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Understanding Magnetic Induction: Faraday's Law Explained

Explore Faraday’s experiments and laws on magnetic induction, emf development, and Lenz’s Law. Discover the connection between changing magnetic fields and induced currents in circuits.

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Understanding Magnetic Induction: Faraday's Law Explained

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  1. Magnetic Induction November 2, 2005

  2. Let's DO the Demo !

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

  4. Faraday’s Experiments ? ?

  5. Insert Magnet into Coil

  6. Remove Coil from Field Region

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

  8. Remember Electric Flux? Did you really think you were through with this kind of concept???

  9. q We discussed the normal component of the Electric Field vector

  10. E DA ENORMAL DEFINITION:Element of Flux through a surface DF=ENORMAL x DA (a scalar)

  11. “Element” of Flux of a vector E leaving a surface n is a unit OUTWARD pointing vector.

  12. q This flux was LEAVING the closed surface

  13. Definition of TOTAL ELECTRIC FLUX through a surface:

  14. There is ANOTHER Kind of FLUXF THINK OF MAGNETIC FLUX as the “AMOUNT of Magnetism” passing through a surface. Don’t quote me on this!!!

  15. 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.

  16. 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.

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

  18. 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.

  19. 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.

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

  21. BREAK

  22. NOV 4, 2005 • Quiz Next Friday • WA on board for induction • Next week Inductors and their circuits • Quiz next Friday • Quiz the following Friday • Exam #3 – Nov 23 (Wed before Thanksgiving) • Final 1.5 weeks later (12/5)

  23. The Strange World of Dr. Lentz

  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

  25. We finally stated FARADAY’s LAW

  26. From the equation Lentz Lentz

  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

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

  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

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

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

  32. 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.

  33. BREAK

  34. This is the week to be …. • No quiz this week. • A new WebAssign has already become available to you. • Another one is on the way. • We finish our discussion of Induction and start the circuit implications of an inductive element.

  35. Let’s do the Lentz Warp again ! Last Episode …

  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!) …

  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?

  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.

  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

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

  41. q The calculation of Bz

  42. dx/dt=v More Work In the small loop:

  43. q Which Way is Current in small loop expected to flow?? B

  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.

  45. moving the bar

  46. Moving the Bar takes work v

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

  48. Inductors Back to Circuits for a bit ….

  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!

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