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Lesson 9

Lesson 9. Lesson 9. Faraday’s Law. Faraday’s Law of Induction Motional EMF Lenz’s Law Induced EMF’s and Induced Electric Fields Eddy Currents. Torque on Loop. Current in loop in a magnetic field produces torque on a loop. Induced Current.

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Lesson 9

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  1. Lesson 9 Lesson 9 Faraday’s Law • Faraday’s Law of Induction • Motional EMF • Lenz’s Law • Induced EMF’s and Induced Electric Fields • Eddy Currents

  2. Torque on Loop Current in loop in a magnetic field produces torque on a loop

  3. Induced Current Does torque on loop in a magnetic field produces current in a loop ? YES

  4. Picture I B • current depends on the torque • thus on rotational frequency

  5. Change of Flux Picture • Current depends on speed of magnet • Thus rate of change of magnetic Field

  6. Change of Flux Picture Equations Common factors, change of area, change of magnetic field

  7. Induced Current in Wire moving wire in field B produces current I if there is a conduction path I B v FB

  8. Induced emf (y, z1) (y, z2) y1 k j i

  9. Equations I

  10. Equations II Work done per unit charge by F B in moving charges from z to z 1 2 = vBl where l = z - z 2 1 No work is done in moving charges in other sections of path ( ignore Hall effect ) dW Work done per unit charge = emf dQ Thus e = vBl

  11. Equations III Area of loop in magnetic field ( ) ( ) ( ) A t = y t - y l 1 Total magnetic flux through loop ( ) F t Rate of change of magnetic flux e d F dy = -B l = - Bvl = - dt dt

  12. Faraday s Law of Induction for N loops

  13. This defines an Induced Electric Field by

  14. ' Faradays Law of Electromagnetic Induction The work done per unit charge by magnetic force moving charge from z to z 1 2 ò ò ò z 2 dW 1 1 = · = · = · F s F s E s d d d B B ind dQ Q Q z loop loop 1 thus ò e F d = - = · d E s N ind dt loop

  15. Induced Electric Field • An induced EMF is a measure of • An induced Electric Field • If charge is in this region and there is a conduction path it will feel a force from the induced Electric Field and flow

  16. Equations E Remember for a static electric field stat ò b = · E s V d and ab stat a ò = · = E s E d 0 as is conservative stat stat E But for an induced electric field ind ò · ¹ E s d 0 ind thus E is not conservative ind

  17. Magnetic Flux and Induced Electric Field Changing Magnetic Flux produces an Induced Electric Field

  18. Mechanical Work to Electrical work I Pulling at constant velocity v B v l Fappl I Blv y k j i

  19. Mechanical Work to Electrical work II l wire with current I flowing in it B moving in a magnetic field feels a force given by = ´ F l B I = - ´ = - F k i j IlB IlB F This force opposes the applied force appl and must be equal and opposite if the velocity is to remain constant = = F F IlB appl

  20. Mechanical Work to Electrical work III B v F l Fappl I Blv

  21. Mechanical Power to Electrical Power I

  22. Mechanical Power to Electrical Power II Pulling at constant velocity v B v F l Fappl I Blv

  23. Magnetic Field produced by Changing Current Circulating current produces an induced magnetic field I Bind That opposes the external magnetic field B That produces the current

  24. Current produced by Changing Magnetic Field (a) Change of External Magnetic Field Produces Current (b) Current Produces Induced Magnetic Field

  25. Lenz's Law Lenz’s Law Polarity of is such that it opposes the change that caused it Direction of Eis such that it opposes the change that caused it Direction of induced current is such that it opposes the change that caused it

  26. Conservation of Energy Conservation of Energy

  27. AC Generator AC Generator

  28. e AC Potential F d d ( ) ( ) = - = - · B A t dt dt d ( ) ( ) = - = q BACos BA sin d q ( t ) q t dt dt if rotational speed is constant e e ( ) ( ) ( ) w w t wBA sin t sin t = = max e = BAw max

  29. DC Generator DC Generator

  30. Eddy Currents

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