# Class 21: Outline Hour 1: Expt. 9: Faraday’s Law Hour 2:

```Class 21: Outline
Hour 1:
Hour 2:
Transformers
Magnetic Materials
P21- 1
Last Time:
P21- 2
ε
dΦB
= −N
dt
Changing magnetic flux induces an EMF
Lenz: Induction opposes change
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What can change?
d
ε = −N ( BAcosθ )
dt
Quantities which can vary with time:
• Magnitude of B
• Area A enclosed by the loop
• Angle θ between B and loop normal
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Magnet Falling Through a Ring
http://ocw.mit.edu/ans78
70/8/8.02T/f04/visualizati
07FallMAgRes_f54_320.ht
ml
Falling magnet slows as it approaches a copper
ring which has been immersed in liquid nitrogen.
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Example: Magnitude of B
Magnet Falling Through a Ring
Falling magnet approaches a copper ring
or Copper Ring approaches Magnet
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Moving Towards Dipole
Move
ring
down
As ring approaches, what happens to flux?
It increases
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Moving Over Dipole
Flux
Move
down
Flux increases then decreases
Note we have arbitrarily assigned dA
up
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Moving Over Dipole
CCW
Current
Move
down
CW
Current first goes in one direction, then other
It ALWAYS opposes the changing flux
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Five PRS Questions:
Predictions for Experiment 9
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Experiment 9:
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CURRENT
FLUX
Imperfect
current 0
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Four PRS Questions:
Force on A Loop Below Magnet
Moving Upward;
Moving Rail;
Moving Rectangle near Wire;
Generator.
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Brakes
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Magnet Falling Through a Ring
What happened to kinetic energy of
magnet?
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Eddy Current Braking
http://demoroom.physics.ncsu.edu/html/demos
/163.html
What happened to kinetic energy of pendulum?
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Eddy Current Braking
http://demoroom.physics.ncsu.edu/multimedia/video/
5K20.22.1.MOV
What happened to kinetic energy of disk?
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Demonstration:
Eddy Current Braking
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Eddy Current Braking
The magnet induces currents in the metal that
dissipate the energy through Joule heating:
ω
1. Current is induced
counter-clockwise (out
from center)
2. Force is opposing motion
(creates slowing torque)
XX
XX
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Eddy Current Braking
The magnet induces currents in the metal that
dissipate the energy through Joule heating:
ω
XX
XX
1. Current is induced
clockwise (out from
center)
2. Force is opposing motion
(creates slowing torque)
3. EMF proportional to ω
2
4. .
ε
F∝
R
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Demonstration:
Levitating Magnet
Superconductor &amp; Magnet
http://ocw.mit.edu/ans7870/
8/8.02T/f04/visualizations/fa
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PRS Questions:
Loop in Uniform Field
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Mutual Inductance
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Mutual Inductance
A current I2 in coil 2, induces some
magnetic flux Φ12 in coil 1. We
define the flux in terms of a “mutual
inductance” M12:
N1Φ12 ≡ M 12 I 2
M 12 = M 21 = M
N1Φ12
→ M 12 =
I2
ε12 ≡ −M 12
dI 2
dt
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Demonstration:
Remote Speaker
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Transformer
Step-up transformer
εp
dΦB
= Np
dt
εs
dΦB
= Ns
dt
εs
εp
N
=
N
s
p
Ns &gt; Np: step-up transformer
Ns &lt; Np: step-down transformer
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Demonstrations:
One Turn Secondary:
Nail
Many Turn Secondary:
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Transmission of Electric Power
Power loss can be greatly reduced if
transmitted at high voltage
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Example: Transmission lines
An average of 120 kW of electric power is sent from
a power plant. The transmission lines have a total
resistance of 0.40 Ω. Calculate the power loss if the
power is sent at (a) 240 V, and (b) 24,000 V.
(a)
(b)
P 1.2 &times;105W
= 500 A
I= =
2
V 2.4 &times;10 V
PL = I 2 R = (500 A)2 (0.40Ω) = 100kW
P 1.2 &times;105W
I= =
= 5.0 A
4
V 2.4 &times;10 V
PL = I 2 R = (5.0 A) 2 (0.40Ω) = 10W
83% loss!!
0.0083% loss
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Magnetic Materials
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Recall Polar Dielectrics
Dielectric polarization
decreases Electric Field!
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Para/Ferromagnetism
Applied external field B0 tends to align the
atomic magnetic moments
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Para/Ferromagnetism
The aligned moments tend to increase the B field
G
G
B = κ mB0
G
Compare to: E =
G
E0
κE
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Para/Ferromagnetism
Paramagnet: Turn off B0, everything disorders
Ferromagnet: Turn off B0, remains (partially) ordered
This is why some items you can pick up with a
magnet even though they don’t pick up other itemsP21- 34
Magnetization Vector
M=0
M&gt;0
Useful to define “Magnetization” of material:
G
G 1
&micro;
G
M = ∑ &micro;i =
V i =1
V
N
G G
G
B = B0 + &micro;0M
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Hysteresis in Ferromagnets
The magnetization M of a ferromagnetic material
depends on the history of the substance
Magnetization remains even with B0 off !!!
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