Electromagnetic Induction Chapter 29 Electromagnetic Induction
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 magnetic flux To determine the direction of an induced emf
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
Introduction How is a credit card reader related to magnetism? Energy conversion makes use of electromagnetic induction.
Magnetic flux from Chapter 27
Induced current A changing magnetic flux causes an induced current. No change => NO induced current!
Induced current A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current.
Whether the source is a magnet or electromagnet doesn’t matter! Induced current A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current. Whether the source is a magnet or electromagnet doesn’t matter!
Whether the source is moving or its current changes doesn’t matter Induced current A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current. Whether the source is moving or its current changes doesn’t matter
Induced current A changing magnetic flux causes an induced current. The induced emf is the corresponding emf causing the current. Change B flux Create EMF Create Current!
Magnetic flux through an area element
Flux revisited Flux depends on orientation of surface with respect to B field.
Flux revisited Flux depends on orientation of surface with respect to B field.
Flux revisited Flux depends on orientation of surface with respect to B field.
Faraday’s law Induced emf in a closed loop equals negative of time rate of change of magnetic flux through the loop = –dB/dt = VOLTS (Electromotive Force) dB/dt = Rate of Change of B field FLUX through surface – sign means EMF opposes change
Faraday’s law Induced emf in a closed loop equals negative of time rate of change of magnetic flux through the loop = –dB/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!
Faraday’s law Induced emf in a closed loop equals negative of time rate of change of magnetic flux through the loop = –dB/dt [B ]= Tesla-m2 [d B/ dt] = Tesla-m2/sec and from F = qv x B Teslas = Newtons-sec/Coulomb-meters [N/C][sec/meters] [d B/ dt] = [N/C][sec/meter][m2/sec] = Nm/C = Joule/C = VOLT!
Emf and the current induced in a loop Example 29.1: What is induced EMF & Current?
Emf and the current induced in a loop Example 29.1: What is induced EMF & Current? df/dt = d(BA)/dt = (dB/dt) A = 0.020 T/s x 0.012 m2 = 0.24 mV I = E/R = 0.24 mV/5.0W = 0.048 mA
What are fundamental differences between Goal What are fundamental differences between Generators Motors Alternators
How do you solve HW problem like 29.30? Goal What are fundamental differences between generators, motors, & alternators? How do you solve HW problem like 29.30? A 0.850 m-long metal bar is pulled to the right at a steady 6.0 m/s perpendicular to a uniform, 0.850-T magnetic field. The bar rides on parallel metal rails connected through a 25-Ohm, resistor so the apparatus makes a complete circuit. Ignore the resistance of the bar and the rails. Calculate the magnitude & direction of the emf induced in the circuit, and the current.
Direction of the induced emf Direction of induced current from EMF creates B field to KEEP original flux constant! Increasing FLUX N v
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
Direction of the induced emf Direction of induced current from EMF creates B field to KEEP original flux constant!
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
Direction of the induced emf Direction of induced current from EMF creates B field to KEEP original flux constant!
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
Direction of the induced emf Direction of induced current from EMF creates B field to KEEP original flux constant!
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
Lenz’s law Lenz’s law: The direction of any magnetic induction effect is such as to oppose the cause of the effect.
Lenz’s law Lenz’s law: The direction of any magnetic induction effect is such as to oppose the cause of the effect. WHY???
Suppose induced current went this way! Why Lenz’s Law? Suppose the opposite was true – increasing flux generated supportive current… Suppose induced current went this way! N v
Why Lenz’s Law? Suppose the opposite was true – increasing flux generated supportive current… Induced current creates B field! N S N v Remember – this isn’t the case!
Why Lenz’s Law? Suppose the opposite was true – increasing flux generated supportive current… B field would ATTRACT incoming magnet! N S N v Force Remember – this isn’t the case!
Why Lenz’s Law? Suppose the opposite was true – increasing flux generated supportive current… Magnet would accelerate! N S N V + at Remember – this isn’t the case!
Why Lenz’s Law? Suppose the opposite was true – increasing flux generated supportive current… KE increases with no work done! N S N V + at Remember – this isn’t the case!
Lenz’s Law is like a conservation of energy relation! Direction of induced current from EMF creates B field to KEEP original flux constant! Induced B field opposes increase in flux! N v
Magnitude and direction of an induced emf 500 loop circular coil with radius 4.00 cm between poles of electromagnet. B field decreases at 0.200 T/second. What are magnitude and direction of induced EMF?
Magnitude and direction of an induced emf 500 loop circular coil with radius 4.00 cm between poles of electromagnet. B field decreases at 0.200 T/second. What are magnitude and direction of induced EMF? Careful with flux ANGLE! f between A and B! = –N dB/dt = [NdB/dt] x [A cos f] Direction? Since B decreases, EMF resists change…
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 – w comes from an external rotating force! Water turning a turbine (hydroelectric) Gasoline Motor turning a shaft (AC generator)
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 Recall DC motors! DIFFERENT!
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 w, what is the induced EMF?
