1. Physics 212
Lecture 17
Faraday’s Law

2. Music Who is the Artist? Oscar Peterson Kenny Barron Dave Brubeck
Thelonius Monk
Marcus Roberts
Why? Time to return to classic jazz
Most unique piano player??
Check out the Jazz Biography CD (couldn’t find a picture) great recordings from 40’s and 50’s
Also: MUST SEE DVD: “Straight No Chaser”: 2000
Physics 212 Lecture 23

3. Music Will I get points for this question? Yes and no Maybe
Who is “I”? You? You won’t get points.
I get The point
It’s a pointless question
Physics 212 Lecture 23

4. Your Comments
“Everything is coming together, electricity and magnetism...woah!”
“Teardrop =(”
We’ll go through the concepts in some detail again.
“I HAVE NO IDEA WHAT IS GOING ON! I think the best way to understand electricity would be to put a fork into an outlet.”
“THIS LECTURE IS WAY TOO HARD”
Some of the derivations were a little unclear. Specifically, is Faraday's Law simply a product of experiment or can it be mathematically derived from things we've already learned?
Checkpoints and demos!
“The falling loop problem”
“DEMOS”
“The most difficult part of this section is determining which direction a current is induced when it has a changing magnetic flux through it.”
The generator example makes me totally confused and I don't understand the second checkpoint in the prelecture.
Why was magnetic flux on the homework that's due tomorrow morning?
“I never thought I would B INtroDUCED to a concept as confusing as this”
“Man, this stuff if giving me acid reFLUX.”
Hour Exam II – Wed. Oct. 26: Lect 9-18
Signup for conflicts TODAY! (Hard deadline Thu. Oct :00 p.m.)
Please do not display this in lecture but that picture on this checkpoint with the falling conducting loop looked a LOT McDonalds like french fries. 05
this is so frust... so frux.... so flux-terating!!
Daniel Faraday is my favorite Faraday. LOST 4

5. *Remember: we started by applying to wires
Faraday’s Law:
where
Looks scary but it’s not – its amazing and beautiful !
A changing magnetic flux produces an electric field.
Electricity and magnetism are deeply connected
*Remember: we started by applying to wires

6. When B-dot-A changes, what “f” causes the EMF?
Faraday’s Law:
where
and f is force / unit charge:
A changing magnetic flux can drive current around a loop  electromagnetic battery!
When B-dot-A changes, what “f” causes the EMF?
“A” or “dot” changes (moving or rotating loops)  f = v x B = familiar magnetic force
B changes  f = E = induced electric field
NEW TYPE OF ELECTRIC FIELD! Caused by dB/dt not charges; its field lines make loops!

7. Faraday’s Law: B A In Practical Words: Flux
Think of FB as the number of field lines passing through the surface
Flux
Faraday’s Law:
where
In Practical Words:
1) When the flux FB through a loop changes, an emf is induced in the loop. B A
There are many ways to change this…

8. EMF caused by magnetic force: f = v x B
Faraday’s Law:
where
In Practical Words:
1) When the flux FB through a loop changes, an emf is induced in the loop. A B
Move loop to a place where the B field is different
EMF caused by magnetic force: f = v x B

9. EMF caused by magnetic force: f = v x B
Faraday’s Law:
where
In Practical Words:
1) When the flux FB through a loop changes, an emf is induced in the loop. A B
EMF caused by magnetic force: f = v x B
Rotate the loop

10. EMF caused by magnetic force: f = v x B
Faraday’s Law:
where
In Practical Words:
1) When the flux FB through a loop changes, an emf is induced in the loop. B A
EMF caused by magnetic force: f = v x B
Rotate the loop

11. EMF caused by magnetic force: f = v x B
Faraday’s Law:
where
In Practical Words:
1) When the flux FB through a loop changes, an emf is induced in the loop. B A
EMF caused by magnetic force: f = v x B
Rotate the loop

12. Faraday’s Law: B A In Practical Words:
where
In Practical Words:
1) When the flux FB through a loop changes, an emf is induced in the loop. A
Nothing’s moving ... So no magnetic force … B
Change the B field
EMF caused by electric force: f = E
dB/dt creates an electric field ! often called an “induced E-field”

13. Faraday’s Law: I In Practical Words:
where
In Practical Words:
1) When the flux FB through a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery). I

14. Faraday’s Law: I In Practical Words:
where
In Practical Words:
1) When the flux FB through a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery).
3) The current that flows generates a new magnetic field. I

15. Checkpoint 1
Suppose a current flows in a horizontal conducting loop in such a way that the magnetic flux produced by this current points upward.
As viewed from above, in which direction is this current flowing?

