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