Electromagnetic InductionElectromagnetic Induction

Create electric current from changing magnetic fields

ObjectivesObjectives

Explain how a changing magnetic field Explain how a changing magnetic field produces an electric currentproduces an electric currentDefine electromotive force and solve Define electromotive force and solve problems involving wires moving in a problems involving wires moving in a magnetic fieldmagnetic fieldDescribe how an electric generator works Describe how an electric generator works and how it differs from a motorand how it differs from a motorRecognize the difference between peak and Recognize the difference between peak and effective voltage and currenteffective voltage and current

ObjectivesObjectives

State Lenz’s Law and explain “back-EMF” State Lenz’s Law and explain “back-EMF” and how it affects the operation of motors and and how it affects the operation of motors and generatorsgeneratorsExplain self-inductance and how it affects Explain self-inductance and how it affects circuitscircuitsDescribe a transformer and solve problems Describe a transformer and solve problems involving voltage, current, and turns ratiosinvolving voltage, current, and turns ratios

ElectromagnetismElectromagnetism

Force on a moving charged particle in a Force on a moving charged particle in a magnetic fieldmagnetic fieldForce on a current-carrying wire in a Force on a current-carrying wire in a magnetic fieldmagnetic fieldVoltage (and current) induced in a wire Voltage (and current) induced in a wire forced to move in a magnetic fieldforced to move in a magnetic fieldVoltage (and current) induced by a Voltage (and current) induced by a changing magnetic fieldchanging magnetic fieldBasis of motors and generators, and Basis of motors and generators, and electromagnetic waveselectromagnetic waves

Electromagnetic InductionElectromagnetic Induction

Faraday’s LawFaraday’s LawLenz’s LawLenz’s LawThe AC GeneratorThe AC GeneratorThe DC GeneratorThe DC GeneratorBack EMF in a MotorBack EMF in a MotorThe TransformerThe Transformer

Faraday’s LawFaraday’s LawFaraday’s Law:Faraday’s Law:Moving a conductorMoving a conductor through magnetic flux lines causes an through magnetic flux lines causes an emfemf to be induced in the conductor.to be induced in the conductor.

• Relative motionRelative motion between a conductor and a between a conductor and a magnetic field induces an emf in the conductor. magnetic field induces an emf in the conductor. • The The direction of the induced emfdirection of the induced emf depends on depends on the the direction of motiondirection of motion of the conductor with of the conductor with respect to the field. respect to the field. • The The magnitude of the emfmagnitude of the emf is directly is directly proportional to the proportional to the raterate at which magnetic flux at which magnetic flux lines are cut by the conductor. lines are cut by the conductor. • The The magnitudemagnitude of the emf is directly of the emf is directly proportional to the proportional to the number of turnsnumber of turns of the of the conductor crossing the flux lines.conductor crossing the flux lines.

N

t

N

t

Textbook, Pg. 582

Induced VoltageInduced Voltage

Voltage induced in a wire moving Voltage induced in a wire moving perpendicular to a magnetic fieldperpendicular to a magnetic field

E = induced voltageE = induced voltage(electromotive force)(electromotive force)

B = magnetic field B = magnetic field strengthstrength

L = length of wireL = length of wire

v = velocity of wire v = velocity of wire moving perpendicular to moving perpendicular to magnetic fieldmagnetic field

E BLv

Induced VoltageInduced Voltage

EMF Induced by a Moving WireEMF Induced by a Moving Wire

An An emf is inducedemf is induced in a wire that is in a wire that is moving perpendicularmoving perpendicular to a magnetic to a magnetic field.field.

