1) Faraday's law of induction states that an induced electromotive force (emf) is generated in a loop of wire when there is a change in the magnetic flux through the loop. The magnitude of the induced emf is equal to the negative rate of change of the magnetic flux. 2) Lenz's law describes the direction of the induced current and states that it will flow in the direction that opposes the change which produced it. This means the induced magnetic field will be in a direction opposite to the change in the external magnetic field. 3) Some examples covered include motional emf from a moving conductor in a magnetic field, an induction cannon demonstration where a coil produces a changing magnetic field

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

2. Physics 102: Lecture 10, Slide 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. Physics 102: Lecture 10, Slide 3
Motional EMF
V
• 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 bar acts like a battery (i.e. generates EMF)!!
Fq
(Recall that e- actually move,
opposite current)
+qI

4. Physics 102: Lecture 10, Slide 4
Faraday’s Law of Induction:
“induced EMF” = rate of change of magnetic flux
� = −
∆Φ
Δ�
= −
Φf − Φi
�� − ��
• 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. Physics 102: Lecture 10, Slide 5
First a preliminary: Magnetic Flux
• “Counts” number of field lines through loop.
Uniform magnetic field, B, passes
through a plane surface of area A.
A Magnetic flux Φ = B A
(Units Tm2
= Wb)
Magnetic flux Φ ≡ B A cos(φ)
φ is angle between normal and B
B
A
φ
normal
B
Note: The flux can be negative
(if field lines go thru loop in opposite direction)

6. Physics 102: Lecture 10, Slide 6
Preflight 10.7
Compare the flux through loops a and b.
1) Φa>Φb 2) Φa< Φb
a
b
n
n B
ΦA = B A cos(0) =
BAΦB = B A cos(90) = 0
“more lines pass through
its surface in that
position.”

7. Physics 102: Lecture 10, Slide 7
Faraday’s Law of Induction:
“induced EMF” = rate of change of magnetic flux
Since Φ= B A cos(φ), 3 things can change Φ
1. Area of loop
2. Magnetic field B
3. Angle φ between normal and B
� = −
∆Φ
Δ�
= −
Φf − Φi
�� − ��

8. Physics 102: Lecture 10, Slide 8
ACT: Change Area
1
v
v
3
Which loop has the greatest induced EMF at the
instant shown above?
L
W
2
v

9. Physics 102: Lecture 10, Slide 9
Faraday: Change Area
V
t=0
Φ0=BLW
t
Φt=BL(W+vt)
L
W
V
W vt
EMF Magnitude:
Φ = B A cos(θ)
ȁ�ȁ=
∆Φ
Δ�
=
Φf − Φi
� − 0
=
𝐵�(� + 𝑣�) − 𝐵��
� − 0
= 𝐵�𝑣
What about the sign of the EMF?

10. Physics 102: Lecture 10, Slide 10
Lenz’s Law (EMF direction)
V V
• Flux is increasing
• Induced current is clockwise
• Current loop generates induced B field
– from RHR2, into page, opposite external B field!
I
Bind
What happens if the velocity is reversed?

11. Physics 102: Lecture 10, Slide 11
Lenz’s Law (EMF direction)
V
V
• Flux is decreasing
• Induced current is counterclockwise
• Current loop generates induced B field
– from RHR2, out of the page, along external B field!
I
Induced EMF opposes change in flux
Bind

12. Physics 102: Lecture 10, Slide 12
Lenz’s Law (EMF Direction)
Induced emf opposes change in flux
EMF does NOT oppose B field, or flux!
EMF opposes the 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
� = −
∆Φ
Δ�
= −
Φf − Φi
�� − ��

13. Physics 102: Lecture 10, Slide 13
Motional EMF circuit
• Direction of Current
• B field generates force on current-carrying bar
I = ε/R
• Magnitude of current
Clockwise (+ charges go down thru bar, up thru
bulb)
Fbar = ILB sin(θ), to left (RHR1)
V
Fbar opposes v!
= vBL/R
I
Fq
+q
Fbar
• Careful! There are two forces:
Fbar = force on bar from induced current
Fq = force on + charges in bar driving induced current

14. Physics 102: Lecture 10, Slide 14
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
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
x x x x x x x x x x x x x
x x x x
Motional EMF circuit
I = ε/R = vBL/R
Still to left, opposite v
What happens if field is reversed? (TRY IT AT HOME)
V
• Direction of Current
• Direction of force (F=ILB sin(θ)) on bar due to
magnetic field
• Magnitude of current
Counter-Clockwise (+ charges go up thru bar, down
thru bulb)
F always opposes v, bar slows down
Must apply external force to keep
bar moving

15. Physics 102: Lecture 10, Slide 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(θ)

16. Physics 102: Lecture 10, Slide 17
Faraday’s Law of Induction:
“induced EMF” = rate of change of magnetic flux
Since Φ= B A cos(φ), 3 things can change Φ
1. Area of loop
2. Magnetic field B
3. Angle φ between normal and B
� = −
∆Φ
Δ�
= −
Φf − Φi
�� − ��


17. Physics 102: Lecture 10, Slide 18
ACT: Induction cannon (Demo)
As current increases in the solenoid, what direction
will induced current be in ring?
1) Same as solenoid
2) Opposite of solenoid
3) No current
Bsol
A solenoid is driven by an increasing current. A loop of wire is placed
around it

18. Physics 102: Lecture 10, Slide 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?

19. Physics 102: Lecture 10, Slide 20
Which way is the magnet moving if it is
inducing a current in the loop as shown?
1) Up
2) Down
ACT: Change B (Demo)
Demo 371

20. Physics 102: Lecture 10, Slide 21
ACT: Change B II (cont’d)
If I reduce the resistance in the wire, the
magnet will fall
1) faster
2) slower
3) at the same speed N
S

21. Physics 102: Lecture 10, Slide 24
Faraday’s and Lenz’s Law
Faraday: Induced emf = rate of change of magnetic flux
Since Φ= B A cos(φ), 3 things can change Φ
1. Area of loop
2. Magnetic field B
3. Angle φ between normal and B
� = −
∆Φ
Δ�
= −
Φf − Φi
�� − ��


Next lecture
Lenz: Induced emf opposes change in flux