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 Does torque on loop in a magnetic field produces current in a loop ? YES

Picture ¨current depends on the torque ¨thus on rotational frequency I B

Change of Flux Picture  Current depends on speed of magnet  Thus rate of change of magnetic Field

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

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

Induced emf j i k z2)z2) y1y1 (y, z1)z1)

Equations I

Equations II Work done per unit charge byF B in moving charges fromz 1 toz 2  vBl wherel  z 2  z 1 No work is done in moving charges in other sections of path(ignore Hall effect) Work done per unit charge dW dQ = emf Thus  vBl

Equations III Area of loop in magnetic field At   yt   y 1  l Total magnetic flux through loop  t  Rate of change of magnetic flux d  dt  -B dy dt l  Bvl  

Faradays Law of Induction for N loops

This defines an Induced Electric Field by

Faradays Law of Electromagnetic Induction '        The work done per unit charge by magnetic force moving charge fromz 1 toz 2 dW dQ  1 Q F B  d s z 1 z 2   1 Q F B  d s loop   E ind  d s loop  thus   N d  dt  E ind  d s loop 

 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  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 Induced Electric Field

Equations Remember for a static electric field E stat V ab  E stat  d s a b  and  E stat  d s   0 as E stat is conservative But for an induced electric field E ind E  d s   0 thus E ind is not conservative

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

Mechanical Work to Electrical work I I F appl v l B  B l v Pulling at constant velocity v k j i y

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

Mechanical Work to Electrical work III I F appl v l B  B l v F

Mechanical Power to Electrical Power I

Mechanical Power to Electrical Power II I F appl v l B  B l v Pulling at constant velocity v F

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

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

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

Conservation of Energy

AC Generator

AC Potential  t   d  dt  d B  A   d BACos    BA sin  t  if rotational speed is constant  t    BA sin  t    max sin  t   max  BA  d dt   t

DC Generator

Eddy Currents