Slide 4

5. Motional EMF circuit Magnitude of current Direction of Current
Moving bar acts like battery E = vBL B - +
Magnitude of current V
I = E /R
= vBL/R
Direction of Current
Clockwise (+ charges go down thru bar, up thru bulb)
Direction of force (F=ILB sin(q)) on bar due to magnetic field
What changes if B points into page?
To left, slows down
Physics 102: Lecture 10, Slide 5

6. Motional EMF, Preflight 10.1B L v
F = q v B sin(q)
Which of the following statements is true?
positive charge accumulates at the top of the bar, negative at the bottom
since there is not a complete circuit, no charge accumulates at the bar's ends
negative charge accumulates at the top of the bar, positive at the bottom
Physics 102: Lecture 10, Slide 6

7. Motional EMF, Preflight 10.1B
Moving + charge feels force downwards:
F = q v B sin(q) v
Velocity + B
Moving + Charge still feels force downwards: L v
Potential Difference  F d/q
EMF = q v B sin(q) L/q =
Physics 102: Lecture 10, Slide 7

8. Motional EMF, Preflight 10.1B
Moving + charge feels force downwards:
F = q v B sin(q) v
Velocity + B
Moving + charge still feels force downwards: + - L v - +
|ΔV|  |ΔU| = Fd
EMF = q v B sin(q) L/q
= v B L q q
Velocity
Physics 102: Lecture 10, Slide 8

9. Preflight 10.2 Which bar has the larger motional emf? v a b v
E = v B L sin(q)
q is angle between v and B
Case a:
Case b:
Physics 102: Lecture 10, Slide 9

10. Preflight 10.2 Which bar has the larger motional emf? v a b v
E = v B L sin(q)
q is angle between v and B
Case a:
Case b:
v perpendicular to B
Physics 102: Lecture 10, Slide 10

11. Preflight 10.4, 10.5
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:
Increase Stay the Same Decrease
To keep the bar moving to the right, the hand will have to supply a
force in the opposite direction:
True False
Physics 102: Lecture 10, Slide 11

12. Preflight 10.4 Increase Stay the Same Decrease F = ILB sin(q)
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:
Increase
Stay the Same
Decrease
F = ILB sin(q)
B and v still perpendicular (q=90), so F=ILB just like before!
Physics 102: Lecture 10, Slide 12

13. Preflight 10.5
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.
True
False
Current flows in the opposite direction, so force from the B field remains the same!
Physics 102: Lecture 10, Slide 13

14. Magnetic Flux Count 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 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)
Physics 102: Lecture 10, Slide 14

15. Preflight 10.7 Compare the flux through loops a and b.
FA =
FB =
Compare the flux through loops a and b.
1) Fa>Fb ) Fa< Fb
Physics 102: Lecture 10, Slide 15

16. Preflight 10.7 Compare the flux through loops a and b.
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
Physics 102: Lecture 10, Slide 16

17. Faraday’s Law (EMF Magnitude)
Emf = Change in magnetic Flux/Time
Since F= B A cos(f), 3 things can change F 1. 2. 3.
Physics 102: Lecture 10, Slide 17

18. Faraday’s Law (EMF Magnitude)
Emf = Change in magnetic Flux/Time
Since F= B A cos(f), 3 things can change F
Area of loop
Magnetic field B
Angle f between A and B
Physics 102: Lecture 10, Slide 18

19. Lenz’s Law (EMF Direction)
Emf opposes change in flux
If flux increases:
New EMF makes new field _________ original field
If flux decreases:
Put example here for directions
Physics 102: Lecture 10, Slide 19

20. Lenz’s Law (EMF Direction)
Emf opposes change in flux
If flux increases:
New EMF makes new field opposite to the original field (to oppose the increase)
If flux decreases:
New EMF makes new field in the same direction as the original field (to oppose the decrease)
Put example here for directions
Physics 102: Lecture 10, Slide 20

21. Preflight 10.9 a n B a n B
The magnetic field strength through the loop is cut in half (decreasing the flux). If you wanted to create a second magnetic field to oppose the change in flux, what would be its direction?
Left Right
Physics 102: Lecture 10, Slide 21

22. Preflight 10.9 a n B a n B
The magnetic field strength through the loop is cut in half (decreasing the flux). If you wanted to create a second magnetic field to oppose the change in flux, what would be its direction?
Left Right
The original flux is to the right and decreasing. To oppose the change and keep the total field strength the same, add another field in the same direction.
Physics 102: Lecture 10, Slide 22

