preparing the lecture we applied figures from:
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Preparing the lecture we applied figures from: Nondestructive Testing Resource Center www.ndt-ed.org Lectures of Dr. Ali R. Koymen, University of Texas, Arlington USA www.uta.edu./physics/main/faculty/koymen/ - PowerPoint PPT PresentationTRANSCRIPT
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Preparing the lecture we applied figures from:• Nondestructive Testing Resource Center www.ndt-ed.org• Lectures of Dr. Ali R. Koymen, University of Texas, Arlington USA www.uta.edu./physics/main/faculty/koymen/• Lectures of Prof. John G. Cramer, University of Washington, Seattle
USA, faculty.washington.edu/jcramer/• Lectures of Prof. Alan Murray, University of Edinburgh UK, http://
www.see.ed.ac.uk/~afm/?http://oldeee.see.ed.ac.uk/~afm/• Lectures of Prof. Horst Wahl, Florida State University, Tallahassee
USA, http://www.hep.fsu.edu/~wahl/• Lectures of G.L. Pollack and D.R. Stump, Michigan State University,
USA, http://www.pa.msu.edu/• Lectures of Professor Joachim Raeder, University of New Hampshire
USA, www.physics.unh.edu/phys408/
W. Borys and K. Zubko
Military University of Technology, Institute of Applied Physics, Warsaw Poland
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Faraday's Law
by W. Borys and K. Zubko
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(electro)magnetic induction - indukcja (elektro)magnetyczna [repelling; attracting] force - siła [odpychania; przyciągania]
[N; S] pole of a magnet - biegun [pn; płd] magnesu [electric; magnetic (E-, B-)] field - pole [elektryczne; magnetyczne]
electric field intensity E - natężenie pola elektrycznego E[tangent; perpendicular] to the curve - [styczny; prostopadły] do krzywej
electromotive force (emf) - siła elektromotorycznamagnetic flux - strumień pola magnetycznego
rate of change - szybkość zmian X to Y ratio = stosunek X/Y voltage - napięcie elektryczne
current intensity I - natężenie prądu Ielectric circuit - obwód elektryczny
current [increase; decrease (= decay)] - [wzrost; zanik] prądutime derivative of a function - pochodna funkcji po czasie
equation - równanielength = długość
sense of a vector = zwrot wektora[scalar; vector] product = iloczyn [skalarny; wektorowy]
infinitely small = nieskończenie mały line integral - całka liniowa, cyrkulacja
closed surface integral - całka po powierzchni zamkniętej[coil; turn of winding] - zwój, pętla
[mutual; self-] inductance - indukcyjność [wzajemna; własna]eddy currents - prądy wirowe
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ELECTROMAGNETIC INDUCTIONELECTROMAGNETIC INDUCTION
• Review of some magnetic phenomenaReview of some magnetic phenomena• Motional Electromotive Force (emf)Motional Electromotive Force (emf)• Faraday’s Law of Eectromagnetic InductionFaraday’s Law of Eectromagnetic Induction• Lenz’s LawLenz’s Law• Induced Electric FieldsInduced Electric Fields• Mutual Mutual IInductancenductance• Self Self - I- Inductancenductance• Energy in Energy in IInductornductor• LR LR CCircuitircuit
• Eddy CurrentsEddy Currents• Electromagnetic Waves-introductionElectromagnetic Waves-introduction
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Magnetic field around a permanent magnet.
B
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Interaction of two permanent bar magnets.
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Magnetic field around a straight conductor carrying a steady current I.
Magnitude of B is directly proportional to the current I value and inversely proportional to the distance from the conductor.
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Properties of the magnetic force F
sinBvqF
)( BvqF
BvqF 2
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Magnetic flux
S
B SdB
cos S
B dsB
211 mTWb
WbB
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How is Electricity Produced?
• Friction: “static electricity” from rubbing (walking across a carpet)
• Pressure: piezoelectricity from squeezing crystals together (quartz watch)
• Heat: voltage produced at junction of dissimilar metals (thermocouple)
• Light: voltage produced from light striking photocell (solar power)
• Chemical: voltage produced from chemical reaction (wet or dry cell battery)
• Magnetism: voltage produced using electromotive induction (AC or DC generator).
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Basic Terminology
• Electromotive Force ( ,E, V)
– known as emf, potential difference, or voltage– unit is volt [V]– „force” which causes electrons to move from one
location to another– operates like a pump that moves charges
(predominantly electrons) through “pressure” (= voltage)
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Separating Charge and EMF
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Separating Charge and EMF
vlBE
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Motional emfMotional emfApply the Lorentz Force Apply the Lorentz Force quation:quation:
0qvBqEF
vBE
vBE
vB
qvBqE
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Faraday’s Law
md d dxBl x Bl
dt dt dt
dxBlv Bl
dt E
mTherefore, d
dt
E
CONCLUSION: to produce emf one should make ANY change in a magnetic flux with time!
