Transcript induction_2014mar

VIII. Magnetic Induction
Dr. Bill Pezzaglia
Updated 2014Mar
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VIII. Magnetic Induction
A. Dynamos & Generators
B. Faraday’s Law
C. Inductance
Michael Faraday (1791 - 1867)
• 1821 Creates first motor
• 1831 Creates “dynamo”, a DC
generator
• 1831 Law of induction
• 1846 Discovers Diamagnetism
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A. Dynamos & Generators
1) Dynamo Rule
2) Motional EMF
3) Mechanical to Electric Power
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1. Dynamo Rule
(a) Faraday (1831)
•
Move a wire so that it “cuts”
magnetic field lines will generate
current

 
F  qvB
•
Recall
•
Positive charges in wire will move
one direction, negative the other
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1.(a).ii Planetary Dynamos
Moon Io moving orbiting through Jupiters magnetic field
generates BIG current
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1.(a).iii Planetary Dynamos
The electric currents generate so much heat the moon
has active volcanoes!
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(b) Magnetohydrodynamic Generators (MHD)
1832 Faraday’s Fluid Generator experiment at Waterloo Bridge:
attempts to measure current generated from velocity of Thames cutting
through earth’s magnetic field (didn’t work too well).

 
F  qvB
+
(b).ii
MHD Generators
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(c). Faraday’s Disk Dynamo (1831)
This was the first practical DC generator. It gives
high current, but low voltage.
I
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2. EMF (Electromotive Force)
(a) Definition of EMF ()
•
Misnomer: its not really a “force”, it’s a
“voltage” (i.e. ENERGY per charge)
•
Chemical EMF: A battery is like a
“pump”. When charges pass through,
their energy is increased. Change in
voltage=“EMF”
Work

q
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2.(b). Motional EMF
•
Magnetic (“Dynamo”) Work done by
moving a length “L” wire through magnetic
field “B” with velocity “v” generates an EMF
Work FL (qvB) L



q
q
q
•
General Result, only the part
of velocity, magnetic field and
wire path which are mutually
perpendicular will contribute.
  
  (v  B )  L
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2.(c). AC Generator
1892 Tesla (working for Edison) invents AC Generator.
Edison hates the idea (he is using DC dynamos), and so
Tesla sells it to Westinghouse. Edison goes on a campaign
to convince people AC is DANGEROUS while DC is safe.
http://www.youtube.com/v/i-j-1j2gD28
2.(c).ii AC Generator Details
•
Rectangle area: A=ab
•
a
Velocity: v  
2
•
EMF:
  
  (v  B )  L  vBL sin 
 a 
    B (2b) sin 
 2 
  BA sin 
  t
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3. Mechanical to Electric Power
(a) Electric Power Output:
P  I
(b) Current created will experience
force from magnetic field, which
is in opposite direction as “v”

 
F  I LB
(c) Mechanical Work: by Newton’s
3rd law, we must PUSH the wire
through with force F, or power:
 
P  F  v  ( ILB )v  I ( LBV )  I
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B. Faraday’s Law
1) Magnetic Flux
2) Faraday’s Law
3) Lenz’s Law
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1831 Faraday’s Three Experiments
Generated current by:
• Moving a coil in and out of a
magnetic field
• Moving magnet in and out of coil
• When current turned on or off in a
coil, current is generated in a nearby
coil.
He explained all of these effects with one single law
Michael Faraday
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1. Magnetic Flux
(a) Definition:
• Magnetic Flux is the Magnetic Field “B”
(aka “Magnetic Intensity Vector”) times
area it “flows” through
BA
•
Units: Weber=Teslam2
Greek Letter: “phi”  or 
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(b) Lambert’s Law (Orientation matters!)
Lambert’s Law (1760)
Intensity is reduced by
cosine of angle of
incidence
Sunlight coming in
at a low altitude
angle will have its
energy spread out
over more area.
Flux is the dot product of
the electric field vector
with the “area vector”
(which is “normal” to the
surface)
 
  B  A  BA cos 
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(c) Magnetic Flux is Conserved
•
Because there are no
magnetic monopoles, there
are no “sources” of
magnetic field lines.
•
Magnetic Field Lines must
be continuous (i.e. continue
through magnet)
•
Gauss’s law for magnetism: total
magnetic flux through a closed
surface is ZERO.
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2. Faraday’s Law of Induction (1831)
•
Possibly done 1830 by Henry (unpublished)
•
The EMF generated in a loop of wire is equal to the
change in magnetic flux through the loop (with
respect to time)

 
t
•
You can get a change of flux in 2 ways

  
  (B )  A  B  ( A)
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(a) Change the Area of Loop
•
Consider sliding wire in constant magnetic field