16. Faraday’s Law: B dB/dt In Practical Words:
where
In Practical Words:
1) When the flux FB through a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery).
3) The current that flows induces a new magnetic field.
4) The new magnetic field opposes the change in the original magnetic field that created it  Lenz’s Law B
dB/dt

17. Demo Faraday’s Law: B dB/dt In Practical Words:
where
In Practical Words:
1) When the flux FB through a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery).
3) The current that flows induces a new magnetic field.
4) The new magnetic field opposes the change in the original magnetic field that created it  Lenz’s Law B
Demo
dB/dt

18. Checkpoint 2
A magnet makes the vertical magnetic field shown by the red arrows. A horizontal conducting loop is entering the field as shown.
At the instant shown, what is the direction of the additional flux produced by the current induced in the loop?

19. Checkpoint 3
A magnet makes the vertical magnetic field shown by the red arrows. A horizontal conducting loop passes through the field from left to right as shown.
The upward flux through the loop as a function of time is shown by the blue trace. Which of the red traces best represents the current induced in the loop as a function of time as it passes over the magnet? (Positive means counter-clockwise as viewed from above.)

20. Executive Summary: Faraday’s Law:
where
Executive Summary:
emf→current→field a) induced only when flux is changing
b) opposes the change

21. Old Checkpoint 2
A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet
“Please do not display this in lecture but that picture on this checkpoint with the falling conducting loop looked a LOT McDonalds like french fries.”
(copper is not ferromagnetic)
Will the acceleration a of the falling ring in the presence of the magnet be any different than it would have been under the influence of just gravity (i.e. g)?
A. a > g B. a = g C. a < g

22. Old Checkpoint 2 F B Like poles repel Ftotal < mg a < g
A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet
Like poles repel F X O B
(copper is not ferromagnetic)
Ftotal < mg
Will the acceleration a of the falling ring in the presence of the magnet be any different than it would have been under the influence of just gravity (i.e. g)?
A. a > g B. a = g C. a < g
a < g
This one is hard !
B field increases upward as loop falls
Clockwise current (viewed from top) is induced

23. Old Checkpoint 2 Demo ! HOW IT WORKS Looking down B I IL X B points UP
A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet
HOW IT
WORKS I
Looking down B
IL X B points UP
(copper is not ferromagnetic)
Will the acceleration a of the falling ring in the presence of the magnet be any different than it would have been under the influence of just gravity (i.e. g)?
A. a > g B. a = g C. a < g
Ftotal < mg
a < g
This one is hard !
B field increases upward as loop falls
Clockwise current (viewed from top) is induced
Demo !
dropping magnets
e-m cannon
Main Field produces horizontal forces
“Fringe” Field produces vertical force

24. Calculation Conceptual Analysis Strategic Analysis
A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction.
What is the direction and the magnitude of the force on the loop when half of it is in the field? y B b
x x x x x x x a v0 x
Conceptual Analysis
Once loop enters B field region, flux will be changing in time
Faraday’s Law then says emf will be induced
Strategic Analysis
Find the emf
Find the current in the loop
Find the force on the current

25. In a time dt it moves by v0dt
Calculation
A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. y x v0 a b
x x x x x x x B
What is the magnitude of the emf induced in the loop just after it enters the field?
(A) e = Babv02 (B) e = ½ Bav0 (C) e = ½ Bbv0 (D) e = Bav0 (E) e = Bbv0 y x v0 a b
x x x x x x x B
Change in Flux = dFB = BdA = Bav0dt a
The area in field changes by dA = v0dt a
In a time dt it moves by v0dt

26. Calculation
A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. y B b
x x x x x x x a v0 x
What is the direction of the current induced in the loop just after it enters the field?
(A) clockwise (B) counterclockwise (C) no current is induced
emf is induced in direction to oppose the change in flux that produced it y x v0 a b
x x x x x x x B
Flux is increasing into the screen
Induced emf produces flux out of screen

27. Force on a current in a magnetic field:
Calculation
A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. y B b
x x x x x x x a v0 x
What is the direction of the net force on the loop just after it enters the field?
(A) +y (B) -y (C) +x (D) -x
Force on a current in a magnetic field: x y v0 a b
x x x x x x x B I
Force on top and bottom segments cancel (red arrows)
Force on right segment is directed in –x direction.