Where:

= the induced emf

B = strength of the magnetic field

l = length of the wire

v = velocity of motion

= angle of the wire relative to the flux lines

Where:

= the induced emf

B = strength of the magnetic field

l = length of the wire

v = velocity of motion

= angle of the wire relative to the flux lines

Blv sin Blv sin

ExampleExampleA straight wire 0.20 m long moves at a constant speed of 7.0 m/s A straight wire 0.20 m long moves at a constant speed of 7.0 m/s perpendicular to a magnetic field of strength 8.0 x 10perpendicular to a magnetic field of strength 8.0 x 10-2-2 T TWhat EMF is induced in the wire?What EMF is induced in the wire?The wire is part of a circuit that has a resistance of 0.50 The wire is part of a circuit that has a resistance of 0.50 ΩΩ. What is . What is the current through the wire?the current through the wire?

Textbook, Pg. 584-5Practice Problems 1-4

Known:v = 7.0 m/sL = 0.20 mB = 8.0 x 10-2 TR = 0.50 Ω

Unknown:EMF = ? (V)I = ? (A)

EMF BLv

x T m ms

V

IV

R

EMF

RV

A

8 0 10 0 20 7 0

011

011

0 500 22

2. . .

.

.

..

c hb ge j

counterclockwise

The AC GeneratorThe AC GeneratorAn An electric generatorelectric generator converts mechanical energy into electric converts mechanical energy into electric energy.energy.

The three main The three main components are:components are:a field magneta field magnetan armaturean armatureslip rings with brushesslip rings with brushes

IfIf the armature is rotating the armature is rotating with a with a constantconstant angular angular velocity in a constant velocity in a constant magnetic field, the magnetic field, the magnitude of the induced magnitude of the induced emf and current emf and current varies varies sinusoidallysinusoidally withwith respect to respect to time. time.

inst maxsin 2 ft inst maxsin 2 ft

i iinst maxsin 2 ft i iinst maxsin 2 ft

““Effective” Current & VoltageEffective” Current & VoltagePower is the product of voltage and currentPower is the product of voltage and current

Both vary with an alternating currentBoth vary with an alternating currentAverage power is half the maximumAverage power is half the maximum

““EffectiveEffective” current and “” current and “effectiveeffective” voltage” voltageEquivalent constant voltage and current that would Equivalent constant voltage and current that would generate the same average powergenerate the same average power

Textbook, Pg. 588-9Practice Problems 5-8

P P I RV

R

I R I R I I

I I

V V

avg effeff

eff eff

eff

eff

12

12

12

0 707

0 707

22

2 2

max

max max

max

max

.

.Likewise,

The DC GeneratorThe DC GeneratorA simple A simple ac generatorac generator can be can be converted easily to a converted easily to a dc generatordc generator by substituting a split-ring by substituting a split-ring commutatorcommutator for the slip rings. for the slip rings.

Lenz's LawLenz's Law

Lenz’s Law:Lenz’s Law: An induced current will flow in such a direction An induced current will flow in such a direction that it will oppose by its magnetic field the motion of the that it will oppose by its magnetic field the motion of the magnetic field that is producing it.magnetic field that is producing it.

Fleming’s Rule:Fleming’s Rule: If the thumb, If the thumb, forefinger, and middle finger of the forefinger, and middle finger of the right hand are held at right angles right hand are held at right angles to each other, with the thumb to each other, with the thumb pointing in the direction in which pointing in the direction in which the wire is moving and the the wire is moving and the forefinger pointing in the field forefinger pointing in the field direction (N to S), the middle finger direction (N to S), the middle finger will point in the direction of induced will point in the direction of induced conventional current.conventional current. Textbook, Pg. 590

Back EMF in a MotorBack EMF in a Motor• In an In an electric motorelectric motor, a magnetic torque turns a current-, a magnetic torque turns a current-

carrying loop in a constant magnetic field. carrying loop in a constant magnetic field. • A A coil rotatingcoil rotating in a magnetic field induces an emf that opposes in a magnetic field induces an emf that opposes

the cause that gave rise to it.the cause that gave rise to it.• Thus, Thus, every motor is alsoevery motor is also a generatora generator..

According to According to Lenz's lawLenz's law, , such an induced emf must such an induced emf must oppose the current oppose the current delivered to the motor. For delivered to the motor. For this reason, the emf induced this reason, the emf induced in a motor is called in a motor is called back back emfemf or or counter emfcounter emf..