23. ACT: Change Area 3 W 2 1 v L v v
Which loop has the greatest induced EMF at the instant shown above?
Loop 1 Loop Loop 3
Physics 102: Lecture 10, Slide 23

24. ACT: Change Area 3 W 2 1 v L v v
Which loop has the greatest induced EMF at the instant shown above?
1 moves right - gets 4 more field lines.
2 moves down - gets 0 more field lines.
3 moves down - only gets 2 more lines.
1 is gaining flux fastest!
E 1 = vBL
E 2 = 0
E 3 = vBW
Physics 102: Lecture 10, Slide 24

25. Change Area II F = B A cos(f) W V W vt V L I t=0 F0=BLW t Ft=BL(W+vt)??
EMF Magnitude: = =
EMF Direction: B is out of page and F is increasing so EMF creates B field (inside loop) going ________.
Physics 102: Lecture 10, Slide 25

26. Change Area II F = B A cos(f) W V W vt V L I t=0 F0=BLW t Ft=BL(W+vt)
EMF Magnitude:
EMF Direction: B is out of page and F is increasing so EMF creates B field (inside loop) going into page.
Physics 102: Lecture 10, Slide 26

27. ACT: Change B
As current is increasing in the solenoid, what direction will current be induced in ring? N
Same as solenoid
Opposite of solenoid
No current S
Physics 102: Lecture 10, Slide 27

28. ACT: Change B SN
As current is increasing in the solenoid, what direction will current be induced in ring?
Same as solenoid
Opposite of solenoid
No current
 Solenoid current (counter-clockwise)
 B-field (upwards) =>  Flux thru loop
EMF will create opposite B-field (downwards)
Induced loop current must be clockwise
Physics 102: Lecture 10, Slide 28

29. ACT: Change B II
Which way is the magnet moving if it is inducing a current in the loop as shown? Up
Down S N N S
If I reduce the resistance in the wire, the magnet will fall
Faster slower at the same speed
Physics 102: Lecture 10, Slide 29

30. ACT: Change B II
Which way is the magnet moving if it is inducing a current in the loop as shown? Up
Down S N N S
If I reduce the resistance in the wire, the magnet will fall
Faster slower at the same speed
larger induced current, stronger magnetic field
Physics 102: Lecture 10, Slide 30

31. Change f
A flat coil of wire has A=0.2 m2 and R=10W. At time t=0, it is oriented so the normal makes an angle f0=0 w.r.t. a constant B field of 0.12 T. The loop is rotated to an angle of =30o in 0.5 seconds. Calculate the induced EMF.
Example n B A f
What direction is the current induced?
Physics 102: Lecture 10, Slide 31

32. Change f
A flat coil of wire has A=0.2 m2 and R=10W. At time t=0, it is oriented so the normal makes an angle f0=0 w.r.t. a constant B field of 0.12 T. The loop is rotated to an angle of =30o in 0.5 seconds. Calculate the induced EMF.
Example
Fi = B A cos(0)
Ff = B A cos(30) n B A f
e = 6.43x10-3 Volts
What direction is the current induced?
F upwards and decreasing. New field will be in same direction (opposes change). Current must be counter clockwise.
Physics 102: Lecture 10, Slide 32

33. Magnetic Flux Examples
A conducting loop is inside a solenoid (B=monI). What happens to the flux through the loop when you…
Increase area of solenoid?
Increase area of loop?
Increase current in solenoid?
F  B A cos(f)
Rotate loop slightly?
Physics 102: Lecture 10, Slide 33

34. Magnetic Flux Examples
A conducting loop is inside a solenoid (B=monI). What happens to the flux through the loop when you…
Increase area of solenoid? No change
Increase area of loop? Increases
Increase current in solenoid? Increases
F  B A cos(f)
Rotate loop slightly? Decreases
Physics 102: Lecture 10, Slide 34

35. Magnetic Flux II Example
A solenoid (B=monI) is inside a conducting loop. What happens to the flux through the loop when you…
Increase area of solenoid Increases
Increase area of loop No change
Increase current in solenoid Increases
F  B A cos(f)
Physics 102: Lecture 10, Slide 35

36. See you later!
Read Sections 20.2, 6
Physics 102: Lecture 10, Slide 36