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Induction

Induction. March 29, 2006. Calendar…. Today we finish up some material from the last chapter and begin the chapter on induction. Friday – Quiz on LAST chapter (30) Next Friday … still likely date for the next exam.

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Induction

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  1. Induction March 29, 2006 Induction - Spring 2006

  2. Calendar… • Today we finish up some material from the last chapter and begin the chapter on induction. • Friday – Quiz on LAST chapter (30) • Next Friday … still likely date for the next exam. • If you have a problem with this date please email me with reason and we will try to figure out how to deal with it. Induction - Spring 2006

  3. Let’s Finish Some Details Displacement Current Induction - Spring 2006

  4. Magnetic Flux For a CLOSED Surface we might expect this to be equal to some constant times the enclosed poles … but there ain’t no such thing! Induction - Spring 2006

  5. Examples S N Induction - Spring 2006

  6. Consider the poor little capacitor… i i ? CHARGING OR DISCHARGING …. HOW CAN CURRENT FLOW THROUGH THE GAP?? Induction - Spring 2006

  7. Through Which Surface Do we measure the current for Ampere’s Law? I=0 Induction - Spring 2006

  8. In the gap… DISPLACEMENT CURRENT Fixes the Problem! Induction - Spring 2006

  9. Let's DO the Demo ! Induction - Spring 2006

  10. From The Demo .. A changing magnetic field INDUCES a current in a circuit loop. Induction - Spring 2006

  11. Faraday’s Experiments ? ? Induction - Spring 2006

  12. Insert Magnet into Coil Induction - Spring 2006

  13. Remove Coil from Field Region Induction - Spring 2006

  14. That’s Strange ….. These two coils are perpendicular to each other Induction - Spring 2006

  15. Definition of TOTAL ELECTRIC FLUX through a surface: Induction - Spring 2006

  16. Magnetic Flux:F THINK OF MAGNETIC FLUX as the “AMOUNT of Magnetism” passing through a surface. Don’t quote me on this!!! Induction - Spring 2006

  17. xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx Consider a Loop • Magnetic field passing through the loop is CHANGING. • FLUX is changing. • There is an emf developed around the loop. • A current develops (as we saw in demo) • Work has to be done to move a charge completely around the loop. Induction - Spring 2006

  18. xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx Faraday’s Law (Michael Faraday) • For a current to flow around the circuit, there must be an emf. • (An emf is a voltage) • The voltage is found to increase as the rate of change of flux increases. Induction - Spring 2006

  19. xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx Faraday’s Law (Michael Faraday) We will get to the minus sign in a short time. Induction - Spring 2006

  20. xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx Faraday’s Law (The Minus Sign) Using the right hand rule, we would expect the direction of the current to be in the direction of the arrow shown. Induction - Spring 2006

  21. xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx Faraday’s Law (More on the Minus Sign) The minus sign means that the current goes the other way. This current will produce a magnetic field that would be coming OUT of the page. The Induced Current therefore creates a magnetic field that OPPOSES the attempt to INCREASE the magnetic field! This is referred to as Lenz’s Law. Induction - Spring 2006

  22. xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx How much work? emf Faraday's Law A magnetic field and an electric field are intimately connected.) Induction - Spring 2006

  23. The Strange World of Dr. Lentz Induction - Spring 2006

  24. MAGNETIC FLUX • This is an integral over an OPEN Surface. • Magnetic Flux is a Scalar • The UNIT of FLUX is the weber • 1 weber = 1 T-m2 Induction - Spring 2006

  25. We finally stated FARADAY’s LAW Induction - Spring 2006

  26. From the equation Lentz Lentz Induction - Spring 2006

  27. Flux Can Change • If B changes • If the AREA of the loop changes • Changes cause emf s and currents and consequently there are connections between E and B fields • These are expressed in Maxwells Equations Induction - Spring 2006

  28. Maxwell’s Equations(Next Course .. Just a Preview!) Gauss Faraday Induction - Spring 2006

  29. The Flux into the page begins to increase. An emf is induced around a loop A current will flow That current will create a new magnetic field. THAT new field will change the magnetic flux. xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx Another View Of That damned minus sign again …..SUPPOSE that B begins to INCREASE its MAGNITUDE INTO THE PAGE Induction - Spring 2006

  30. Lenz’s Law Induced Magnetic Fields always FIGHT to stop what you are trying to do! i.e... Murphy’s Law for Magnets Induction - Spring 2006

  31. Example of Nasty Lenz The induced magnetic field opposes the field that does the inducing! Induction - Spring 2006

  32. Induction - Spring 2006

  33. Don’t Hurt Yourself! The current i induced in the loop has the direction such that the current’s magnetic field Bi opposes the change in the magnetic field B inducing the current. Induction - Spring 2006

  34. Let’s do the Lentz Warp again ! Induction - Spring 2006

  35. OR The toast will always fall buttered side down! Lenz’s Law An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current. (The result of the negative sign!) … Induction - Spring 2006

  36. An Example • The field in the diagram • creates a flux given by • FB=6t2+7tin milliWebers • and t is in seconds. • What is the emf when • t=2 seconds? • (b) What is the direction • of the current in the • resistor R? Induction - Spring 2006

  37. This is an easy one … Direction? B is out of the screen and increasing. Current will produce a field INTO the paper (LENZ). Therefore current goes clockwise and R to left in the resistor. Induction - Spring 2006

  38. Figure 31-36 shows two parallel loops of wire having a common axis. The smaller loop (radius r) is above the larger loop (radius R) by a distance x >>R. Consequently, the magnetic field due to the currenti in the larger loop is nearly constant throughout the smaller loop. Suppose that x is increasing at the constant rate of dx/dt = v. (a) Determine the magnetic flux through the area bounded by the smaller loop as a function of x. (Hint: See Eq. 30-29.) In the smaller loop, find (b) the induced emf and (c) the direction of the induced current. v Induction - Spring 2006

  39. q B is assumed to be constant through the center of the small loop and caused by the large one. Induction - Spring 2006

  40. q The calculation of Bz Induction - Spring 2006

  41. dx/dt=v More Work In the small loop: Induction - Spring 2006

  42. q Which Way is Current in small loop expected to flow?? B Induction - Spring 2006

  43. What Happens Here? • Begin to move handle as shown. • Flux through the loop decreases. • Current is induced which opposed this decrease – current tries to re-establish the B field. Induction - Spring 2006

  44. moving the bar Induction - Spring 2006

  45. Moving the Bar takes work v Induction - Spring 2006

  46. What about a SOLID loop?? Energy is LOST BRAKING SYSTEM METAL Pull Eddy Currents Induction - Spring 2006

  47. Inductors Back to Circuits for a bit …. Induction - Spring 2006

  48. Definition Current in loop produces a magnetic field in the coil and consequently a magnetic flux. If we attempt to change the current, an emf will be induced in the loops which will tend to oppose the change in current. This this acts like a “resistor” for changes in current! Induction - Spring 2006

  49. Remember Faraday’s Law Lentz Induction - Spring 2006

  50. Look at the following circuit: • Switch is open • NO current flows in the circuit. • All is at peace! Induction - Spring 2006

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