The TransformerThe Transformer

The basic parts of a simple The basic parts of a simple transformer are:transformer are:A A primary coilprimary coil connected connected to an ac source.to an ac source.A A secondary coilsecondary coil connected to a load.connected to a load.A soft iron A soft iron corecore..

primary voltage

secondary voltage

primary turns

secondary turns

primary voltage

secondary voltage

primary turns

secondary turns

p

s

p

s

N

N

p

s

p

s

N

N

A transformer that produces a A transformer that produces a higher secondaryhigher secondary voltage is called a voltage is called a step-upstep-up transformertransformer..

A transformer that produces a A transformer that produces a lower secondarylower secondary voltage is called a voltage is called a step-down transformerstep-down transformer..

Textbook, Pg. 594

New TermsNew Terms

induced emfinduced emf

ac generatorac generator

dc generatordc generator

electromagnetic inductionelectromagnetic induction

back emfback emf

step-up transformerstep-up transformer

step-down transformerstep-down transformer

transformer efficiencytransformer efficiency

EquationsEquations

N

t

N

t

inst maxsin 2 ft inst maxsin 2 ft

i iinst maxsin 2 ft i iinst maxsin 2 ft

primary voltage

secondary voltage

primary turns

secondary turns

primary voltage

secondary voltage

primary turns

secondary turns

p

s

p

s

N

N

p

s

p

s

N

N

Blv sin Blv sin

SummarySummary

Michael Faraday discovered that if a Michael Faraday discovered that if a wire moves through a magnetic field, an wire moves through a magnetic field, an electric current can flowelectric current can flow

The current produced depends upon the The current produced depends upon the angle between the velocity of the wire and angle between the velocity of the wire and the magnetic fieldthe magnetic field

Maximum current occurs when the wire is Maximum current occurs when the wire is moving at right angles to the fieldmoving at right angles to the field

Electromotive force (EMF) is the potential Electromotive force (EMF) is the potential difference created across the moving wiredifference created across the moving wire

EMF is measured in voltsEMF is measured in voltsContinued on next slide

SummarySummary

The EMF in a straight length of wire moving The EMF in a straight length of wire moving through a uniform magnetic field is the through a uniform magnetic field is the product of the magnetic field (B), the length of product of the magnetic field (B), the length of the wire (L), and the component of the the wire (L), and the component of the velocity of the moving wire (v), perpendicular velocity of the moving wire (v), perpendicular to the fieldto the fieldA generator and a motor are similar devicesA generator and a motor are similar devices

A generator converts mechanical energy to A generator converts mechanical energy to electrical energyelectrical energyA motor converts electrical energy to mechanical A motor converts electrical energy to mechanical energyenergy

Continued on next slide

SummarySummary

Lenz’s Law states that an induced Lenz’s Law states that an induced current is always produced in a current is always produced in a direction such that the magnetic field direction such that the magnetic field resulting from the induced current resulting from the induced current opposes the change in the magnetic field opposes the change in the magnetic field that is causing the induced currentthat is causing the induced current

Self-inductance is a property of a wire Self-inductance is a property of a wire carrying a changing currentcarrying a changing currentThe faster the current is changing, the The faster the current is changing, the greater the induced EMF that opposes that greater the induced EMF that opposes that changechange

Continued on next slide

SummarySummary

A transformer has two coils wound A transformer has two coils wound about the same coreabout the same core

An AC current through the primary coil An AC current through the primary coil induces an alternating EMF in the induces an alternating EMF in the seondary coilseondary coilThe voltages in alternating-current The voltages in alternating-current circuits may be increased of decreased by circuits may be increased of decreased by transformerstransformers

CreditsCredits

•Physics, Sixth EditionPhysics, Sixth Edition

•Paul E. TippensPaul E. Tippens

•Physics: Principles and ProblemsPhysics: Principles and Problems

•Paul W. ZitzewitzPaul W. Zitzewitz