Consider the loop shown:
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FARADAY’S LAWFARADAY’S LAW
• Changing magnetic flux produces an emfChanging magnetic flux produces an emf
(o(or r cchanging B-Field produces E-Fieldhanging B-Field produces E-Field))
• The rate of change of magnetic flux is The rate of change of magnetic flux is requiredrequired
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Changing Flux due to moving Changing Flux due to moving permanent magnetpermanent magnet
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Polarity of the Induced Emf
The polarity (direction) of the induced emf is determined by Lenz’s law.
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LENZ’S Law
The direction of the The direction of the emf induced by emf induced by changing flux will changing flux will produce a current that produce a current that generates a magnetic generates a magnetic field opposing the flux field opposing the flux change that produced itchange that produced it..
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Lenz’s Law
B, H
Lenz’s Law: emf appears and current flows that creates a magnetic field that opposes the change – in this case an decrease – hence the negative sign in Faraday’s Law.
B, H
N S
V+, V-
Iinduced
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Lenz’s Law
B, H
Lenz’s Law: emf appears and current flows that creates a magnetic field that opposes the change – in this case an increase – hence the negative sign in Faraday’s Law.
B, H
N S
V-, V+
Iinduced
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Faraday’s Law for a Single Loop
dt
dE
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Faraday’s Law for a coil having N turnsFaraday’s Law for a coil having N turns
dt
dNE
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Lenz's Law
Claim: Direction of induced current must be so as to oppose the change; otherwise conservation of energy would be violated.
• Why???
– If current reinforced the change, then the change would get bigger and that would in turn induce a larger current which would increase the change, etc..
– No perpetual motion machine!
Conclusion: Lenz’s law results from energy conservation principle.
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Induced Current – quantitative
Suppose we pull with velocity v a coil of resistance R through a region of constant magnetic field
vw
x
Ix x x x x x
x x x x x x
x x x x x x
x x x x x x
We must supply energy to produce the current and to move the loop (until it is completely out of the B-field region). The work we do is exactly equal to the energy dissipated in the resistor, i.e. W=I2Rt
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Nature of a changing fluxNature of a changing flux
• How can we induce emf?How can we induce emf?
B B dA
cosB dA
- - BB can change can change with time with time
- - AA can change can change with time with time
-- can changecan change with time with time
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Generators
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Applications of Magnetic Induction
• AC Generator
Water turns wheel rotates magnet changes flux induces emf drives current
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Single-Phase Generator
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Three Phase Generator
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Three Phase Voltage
-1.5000
-1.0000
-0.5000
0.0000
0.5000
1.0000
1.5000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Sine
Sine + 120
Sine + 240
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Some Other Applications of Magnetic Induction
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The Magnetic Playback Head of a Tape Deck
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• Tape / Hard Drive etc– Tiny coil responds to change in flux as the magnetic
domains go by (encoding 0’s or 1’s).
– Credit Card Reader– Must swipe card generates changing flux– Faster swipe bigger signal
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Electric Guitar
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Mutual inductMutual inductionion
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Mutual inductMutual inductionion• A changing flux in one element induces an A changing flux in one element induces an
emf in anotheremf in another
2121211
1212122
iMN
iMN
total
total
dt
diM
dt
dN 1
2121
22
dt
diM
dt
dN 2
1212
11
1
21221 i
NM
2
12112 i
NM
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Measurement of induced emf in coil C
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),,( 202 nnIfUU
tII sin01
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U () = cos( t) const
y = 0,0655x - 1,4864
R2 = 0,9637
0,000
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
11,000
20,0 40,0 60,0 80,0 100,0 120,0 140,0 160,0 180,0
f [kHz]
U [mV
]
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Transformers
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Transformers
The changing magnetic flux produced by the current in the primary coil induces an emf in the secondary coil.
At the far right is the symbol for a transformer.
A transformer is a device for increasing or decreasing an ac voltage.
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Transformer EquationsUsing Faraday’s law we can write expressions for the primary and secondary voltages as follows:
.t
NV SS
.t
NV PP
.P
S
P
S
N
N
V
V
Dividing the above equations we get,
Assuming that there is no power loss, we can write,
.PPSS IVIV
.P
S
S
P
P
S
N
N
I
I
V
V
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Power Loss in Transmission Lines
RIPLoss2
Transformers play a key role in the transmission of electric power.
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Self-induction
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Self-inductance (L)
The alternating current in the coil generates an alternating magnetic field that induces an emf in the same circuit.
The effect in which a changing current in a circuit induces an emf in the same circuit is referred to as self-induction.
