Copyright © 2012 Pearson Education Inc. PowerPoint ® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Chapter 29 Electromagnetic Induction

Copyright © 2012 Pearson Education Inc. Goals for Chapter 29 To examine experimental evidence that a changing magnetic field induces an emf To learn how Faraday’s law relates the induced emf to the change in flux To determine the direction of an induced emf

Copyright © 2012 Pearson Education Inc. Goals for Chapter 29 To calculate the emf induced by a moving conductor To learn how a changing magnetic flux generates an electric field To study Maxwell’s Equations – the four fundamental equations that describe electricity and magnetism

Copyright © 2012 Pearson Education Inc. Introduction How is a credit card reader related to magnetism? Energy conversion makes use of electromagnetic induction. Faraday’s law and Lenz’s law tell us about induced currents.

Copyright © 2012 Pearson Education Inc. Induced current A changing magnetic flux causes an induced current. No change => NO induced current!

Copyright © 2012 Pearson Education Inc. Induced current A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current.

Copyright © 2012 Pearson Education Inc. Induced current A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current.

Copyright © 2012 Pearson Education Inc. Induced current A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current.

Copyright © 2012 Pearson Education Inc. Magnetic flux through an area element

Copyright © 2012 Pearson Education Inc. Faraday’s law Flux depends on orientation of surface with respect to B field.

Copyright © 2012 Pearson Education Inc. Faraday’s law Flux depends on orientation of surface with respect to B field.

Copyright © 2012 Pearson Education Inc. Faraday’s law Flux depends on orientation of surface with respect to B field.

Copyright © 2012 Pearson Education Inc. Faraday’s law Faraday’s law: Induced emf in a closed loop equals negative of time rate of change of magnetic flux through the loop  = –d  B /dt In this case, if the flux changed from maximum to minimum in some time t, and loop was conducting, an EMF would be generated!

Copyright © 2012 Pearson Education Inc. Faraday’s law Faraday’s law: Induced emf in a closed loop equals negative of time rate of change of magnetic flux through the loop  = –d  B /dt [  B ]= Tesla-m 2 [d  B / dt] = Tesla-m 2 /sec and from F = qv x B Teslas = Newtons-sec/Coulomb-meters [N/C][sec/meters] [d  B / dt] = [N/C][sec/meter][m 2 /sec] = Nm/C = Joule/C = VOLT!

Copyright © 2012 Pearson Education Inc. Emf and the current induced in a loop Example 29.1: What is induced EMF & Current?

Copyright © 2012 Pearson Education Inc. Emf and the current induced in a loop Example 29.1: What is induced EMF & Current? d  /dt = d(BA)/dt = (dB/dt) A = T/s x m 2 = 0.24 mV I = E /R = 0.24 mV/5.0  = mA

Copyright © 2012 Pearson Education Inc. Direction of the induced emf Direction of induced current from EMF creates B field to KEEP original flux constant!

Copyright © 2012 Pearson Education Inc. Direction of the induced emf Direction of induced current from EMF creates B field to KEEP original flux constant! Induced current generates B field flux opposing change

Copyright © 2012 Pearson Education Inc. Direction of the induced emf Direction of induced current from EMF creates B field to KEEP original flux constant!

Copyright © 2012 Pearson Education Inc. Direction of the induced emf Direction of induced current from EMF creates B field to KEEP original flux constant! Induced current generates B field flux opposing change

Copyright © 2012 Pearson Education Inc. Direction of the induced emf Direction of induced current from EMF creates B field to KEEP original flux constant!

Copyright © 2012 Pearson Education Inc. Direction of the induced emf Direction of induced current from EMF creates B field to KEEP original flux constant! Induced current generates B field flux opposing change

Copyright © 2012 Pearson Education Inc. Direction of the induced emf Direction of induced current from EMF creates B field to KEEP original flux constant!

Copyright © 2012 Pearson Education Inc. Direction of the induced emf Direction of induced current from EMF creates B field to KEEP original flux constant! Induced current generates B field flux opposing change

Copyright © 2012 Pearson Education Inc. Lenz’s law Lenz’s law: The direction of any magnetic induction effect is such as to oppose the cause of the effect.

Copyright © 2012 Pearson Education Inc. Magnitude and direction of an induced emf Example 29.2 – 500 loop circular coil with radius 4.00 cm between poles of electromagnet. B field decreases at T/second. What are magnitude and direction of induced EMF?

Copyright © 2012 Pearson Education Inc. Magnitude and direction of an induced emf Example 29.2 – 500 loop circular coil with radius 4.00 cm between poles of electromagnet. B field decreases at T/second. What are magnitude and direction of induced EMF? Careful with flux ANGLE!  between A and B!  = –N d  B /dt = [NdB/dt] x [A cos  Direction? Since B decreases, EMF resists change…

Copyright © 2012 Pearson Education Inc. A simple alternator – Example 29.3 An alternator creates alternating positive and negative currents (AC) as a loop is rotated by an external torque while in a fixed magnetic field (or vice-versa!) Note –  comes from an external rotating force! Water turning a turbine (hydroelectric) Gasoline Motor turning a shaft (AC generator)

Copyright © 2012 Pearson Education Inc. A simple alternator – Example 29.3 An alternator creates alternating positive and negative currents (AC) as a loop rotates in a fixed magnetic field (or vice-versa!) Note – NO commutator to reverse current direction in the loop – so you will get ALTERNATING current

Copyright © 2012 Pearson Education Inc. A simple alternator – Example 29.3 An alternator creates alternating positive and negative currents (AC) as a loop rotates in a fixed magnetic field (or vice-versa!) For simple alternator rotating at angular rate of , what is the induced EMF?

