chapter 29

Copyright © 2012 Pearson Education Inc.

PowerPoint® Lectures forUniversity Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman

Lectures by Wayne Anderson

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 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.

• Faraday’s law and Lenz’s law tell us about induced currents.


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.


Magnetic flux through an area element


Faraday’s law

• Flux depends on orientation of surface with respect to B field.


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

= –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

• 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 BTeslas = 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?

d/dt = d(BA)/dt = (dB/dt) A = 0.020 T/s x 0.012 m2

= 0.24 mV

I = E/R = 0.24 mV/5.0 = 0.048 mA


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.


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 0.200 T/second. What are magnitude and direction of induced EMF?


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 0.200 T/second. What are magnitude and direction of induced EMF?

Careful with flux ANGLE!

between A and B!

= –N dB/dt = [NdB/dt] x [A cos

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 rotates in a fixed magnetic field (or vice-versa!)

For simple alternator rotating at angular rate of , what is the

induced EMF?


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)


A simple alternator

• EMF = BAsin(t)


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 generatorAC alternator




AC alternator DC generator

Commutator



• Commutator results in ONLY unidirectional (“direct”) current flow:

EMF(DC gen) = | BAsin(t) |




DC generator

“Back EMF”Generated from

changing flux through the loop



• Average EMF generated = AVG( | BAsin(t) | ) over Period T where T = 1/f = 2/



• Example 29.4: 500 turn coil, with sides 10 cm long, rotating in B field of 0.200 T generates 112 V. What is ?


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



• B is constant; A is INCREASING => flux increases!



• Area A = Lx so dA/dt = L dx/dt = Lv

Width x


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?



• EMF = -BLv

• I = EMF/R = -BLv/R

• Power = I2R = B2L2v2/R



• 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 across the ends of a rod moving perpendicular to a magnetic field is = vBL.



• 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!


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

• 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?


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.


Induced electric fields


Displacement current

• A modified version of Ampere’s Law


Maxwell’s equations

• Maxwell’s equations consist of

Gauss’s law for the electric field

Gauss’s law for the magnetic field

Ampere’s law

Faraday’s law.


Superconductivity

• When a superconductor is cooled below its critical temperature, it loses all electrical resistance.

• Follow the text discussion using Figures 29.23 (below) and 29.24 (right).


Eddy currents

• Follow the text


Using eddy currents

• An airport metal detector & portable metal detector, both of which use eddy currents in their design.

chapter 29

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