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Preparing the lecture we applied figures from:

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/

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Preparing the lecture we applied figures from:

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  1. 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

  2. Faraday's Law by W. Borys and K. Zubko

  3. (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 elektromotoryczna magnetic flux - strumień pola magnetycznego rate of change - szybkość zmian X to Y ratio = stosunek X/Y voltage - napięcie elektryczne current intensity I - natężenie prądu I electric circuit - obwód elektryczny current [increase; decrease (= decay)] - [wzrost; zanik] prądu time derivative of a function - pochodna funkcji po czasie equation - równanie length = 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

  4. ELECTROMAGNETIC INDUCTION • Review of some magnetic phenomena • Motional Electromotive Force (emf) • Faraday’s Law of Eectromagnetic Induction • Lenz’s Law • Induced Electric Fields • Mutual Inductance • Self - Inductance • Energy in Inductor • LR Circuit • Eddy Currents • Electromagnetic Waves-introduction

  5. Magnetic field around a permanent magnet.

  6. Interaction of two permanent bar magnets.

  7. 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.

  8. Properties of the magnetic force F

  9. Magnetic flux

  10. 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).

  11. 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)

  12. Separating Charge and EMF

  13. Separating Charge and EMF

  14. Motional emf Apply the Lorentz Force quation:

  15. Consider the loop shown: Faraday’s Law CONCLUSION: to produce emf one should make ANY change in a magnetic flux with time!

  16. FARADAY’S LAW • Changing magnetic flux produces an emf (or changing B-Field produces E-Field) • The rate of change of magnetic flux is required

  17. Changing Flux due to moving permanent magnet

  18. Polarity of the Induced Emf The polarity (direction) of the induced emf is determined by Lenz’s law.

  19. The direction of the emf induced by changing flux will produce a current that generates a magnetic field opposing the flux change that produced it. LENZ’S Law

  20. B, H Iinduced N S Lenz’s Law B, H C V+, V- 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.

  21. B, H Iinduced N S Lenz’s Law C B, H V-, V+ 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.

  22. Faraday’s Law for a Single Loop

  23. Faraday’s Law for a coil having N turns

  24. Lenz's Law Claim: Direction of induced current must be so as to oppose the change; otherwise conservation of energy would be violated. • Why??? • Ifcurrent 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 energyconservation principle.

  25. x x x x x x x x x x x x x x x x x x x x x x x x I w v x Induced Current – quantitative Suppose we pull with velocity v a coil of resistance R through a region of constant magnetic field We must supply energy to produce the currentand 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

  26. - B can change with time • - A can change with time • -qcan change with time Nature of a changing flux • How can we induce emf?

  27. Generators

  28. Applications of Magnetic Induction • AC Generator Water turns wheel  rotates magnet  changes flux  induces emf  drives current

  29. Single-Phase Generator

  30. Three Phase Generator

  31. Three Phase Voltage

  32. Some Other Applications of Magnetic Induction

  33. The Magnetic Playback Head of a Tape Deck

  34. 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

  35. Electric Guitar

  36. Mutual induction

  37. Mutual induction • A changing flux in one element induces an emf in another

  38. Measurement of induced emf in coil C

  39. Transformers

  40. Transformers A transformer is a device for increasing or decreasing an ac voltage. 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.

  41. Transformer Equations Using Faraday’s law we can write expressions for the primary and secondary voltages as follows: Dividing the above equations we get, Assuming that there is no power loss, we can write,

  42. Power Loss in Transmission Lines Transformers play a key role in the transmission of electric power.

  43. Self-induction

  44. 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.

  45. Definition and Units • Unit of L is henry (H):volt-second/meter

  46. Inductors and self inductance Land Back EMF-voltage • Changing flux induces emf in same element that carries current • A “back” emf is generated by a changing current • emf opposes the change causing it (Lenz’s Law)

  47. LR circuit At t=0 the switch is just open. Apply Kirchhoff”s Loop Rule

  48. LR circuit At t = 0, i = 0, and switch is just closed Apply Kirchhoff’s Loop Rule

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