Copyright © 2012 Pearson Education Inc. A simple alternator Example 29.3: For simple alternator rotating at angular rate of , what is induced EMF? B is constant; A is constant Flux  B is NOT constant!  B = BAcos  Angle  varies in time:  =  t EMF = - d [  B ]/dt = -d/dt [BAcos(  t)] So EMF =  BAsin(  t)

Copyright © 2012 Pearson Education Inc. A simple alternator EMF =  BAsin(  t)

Copyright © 2012 Pearson Education Inc. DC generator and back emf in a motor Example 29.4: A DC generator creates ONLY one- directional (positive) current flow with EMF always the same “sign.” Slip rings DC generator AC alternator

Copyright © 2012 Pearson Education Inc. DC generator and back emf in a motor Example 29.4: A DC generator creates ONLY one- directional (positive) current flow with EMF always the same “sign.” AC alternator DC generator Commutator

Copyright © 2012 Pearson Education Inc. DC generator and back emf in a motor Commutator results in ONLY unidirectional (“direct”) current flow: EMF (DC gen) = |  BAsin(  t) |

Copyright © 2012 Pearson Education Inc. DC generator and back emf in a motor Example 29.4: A DC generator creates ONLY one- directional (positive) current flow with EMF always the same “sign.” DC generator “Back EMF” Generated from changing flux through the loop

Copyright © 2012 Pearson Education Inc. DC generator and back emf in a motor Average EMF generated = AVG( |  BAsin(  t) | ) over Period T where T = 1/f = 2  / 

Copyright © 2012 Pearson Education Inc. DC generator and back emf in a motor

Copyright © 2012 Pearson Education Inc. DC generator and back emf in a motor Example 29.4: 500 turn coil, with sides 10 cm long, rotating in B field of T generates 112 V. What is  ?

Copyright © 2012 Pearson Education Inc. Lenz’s law and the direction of induced current

Copyright © 2012 Pearson Education Inc. Lenz’s law and the direction of induced current

Copyright © 2012 Pearson Education Inc. Slidewire generator – Example 29.5 What is magnitude and direction of induced emf? Area A vector chosen to be into page

Copyright © 2012 Pearson Education Inc. Slidewire generator – Example 29.5 B is constant; A is INCREASING => flux increases!

Copyright © 2012 Pearson Education Inc. Slidewire generator – Example 29.5 Area A = Lx so dA/dt = L dx/dt = Lv Width x

Copyright © 2012 Pearson Education Inc. Slidewire generator EMF = - d [  B ]/dt = -BdA/dt = -BLv Induced current creates B OUT of page

Copyright © 2012 Pearson Education Inc. Work and power in the slidewire generator Let resistance of wires be “R” What is rate of energy dissipation in circuit and rate of work done to move the bar?

Copyright © 2012 Pearson Education Inc. Work and power in the slidewire generator EMF = -BLv I = EMF/R = -BLv/R Power = I 2 R = B 2 L 2 v 2 /R

Copyright © 2012 Pearson Education Inc. Work and power in the slidewire generator Work done = Force x Distance Power applied = Work/Time = Force x velocity Power = Fv = iLBv and I = EMF/R Power = (BLv/R)LBv = B 2 L 2 v 2 /R

Copyright © 2012 Pearson Education Inc. Motional electromotive force The motional electromotive force across the ends of a rod moving perpendicular to a magnetic field is  = vBL.

Copyright © 2012 Pearson Education Inc. Motional electromotive force The motional electromotive force across the ends of a rod moving perpendicular to a magnetic field is  = vBL. Across entire (stationary) conductor, E field will push current!

Copyright © 2012 Pearson Education Inc. Motional electromotive force

Copyright © 2012 Pearson Education Inc. Faraday disk dynamo Spinning conducting disc in uniform magnetic field. Generates current in connecting wires!

Copyright © 2012 Pearson Education Inc. Faraday disk dynamo Current increases with B, with Area, and with rotation rate  What is the EMF in terms of these variables?

Copyright © 2012 Pearson Education Inc. Faraday disk dynamo – does this violate Faraday’s Law? NO change in B field! NO change in Area! No change in flux?!! There should NOT be an induced EMF??! But there IS! But if you rotate the *magnet* instead, there is NOT an EMF Shouldn’t it be relative? !$%##

Copyright © 2012 Pearson Education Inc. Faraday disk dynamo – does this violate Faraday’s Law?

Copyright © 2012 Pearson Education Inc. Induced electric fields Wire loop around a solenoid that experiences a changing current. See a NEW current flow in surrounding loop! But… the wire itself is NOT in a B field (no “qv x B” applies to make charges in wire loop move!! AHA! Changing magnetic flux causes an induced electric field.

Copyright © 2012 Pearson Education Inc. Induced electric fields Wire loop around a solenoid that experiences a changing current. See a NEW current flow in surrounding loop! But… the wire itself is NOT in a B field (no “qv x B” applies to make charges in wire loop move!! AHA! Changing magnetic flux causes an induced electric field.

Copyright © 2012 Pearson Education Inc. Induced electric fields Key – the integral path must be stationary And… The E field created is NOT conservative!