A simple alternator Example 29.3: For simple alternator rotating at angular rate of w, what is induced EMF? B is constant; A is constant Flux B is NOT constant! B = BAcos f Angle f varies in time: f = wt EMF = - d [B ]/dt = -d/dt [BAcos(wt)] So EMF = wBAsin(wt)
A simple alternator EMF = wBAsin(wt)
A simple alternator (check out video!) EMF = wBAsin(wt)
AC Alternators vs. DC Generators An AC generator “Alternator” has continuous slip rings so current always “sloshes” back and forth Slip rings DC generator
AC Alternators vs. DC Generators An AC Alternator has continuous slip rings so current always “sloshes” back and forth Slip rings DC generator AC alternator
AC Alternators vs. DC Generators A DC generator creates ONLY one-directional (positive) current flow with EMF always the same “sign.” Commutator AC alternator DC generator
DC generator and back emf in a motor Commutator results in ONLY unidirectional (“direct”) current flow: EMF(DC gen) = | wBAsin(wt) |
DC generator and back emf in a motor A DC generator creates ONLY one-directional (positive) current flow with EMF always the same “sign.” “Back EMF” Generated from changing flux through the loop DC generator
DC generator and back emf in a motor Average EMF generated = AVG( | wBAsin(wt) | ) over Period T where T = 1/f = 2p/w
DC generator and back emf in a motor
DC generator and back emf in a motor Example 29.4: 500 turn coil, with sides 10 cm long, rotating in B field of 0.200 T generates 112 V. What is w?
Lenz’s law Lenz’s law:
Lenz’s law and the direction of induced current
Lenz’s law and the direction of induced current
Slidewire generator – Example 29.5 What is magnitude and direction of induced emf? Area A vector chosen to be into page
Slidewire generator – Example 29.5 B is constant; A is INCREASING => flux increases!
Slidewire generator – Example 29.5 Area A = Lx so dA/dt = L dx/dt = Lv Width x
EMF = - d [B ]/dt = -BdA/dt = -BLv Slidewire generator EMF = - d [B ]/dt = -BdA/dt = -BLv Induced current creates B OUT of page
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?
Work and power in the slidewire generator EMF = -BLv I = EMF/R = -BLv/R Power = I2R = B2L2v2/R
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 = B2L2v2/R
Motional electromotive force The motional electromotive force (VOLTAGE!) across the ends of a rod moving perpendicular to a magnetic field is = vBL.
Motional electromotive force The motional electromotive force across the ends of a rod moving perpendicular to a magnetic field is = vBL. Without any other forces present FE = FB => No net acceleration
Motional electromotive force Make a complete circuit by adding stationary conducting loop Across entire (stationary) conductor, E field from moving bar will push current
Induced motional electromotive force
Motional electromotive force So what happens? Force on Bar = ILB is to LEFT Bar slows down…
Motional electromotive force So what happens? Force on Bar = ILB is to LEFT Bar slows down… Or… equally! B field flux (into page) increases in loop Generate EMF opposing increase from Faraday’s Law
Motional electromotive force Are these saying the same thing??
Motional electromotive force
How can we use Induced EMF? B +V current Push a large current across the bar – it accelerates!
Rail Guns Use induced forces to accelerate particles to amazing speeds! Not science fiction…
Induced electric fields Wire loop around a solenoid that experiences a changing current. See a NEW current flow in surrounding loop! WHY?? There must be an EMF…
Induced electric fields Vary current in solenoid => vary B field through cylinder Vary flux through loop! Faraday’s Law applies! EMF created! A current will flow… But wait a minute!! © 2016 Pearson Education Inc.
Induced electric fields Solenoid doesn’t HAVE a B field outside!! Wire loop 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.
Induced electric fields AHA! Changing magnetic flux causes an induced electric field.
Induced electric fields Key – the integral path must be stationary And… The E field created is NOT conservative!
Induced electric fields Electric field in loop must drive the current When solenoid current I changes with time, B field flux also changes, & induced EMF can be written in terms of induced electric field: © 2016 Pearson Education Inc.
Displacement current Ampere’s law works fine for wires carrying current. But…. It is incomplete! Consider charging a capacitor – with no wires between the plates! Ampere’s Law: Take line integral around wire: i
Displacement current For the plane circular area bounded by the circle, Iencl is the current iC in the left conductor. But surface that bulges out to right is bounded by the same circle, and the current through that surface is zero. This leads to a contradiction.
Displacement current When capacitor is charging, E field is increasing between the plates. Define “fictitious” displacement current iD in region between the plates. Regard this as source of magnetic field between plates.
Eddy currents When a piece of metal moves through a magnetic field or is located in a changing magnetic field, eddy currents of electric current are induced. The metal detectors used at airport security checkpoints operate by detecting eddy currents induced in metallic objects.
Magnetic Braking! Slowing a falling magnet! Slow a saw blade… Magnetic Braking… Magnetic Trains! Eddy Currents
Eddy Currents – what are they good for? Stop a saw blade!
Faraday disk dynamo Spinning conducting disc in uniform magnetic field. Generates current in connecting wires!
Faraday disk dynamo Current increases with B, with Area, and with rotation rate w What is the EMF in terms of these variables?
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? !$%##
Faraday disk dynamo – does this violate Faraday’s Law?
What are fundamental differences between Goal What are fundamental differences between Generators Motors Alternators