28. Calculation
A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. y B b
x x x x x x x a v0 x
What is the magnitude of the net force on the loop just after it enters the field?
e = Bav0
(A) (B) (C) (D)
since x y v0 a b
x x x x x x x B I F
ILB

29. Follow-Up
t = dt: e = Bav0
A rectangular loop (sides = a,b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction.
What is the velocity of the loop when half of it is in the field? y B
x x x x x x x b v0 a x
Which of these plots best represents the velocity as a function of time as the loop moves form entering the field to halfway through ?
(A) (B) (C) D) (E) X
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. v0 a b
x x x x x x x B I
Fright
This is not obvious, but we know v must decrease
Why?
Fright points to left
Acceleration negative
Speed must decrease

30. Follow-Up
A rectangular loop (sides = a,b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction.
What is the velocity of the loop when half of it is in the field? y B
x x x x x x x b v0 a x
e = Bav0
Which of these plots best represents the velocity as a function of time as the loop moves form entering the field to halfway through ?
(A) (D)
Why (D), not (A)?
F is not constant, depends on v
where
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
Claim: The decrease in kinetic energy of loop is equal to the energy dissipated as heat in the resistor. Can you verify??
Challenge: Look at energy

31. Old Checkpoint 1a
A copper loop is placed in a uniform magnetic field as shown. You are looking from the right.
Suppose the loop is moving to the right. The current induced in the loop is:
A. zero B. clockwise C. counterclockwise

32. Old Checkpoint 1a Motional emf is ZERO v X B = 0 no charge separation
A copper loop is placed in a uniform magnetic field as shown. You are looking from the right.
Suppose the loop is moving to the right. The current induced in the loop is:
A. zero B. clockwise C. counterclockwise
Motional emf is ZERO
v X B = 0
no charge separation
no E field
no emf
The flux is NOT changing
B does not change
the area does not change
the orientation of B and A does not change

33. Old Checkpoint 1b Checkpoint 1b
A copper loop is placed in a uniform magnetic field as shown. You are looking from the right.
Now suppose the that loop is stationary and that the magnetic field is decreasing in time. The current induced in the loop is:
A. zero B. clockwise C. counterclockwise
Checkpoint 1b

34. Old Checkpoint 1b Looking from right Checkpoint 1b
A copper loop is placed in a uniform magnetic field as shown. You are looking from the right.
X X X X X X X X
Looking from right
Clockwise restores B
Now suppose the that loop is stationary and that the magnetic field is decreasing in time. The current induced in the loop is:
A. zero B. clockwise C. counterclockwise
Checkpoint 1b
Motional emf is ZERO
There is no motion of conduction electrons !
HOWEVER: The flux IS changing
B decreases in time
current induced to oppose the flux change
clockwise current puts back B that was removed
THIS IS NEW !!
Faraday’s Law explains existence of emf when the motional emf is ZERO!

35. Old Checkpoint 1c
Now suppose that the loop is spun around a vertical axis as shown, and that it makes one
complete revolution every second.
The current induced in the loop:
A. Is zero
B. Changes direction once per second C. Changes direction twice per second

36. (B  dA = max)  d/dt (B  dA ) = 0
Old Checkpoint 1c
Now suppose that the loop is spun around a vertical axis as shown, and that it makes one
complete revolution every second.
The current induced in the loop:
A. Is zero
B. Changes direction once per second C. Changes direction twice per second
Current changes direction every time the loop becomes perpendicular with the B field
emf ~ dF/dt
(B  dA = max)  d/dt (B  dA ) = 0 X O B dA X O B dA