A
 
 B
t
t
  () BvL
•
This is equivalent to
Dynamo Rule
(motional emf)
A
 vL
t
(b) Or, change the orientation of loop
•
Consider AC generator, where we twist the loop
  BA cos 

  
 
 BA sin  

t
 t 
  BA sin 
•
This is equivalent to Dynamo
Rule (motional emf)
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(c) Change Magnetic Field
•
You can NOT explain this one by dynamo rule, as
no wires move!

B
 
 A
t
t
•
However, it makes perfect
sense because motion is
relative. Whether you think
the magnet is moving with the
coil still, or the magnet still
with the coil moving merely
depends upon the motion of
the observer!
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3. Lenz’s Law (1834)
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(a) The law: Direction of induced current is
such as to oppose the cause producing it.
•
It’s the minus sign
in Faraday’s Law

 
t
Heinrich Lenz
1804-1864
(b). Eddy Currents
•
1824, François Arago discovers when conductor is exposed
to changing magnetic field, small circular “eddy currents”
(also known as Foucault currents) are generated.
•
1855, J.B.L. Foucault rotates a copper disc with rim between
poles of magnet and discovers that the induced eddy currents
in the metal cause:
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• Inductive Braking: the force required for the rotation of
a copper disc becomes greater with magnet (even though
copper is not attracted by a magnet)
• Inductive Heating: the disc becomes heated by the eddy
current (i.e. “friction”), because of resistance of metal.
Braking (tubes) http://www.youtube.com/watch?v=sPLawCXvKmg
http://www.magnet.fsu.edu/education/community/slideshows/eddycurrents/index.html
(c). Magnetic Levitation
•
Lenz’s law is usually demonstrated
by “Elihu Thomson's jumping ring”
(1887? 1897?).
•
The induced current in the metal ring
creates an electromagnetic that
opposes the applied field, lifting the
ring.
Jumping Ring: http://www.youtube.com/watch?v=Pl7KyVIJ1iE
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(d). Magnetic Levitation
•
Meissner Effect (1933) for
superconductors, the eddy
currents are so strong that
they become perfectly
diamagnetic, cancelling the
external field, inducing
magnetic levitation.
•
Application: Magnetically
levitated trains!
JR-Maglev EDS suspension is due to
the magnetic fields induced either side
of the vehicle by the passage of the
vehicle's superconducting magnets. -Wikipedia
Meissner Effect: http://www.youtube.com/watch?v=94-Z2QgHl-s&feature=related
Train: http://www.youtube.com/watch?v=GHtAwQXVsuk
C. Inductance
1) Mutual Induction (Transformers)
2) Self Inductance & RL circuits
3) Energy in Inductors
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1. Mutual Induction
(a) 1831 Faraday notes when current
turned on or off in a coil, voltage is
generated in a nearby coil.
• Define Mutual Inductance “M” (units
of Henries=ohmsec)
I 1
 2  M 21
t
• If first coil is solenoid, then can show
A2
M 21   0 N1 N 2
1
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(a).ii Coefficient of Coupling [DETAILS]
• Loosely Coupled: if coils are far apart, not all
of magnetic flux from first coil goes through
the second (flux leakage). Early transformers
were very inefficient because of this.
• Tightly Coupled: either have coils wrapped
around each other, or share same iron core so
that nearly all flux from one goes through
other.
• Reciprocity: If make coils same length with
same area, and tightly coupled, then mutual
inductance is same both ways (“L” is self
inductance to be discussed in next section)
M 21  M 12  L1 L2
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(b) Ruhmkorff Induction Coil
• Probably first invented by invented by Nicholas
Callan in 1836.
• 1851 Ruhmkorff shows if secondary coil has
many more windings than primary, then a BIG
voltage can be generated from a small one.
• DC current in primary creates magnetic field
• Current is periodically “interrupted” by a
vibrating switch, causing field to collapse
• BIG voltage is generated in secondary by
Faraday’s law
• This was how early Cathode Ray, X-ray and
“neon signs” were powered.
https://www.youtube.com/watch?v=1C4lOAPBu7A
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(c) Transformer Equation
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• Nikola Tesla pioneered the idea of using AC
current, transmitting power at high voltages
(low current) and then using transformers to
step it back down to low voltage for user.
• 1884 “Closed Flux Transformer” invented:
the flux through both coils is the same:

