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Induction

Induction. Fall 2006. 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!. CLOSED SURFACE. Examples. S N. A puzzlement . Let’s apply this to the gap of a capacitor.

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Induction

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  1. Induction Fall 2006 Induction - Fall 2006

  2. 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! CLOSED SURFACE Induction - Fall 2006

  3. Examples S N Induction - Fall 2006

  4. A puzzlement .. Let’s apply this to the gap of a capacitor. Induction - Fall 2006

  5. Consider the poor little capacitor… i i ? CHARGING OR DISCHARGING …. HOW CAN CURRENT FLOW THROUGH THE GAP In a FIELD description?? Induction - Fall 2006

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

  7. In the gap… DISPLACEMENT CURRENT Fixes the Problem! Induction - Fall 2006

  8. Let's DO the Demo ! Induction - Fall 2006

  9. OK Let's take a look. Induction - Fall 2006

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

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

  12. Insert Magnet into Coil Induction - Fall 2006

  13. Remove Coil from Field Region Induction - Fall 2006

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

  15. Remember the Definition of TOTAL ELECTRIC FLUX through a CLOSED surface: Induction - Fall 2006

  16. Magnetic Flux:FB • Similar Definition with a special difference! Faraday's Law Induction - Fall 2006

  17. Magnetic Flux • Applies to an OPEN SURFACE only. • “Quantity” of magnetism that goes through a surface. surface Induction - Fall 2006

  18. xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx Consider a Loop • Magnetic field passing through the loop is CHANGING. • FLUX is changing. • There must be 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 - Fall 2006

  19. xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx Faraday’s Law (Michael Faraday) • Again, 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 - Fall 2006

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

  21. 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 - Fall 2006

  22. 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 - Fall 2006

  23. 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 - Fall 2006

  24. The Strange World of Dr. Lentz Induction - Fall 2006

  25. 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 - Fall 2006

  26. We finally stated FARADAY’s LAW Induction - Fall 2006

  27. From the equation Lentz Lentz Induction - Fall 2006

  28. 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 - Fall 2006

  29. Three of Maxwell’s Four Equations(Next Course .. Just a Preview!) Ampere’s Law Gauss Faraday Induction - Fall 2006

  30. 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 - Fall 2006

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

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

  33. Induction - Fall 2006

  34. 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 - Fall 2006

  35. Let’s do the Lentz Warp again ! Induction - Fall 2006

  36. 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 - Fall 2006

  37. 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 - Fall 2006

  38. 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 - Fall 2006

  39. 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 - Fall 2006

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

  41. q The calculation of Bz Induction - Fall 2006

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

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

  44. 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 - Fall 2006

  45. moving the bar Induction - Fall 2006

  46. Moving the Bar takes work v Induction - Fall 2006

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

  48. Inductors Back to Circuits for a bit …. Induction - Fall 2006

  49. 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 - Fall 2006

  50. Remember Faraday’s Law Lentz Induction - Fall 2006

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