# Physics 102 Lecture 10 Faraday’s Law Changing Magnetic Fields create Electric Fields Physics 102 Lecture 10 Slide 1

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```					      Physics 102: Lecture 10
Changing Magnetic Fields create Electric Fields

Physics 102: Lecture 10, Slide 1
Last Two Lectures
•     Magnetic fields
•     Forces on moving charges and currents
•     Torques on current loops
•     Magnetic field due to
– Long straight wire
– Solenoid

Physics 102: Lecture 10, Slide 2
Motional EMF
• A metal bar slides with velocity v on a track in a uniform B field

I          q +
V
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,
Physics 102: Lecture 10, Slide 3
opposite current)
“induced EMF” = rate of change of magnetic flux

∆Φ     Φf − Φi
���� = −     =−
Δ����    �������� − ��������

• 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
Physics 102: Lecture 10, Slide 4
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.
Magnetic flux F = B A
(Units Tm2 = Wb)
B
f                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 5
Preflight 10.7
n B
n                 “more lines pass through
b         its surface in that
a                     position.”

FA = B A cos(0) = BA
FB = B A cos(90) = 0

Compare the flux through loops a and b.
1) Fa>Fb                    2) Fa< Fb

Physics 102: Lecture 10, Slide 6

“induced EMF” = rate of change of magnetic flux

∆Φ     Φf − Φi
���� = −     =−
Δ����    �������� − ��������

Since F= B A cos(f), 3 things can change F
1. Area of loop
2. Magnetic field B
3. Angle f between normal and B
Physics 102: Lecture 10, Slide 7
ACT: Change Area
W            3
v   2
L       1
v
v

Which loop has the greatest induced EMF at the
instant shown above?

Physics 102: Lecture 10, Slide 8
W                                          W          vt

V                                        V
L

t=0                                    t
F0=BLW                              Ft=BL(W+vt)

F = B A cos(q)
∆Φ Φf − Φi ��������(���� + ��������) − ������������
EMF Magnitude: ���� =     =        =                      = ������������
Δ����   ���� − 0       ���� − 0

What about the sign of the EMF?
Physics 102: Lecture 10, Slide 9
Lenz’s Law (EMF direction)
I
V                           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?
Physics 102: Lecture 10, Slide 10
Lenz’s Law (EMF direction)
I          V
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
Physics 102: Lecture 10, Slide 11
Lenz’s Law (EMF Direction)
Induced emf opposes change in flux
∆Φ     Φf − Φi
���� = −     =−
Δ����    �������� − ��������
• 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

EMF does NOT oppose B field, or flux!
EMF opposes the CHANGE in flux
Physics 102: Lecture 10, Slide 12
Motional EMF circuit
• Magnitude of current                  I
q +     V
I = e/R = vBL/R
Fbar      Fq
• Direction of Current
Clockwise (+ charges go down thru bar, up thru bulb)

• B field generates force on current-carrying bar
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
Physics 102: Lecture 10, Slide 13
Motional EMF circuit
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
Still to left, opposite v   Must apply external force to keep
bar moving
Physics 102: Lecture 10, Slide 14
Preflight 10.4

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

Physics 102: Lecture 10, Slide 15

“induced EMF” = rate of change of magnetic flux

∆Φ     Φf − Φi
���� = −     =−
Δ����    �������� − ��������

Since F= B A cos(f), 3 things can change F

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

Physics 102: Lecture 10, Slide 18
Induction cannon (Demo)
A solenoid is driven by an increasing current. A loop of wire is placed
around it

S
• Recall: current loop behaves like bar magnet
• Opposite currents => opposite polarities

N
• Like poles repel! Loop shoots up

N
• What happens when loop has less resistance?

S
• What happens if the loop is broken?
Physics 102: Lecture 10, Slide 19
ACT: Change B (Demo)
Which way is the magnet moving if it is
inducing a current in the loop as shown?

S
1) Up
2) Down

N
Demo 371
Physics 102: Lecture 10, Slide 20
ACT: Change B II (cont’d)
If I reduce the resistance in the wire, the
magnet will fall

S
1) faster
2) slower

N
N
3) at the same speed
S

Physics 102: Lecture 10, Slide 21
Faraday: Induced emf = rate of change of magnetic flux
∆Φ     Φf − Φi
���� = −     =−
Δ����    �������� − ��������
Lenz: Induced emf opposes change in flux

Since F= B A cos(f), 3 things can change F

1.         Area of loop

2.         Magnetic field B
Next lecture 3. Angle f between normal and B
Physics 102: Lecture 10, Slide 24

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