V2  N 2
t

V1  N1
t
Divide the equations to get the transformer rule:
V2 N 2 I 1


V1 N1 I 2
Note that power is conserved!
V1 I1  V2 I 2
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2. Self Inductance
(a) Probably done first by Joseph Henry 1830, a
year before Faraday.
• Current in coil makes a magnetic field. Change
in current changes field, which by Faraday’s law
creates a voltage in the coil (by Lenz law a
“back emf” which opposes change). Definition
of (self) inductance:
I
V L
t
B
LN
I
• Details: Self Inductance “L” is a function only of
geometric (and magnetic permeability) of coil.
Generally goes like square of number of turns N.
For solenoid of length l and area “A” with iron core
of permeability :
A
L  N

2
b. Inductor Combinations
• Rules for networks of inductors is similar to
resistors (hence opposite of capacitors)
• In Series: Inductors ADD
L  L1  L2
• In Parallel: Inductors combine:
1 1 1
 
L L1 L2
or
L1 L2
L
L1  L2
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(c) Inductor Behavior
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•
In brief, Inductors resist change in current
•
The inductor has zero current initially, and when you close the switch,
the inductor creates a back voltage to resist current trying to flow
through it. Instead the current flows freely through the light bulb.
•
Over time, the current starts to flow through the inductor and energy
is stored in the magnetic field it creates.
•
When you open the switch, the inductor
try to keep the current flowing, so it will
attempt to supply any voltage necessary
to do so. The bulb will light until the
magnetic field collapses (exponentially).
However, the BIG voltage surge might
burn the bulb out!
Demo of Back EMF: http://www.youtube.com/watch?v=aSmMFog10D0
(c) RL Circuits (incomplete)
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•
No notes here, see section 26.5 in book
•
In brief, RL circuits behave complementary to RC circuits. Inductors
try to keep the current flowing, so if there is an abrupt loss of current,
inductors will attempt to supply any voltage necessary to keep the
current flowing, the current will decay exponentially with time
constant:
I (t )  I 0 exp  t 
L

R
•
Complementary, the RC circuit: capacitors try to keep the voltage the
same, so if there is an abrupt loss of voltage, the capacitor will
attempt supply any current necessary to keep the voltage up. The
voltage will decay exponentially with time.
3. Energy Stored in Inductor
• Energy in Inductor:
U  LI
1
2
2
• You can think of it as “kinetic energy of
current” stored in the inductor (whereas a
capacitor stores “potential energy” of charge)
• Using the equations for magnetic field and
inductance of a solenoid coil, you can show:
1 2
U
B volume
2
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b. Energy Density
•
Divide by volume (of a solenoid coil)
U
1 2
u

B
vol 2
•
In other words, the energy of an inductor
is stored in the magnetic field itself!
[Whereas for a capacitor its stored in the electric field]
•
This energy creates a “magnetic
pressure” that tries to push a coil apart
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c. Forces on Cores etc.
• If you insert a core, you increase the
inductance by factor Km:
  K m 0
L  Km L
• Hence, increase the energy. Hence
inductors will want to push cores
out (doorbell or induction gun).
• By inserting core, you change
inductance, so more correct formula
for voltage (with possible sign
errors):
I
L
V L
I
t
t
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References
•1831 Faraday Law of Induction
•Neat video: http://www.youtube.com/watch?v=yahQtxBV5vA&feature=related
•http://www.youtube.com/watch?v=VPxdl1zpcC8&feature=related
•Magnetic flux and orientation: http://www.youtube.com/watch?v=KXFXUrBWp-c&feature=related
•AC generator http://www.youtube.com/watch?v=gqA3WoOunEA&feature=related
•Even better AC generator: http://www.youtube.com/watch?v=i-j-1j2gD28&NR=1
•Variable AC generator: http://www.youtube.com/watch?v=mCvXa_VVFh4&feature=related
•Simulations: http://www.esjd.pt/recursos_educativos/phet1.0/new/simulations/index1057.html?cat=All_Sims
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Schedules/Reading
In Knight “College Physics” (2nd ed)
• Faraday’s Law, Chapter 25.1-25.4
• Transformer 26.2
• RL circuit 26.5, and lab notes.
•
Skip 25.5-25.8 for now (Maxwell’s
Equations)