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Induction

Induction. Spring ‘09. Dis here week. We begin the study of magnetic induction There will be a quiz on Friday There is a new WebAssign. Exam #3 is Wednesday4/8 It will include the material covered through April 6 th . The end is in sight … Check the website for the Final Exam Schedule.

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Induction

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  1. Induction Spring ‘09

  2. Dis here week • We begin the study of magnetic induction • There will be a quiz on Friday • There is a new WebAssign. • Exam #3 is Wednesday4/8 • It will include the material covered through April 6th. • The end is in sight … • Check the website for the Final Exam Schedule

  3. Ampere’s Law USE THE RIGHT HAND RULE IN THESE CALCULATIONS

  4. Last Time: A Simple Example

  5. Field Around a Long Straight Wire One Step Shopping!

  6. The figure below shows a cross section of an infinite conducting sheet carrying a current per unit x-length of l; the current emerges perpendicularly out of the page. (a) Use the Biot–Savart law and symmetry to show that for all points P above the sheet, and all points P´ below it, the magnetic field B is parallel to the sheet and directed as shown. (b) Use Ampere's law to find B at all points P and P´.

  7. FIRST PART Vertical Components Cancel

  8. L B Infinite Extent B Apply Ampere to Circuit

  9. B Infinite Extent B The “Math” Bds=0 Distance not a factor!

  10. Infinite Sheet of Charge Infinite sheet of current Both independent of distance from sheet

  11. Coil or Solenoid Valve Application Switches

  12. The Magnetic Field

  13. A Physical Solenoid/Coil Model

  14. Inside the Solenoid For an “INFINITE” (long) solenoid the previous problem and SUPERPOSITION suggests that the field OUTSIDE this solenoid is small!

  15. More on Long Solenoid Field is ZERO far from coil! Field is ZERO far from coil Field looks “UNIFORM”

  16. The real thing….. Finite Length Weak Field Stronger - Leakage Fairly Uniform field

  17. Another Way Far away n=number of turns per unit length. nh=total number of turns.

  18. The length of a solenoid is doubled but the number of turns remains the same. • The magnetic field is doubled. • The magnetic field is cut to a quarter. • The magnetic field does not change. • The magnetic field is quadrupled. • The magnetic field is cut in half.

  19. The number of turns is doubled but the length remains the same. • The magnetic field is quadrupled. • The magnetic field is cut to a quarter. • The magnetic field is doubled. • The magnetic field does not change. • The magnetic field is cut in half.

  20. Application • Creation of Uniform Magnetic Field Region • Minimal field outside • except at the ends!

  21. Two Coils

  22. “Real” Helmholtz Coils Used for experiments. Can be aligned to cancel out the Earth’s magnetic field for critical measurements.

  23. The Toroid Slightly less dense than inner portion

  24. The Toroid

  25. New Concept – Well sorta new MAGNETIC FLUX

  26. Magnetic Flux

  27. Magnetic Flux is a • Vector • Scalar • Tensor

  28. 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

  29. A puzzlement .. Let’s apply this to the gap of a capacitor.

  30. Consider the poor little capacitor… i i ? CHARGING OR DISCHARGING …. HOW CAN CURRENT FLOW THROUGH THE GAP In a FIELD description??

  31. Through Which Surface Do we measure the current for Ampere’s Law? I=0 Huh??

  32. In the gap… DISPLACEMENT CURRENT Fixes the Problem!

  33. So far .. • We found that currents create magnetic fields. • Stationary charges do not. • Static magnetic fields do not create currents. • What about CHANGING magnetic fields?? Changing magnetic fields CAN create currents. This is called induction.

  34. Let's take a look at some induction effects. Demo

  35. From The Demo .. A changing magnetic field INDUCES a current in a circuit loop.

  36. Faraday’s Experiments ? ?

  37. Insert Magnet into Coil

  38. Remove Coil from Field Region

  39. Summary

  40. That’s Strange ….. These two coils are perpendicular to each other

  41. Remember the Definition of TOTAL ELECTRIC FLUX through a CLOSED surface:

  42. Magnetic Flux - Reminder • Applies to an OPEN SURFACE only. • “Quantity” of magnetism that goes through a surface. • A Scalar surface

  43. 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.

  44. 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.

  45. xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx Faraday’s Law (Michael Faraday) We will get to the minus sign in a short time.

  46. 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.

  47. 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.

  48. xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx How much work? emf Faraday's Law A magnetic field and an electric field are intimately connected.)

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