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
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 Presentation
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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
• 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
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..
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
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
Faraday’s Law for a Single Loop
dt
dE
Faraday’s Law for a coil having N turnsFaraday’s Law for a coil having N turns
dt
dNE
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.
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
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
Generators
Applications of Magnetic Induction
• AC Generator
Water turns wheel rotates magnet changes flux induces emf drives current
At At tt = 0, = 0, ii = 0, and = 0, and switch is just closedswitch is just closed
Energy in an inductorEnergy in an inductor
idt
diLIP
it
diLiPdt0
0
2Li2
1W 2Li
2
1WU
Induced electric fieldsInduced electric fields
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.
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
Induced fields
dt
BdErot
dt
dldE
0 ldE
0Erot
E
ReminderReminder: in electrostatics: : in electrostatics:
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.
Eddy Currents
Eddy CurrentsEddy currents are induced electric currents that flow in a
circular path
Eddy Currents
A magnetic braking system.
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.
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
Material Thickness Measurement
Eddy current inspection is often used in the aviation industries to detect material loss due to corrosion and erosion.
Material Thickness Measurement
Eddy current inspection is used extensively to inspect tubing at power generation and petrochemical facilities for corrosion and erosion.
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.
DemoE-M Cannon
v
~
side view
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
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
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
The Electromagnetic Spectrum
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!
The authors appreciate helpful discussion withProf. Mieczysław DEMIANIUK