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Definition and UnitsDefinition and Units
• Unit Unit of L of L is henry (H)is henry (H):: volt-second/metervolt-second/meter
dt
dN
dt
diL
dt
dilAn
dt
dinNA
o
o
2
dt
diL
LiNtotal
VnAnL oo22
i
NL
l
Nn HnIB 00
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Inductors and self inductance Land Back EMF-voltage
Changing flux induces emf in same Changing flux induces emf in same element that carries currentelement that carries current
A A “back” emf “back” emf is generated by a is generated by a changing currentchanging current
emf opposes the change causing it emf opposes the change causing it (Lenz’s Law)(Lenz’s Law)
dt
diL
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LR circuitLR circuit
t
eR
I
R
L
At t=0 the At t=0 the switch is just openswitch is just open. . Apply Kirchhoff”s Loop RuleApply Kirchhoff”s Loop Rule
0 IRL
0IRdt
dIL
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LR circuitLR circuit
L
t
e1R
i
R
LL
Apply Kirchhoff’s Loop RuleApply Kirchhoff’s Loop Rule
0iR L
Li
L
R
dt
di
At At tt = 0, = 0, ii = 0, and = 0, and switch is just closedswitch is just closed
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Energy in an inductorEnergy in an inductor
idt
diLIP
it
diLiPdt0
0
2Li2
1W 2Li
2
1WU
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Induced electric fieldsInduced electric fields
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Induced fields Let us discuss two ways of production of electric field:
(1) A Coulomb electric field that is created by positive or negative charges;
(2) A non-Coulomb electric field that is created by a changing magnetic field.
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Induced electric fieldsInduced electric fieldsLet’s calculate the value of work Let’s calculate the value of work one has to do to moving a charge one has to do to moving a charge along the circular path s:along the circular path s:
0
l
l
ldE
ldEqldFW
dt
dldE
l
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Induced fields
dt
BdErot
dt
dldE
0 ldE
0Erot
E
ReminderReminder: in electrostatics: : in electrostatics:
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ConclusionsConclusions
• The electric field produced by static charge is conservative:The electric field produced by static charge is conservative:
- Zero- Zero work must be done over a closed path (circuit)work must be done over a closed path (circuit)
• The The electric field due to an emf is NOT conservativeelectric field due to an emf is NOT conservative
– Net work must be done over a closed path (circuit)Net work must be done over a closed path (circuit)
• Therefore, the closed path integral of E is non-zeroTherefore, the closed path integral of E is non-zero
– Charges will accelerate parallel to E.Charges will accelerate parallel to E.
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Eddy Currents
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Eddy CurrentsEddy currents are induced electric currents that flow in a
circular path
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Eddy Currents
A magnetic braking system.
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Generation of Eddy Currents (cont.)
Eddy currents flowing in the material will generate their own “secondary” magnetic field which will oppose the coil’s “primary” magnetic field.
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Crack Detection
Crack detection is one of the primary uses of eddy current inspection. Cracks cause a disruption in the circular flow of the eddy currents and weaken their intensity.
Magnetic FieldFrom Test Coil
Magnetic Field From
Eddy Currents
Eddy Currents
Crack
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Material Thickness Measurement
Eddy current inspection is often used in the aviation industries to detect material loss due to corrosion and erosion.
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Material Thickness Measurement
Eddy current inspection is used extensively to inspect tubing at power generation and petrochemical facilities for corrosion and erosion.
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Metal Detectors
Metal detectors like those used at airports can detect any metal objects, not just magnetic materials like iron. They operate by induced currents.
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DemoE-M Cannon
v
~
side view
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More Applications of Eddy Currents• Magnetic Levitation (Maglev) Trains
– Induced surface (“eddy”) currents produce field in opposite direction Repels magnet Levitates train
Maglev trains today can travel up to 310 mphMay eventually use superconducting loops to produce B-field No power dissipation in resistance of wires!
N
S
rails“eddy” current
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Summary
• “Let there be light!!!”
James MAXWELL concluded that a changing magnetic field (B) will produce a changing electric field (E) and the changing E will produce a changing B. The net result of the interaction of the changing E and B fields is the production of a wave which has both an electric and a magnetic component and travels through empty space. This wave is referred to as an electromagnetic wave (EM).
Faraday's law of induction describes the production of an electric field by a changing magnetic field.
dt
BdErot
dt
dldE
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The speed of EM waves in a vacuum is given by
v = 1/(0 o) where 0 is the permittivity of free space 0 = 8.85x10-12 C2/N m2 and
o is the permeablity of free space o = 4 x10-7 T m/A.
v = 3.00x108 m/s speed of light in vacuum
Production of Electromagnetic Waves
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The Electromagnetic Spectrum
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In 1831 Joseph Henry discovered magnetic induction.
The History of Induction
Joseph Henry
(1797-1878)
Michael Faraday(1791-1867)
Michael Faraday's ideas about conservation of energy led him to believe that since an electric current could cause a magnetic field, a magnetic field should be able to produce an electric current. He demonstrated this principle of induction in 1831.
So the whole thing started 176 years ago!
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The authors appreciate helpful discussion withProf. Mieczysław DEMIANIUK
while preparing the lecture.