WileyPLUS Assignment 2 Next Week Midterm Test Faraday's Law ...

WileyPLUS Assignment 2Chapters 20, 21

Due: Wednesday, Feb 11 at 6 pm

Next WeekMidterm Break!

Midterm Test Ch 18-22, 24, 25

20 multiple-choice questions

Thursday, March 5, 7-9 pm,

41Wednesday, February 11, 2009

Faraday’s Law

The induced emf is equal to the

rate of change of magnetic flux.

V = !"/!t

The direction of the induced current is such that the

magnetic field produced by the current opposes the change in

magnetic flux that generated the current.

Lenz’s Law

Magnetic flux: != BAcos"


Prob. 22.70/32: Indicate the direction of the electric field between

the plates of the capacitor if the magnetic field is decreasing in

time. Charge can flow around the circuit and pile up on the capacitor

plates.

++++

– – – –E

I

I

I

BI

BI

BI

Induced magnetic field


#

Prob. 22.26: A 0.5 m copper bar, AC, sweeps around a conducting circular track at 15 rad/s.

A uniform magnetic field points into the page, B = 0.0038 T.

Find the current in the loop ABC.

The loop forms a closed circuit of increasing area, so the magnetic flux passing through the loop increases and an emf is generated.

and I = V/R = 0.00713/3

= 2.4 mA

IBI

$ = 15 rad/s

r = 0.5 m

The flux passing through the loop is: != BA= B

!"

2#

"!#r2 = Br

2!/2

The induced emf is: V =!"

!t=Br

2

2! !#

!t=Br

2$

2

V =0.0038!0.52!15

2= 7.13!10"3 V

θI

$ = 15 rad/s


Guitar pickup

• The strings are magnetizable

• A permanent magnet magnetizes them

• The vibration of a string changes the magnetic flux through the

coil at the frequency of vibration of the string

• An emf is induced in the coil at that frequency


Playback of tape recording

• Recorded tape is magnetized in N-S patches

• The tape passes by the playback head which channels and concentrates

the magnetic field through an iron core

• The changing magnetic flux induces an emf in the coil


Moving coil microphone

• Sound waves cause the diaphragm of the microphone to move in/out

• A coil moves with the diaphragm relative to a permanent magnet,

causing the magnetic flux through the coil to change in step with the

pressure variations of the sound wave

• An emf is set up in the coil at the frequency of the sound wave


Ground fault detector

If the return current (green) is equal to the supply current (red), the

magnetic fluxes around the iron ring are equal and opposite and cancel.

If the currents differ, the fluxes do

not cancel and there is a net flux

varying at 60 Hz, which induces a

current in the sensing coil.


Electric Generator

The magnetic flux passing

through the coil varies as the coil

rotates – an emf is generated.

Flux, != BAcos"= BAcos(#t)


V0

V =V0 sin(!t)

EMF from electric generator,

using rate of change of flux

Flux, != BAcos"= BAcos(#t)

V = V0sin($t), V0 = NBA$

(diff. calculus)


V = BLvsin!

V = BLvsin!

Electric GeneratorEMF generated in moving conductors

Total emf generated: Vtot = 2BLvsin!

Therefore, Vtot = BLW!sin"= BA!sin"

If the coil has N turns, then: Vtot = NBA!sin"=V0 sin"

W

Area, A = LW

v= r!=!W

2

"!, != angular frequency of rotating coil

VV ++–

–

2V

= V0 sin!t


Clicker Question

You have a fixed length of wire and need to design a generator.

You have only two options:

1) a one turn square coil, or

2) a two turn square coil.

Which option should you choose so that your generator will

produce the greatest peak emf for a given frequency and

magnetic field strength?

A) One turn square

B) Two turn square

C) It doesn’t matter

Answer A): V0 ~ NA, with A = a2, and a ~ 1/N, so A ~ 1/N2

So, V0 ~ N/N2 - if you increase the turns you lose on area rapidly.

a

a

a

a

A = a2

L = 4aNV0 = NBA$


Prob. 22.63/39: The cross-

sectional area of the coil is 0.02

m2 and the coil has 150 turns.

Find the rotation frequency of

the coil and the magnetic field.

The period is T = 0.42 s

Therefore, B=V0

NA!=

28

150!0.02!14.96 = 0.624 T

!=2"

T=

2"

0.42 s= 14.96 rad/s

Peak voltage, V0 = 28 V = NBA$.

Alternating Current Electric Generator

V0 = 28 V

f = 1/T = 2.38 Hz V = NBA!sin!t(Could also be V = NBA! cos !t)


TimeTime

Root Mean Square (rms)

Power % V2

V0 = NBA$V0

V2 = V02 sin2 $t

Time

V02

Mean = V02/2

Average power % Vrms2 = V0

2/2

Vrms = V0/!2 = rms voltage

V = V0 sin $t


Prob. 22.40: A generator uses a coil that has 100 turns and a 0.5 T

magnetic field. The frequency of the generator is 60 Hz and its

emf has an rms value of 120 V.

Assuming that each turn of the coil is a square, determine the

length of the wire from which the coil is made.

• What is the peak voltage generated?

• What is the area of the coil?

A = a2...


Electric Generator

Electric Motor

Just like a generator, but use a current to cause the coil to rotate.

Once the coil is rotating, it acts as a generator, producing an emf that opposes the rotation of the coil! – the “back emf.”

L

L As the coil rotates and a current is induced in

it, a magnetic force is generated that opposes

the rotation of the coil.

! Work has to be done to rotate the coil

against this torque.


Back emf

Vback

A power supply drives the motor The motor acts as a generator

Kirchhoff’s loop law: V !Vback = IR

Symbol for

AC

generator


Vback

Prob. 22.38/36: A vacuum cleaner is plugged into a 120 V socket and

draws 3 A of current in normal operation (motor running at full speed,

back emf at maximum value) and the back emf is then 72 V.

Find the coil resistance of the motor.

V !Vback = IR

So, 120 – 72 = 3R

R = (120 – 72)/3 = 16 "

When the motor is first switched on, while it’s still spinning slowly, the

back emf is small and: V – 0 = IR,

Then, I = (120 V)/(16 !) = 7.5 A ! the motor draws extra current while it is speeding up. This is the time it’s most likely to trip the breaker.


Prob. 22.36/38: A 120 volt motor draws a current of 7 A when

running at normal speed. The resistance of the armature wire is

0.72 &.

a) Determine the back emf generated by the motor.

b) What is the current at the instant the motor is turned on and

has not begun to rotate?

c) What series resistance must be added to limit the starting

current to 15 A?


Summary of Chapter 22

• EMF induced in a moving conductor: V = vLB sin#

• Mechanical work has to be done to produce

electrical energy – you don’t get something for

nothing

• Magnetic flux, " = BA cos', proportional to

number of field lines.

• Faraday’s law: V = (–)N !"/!t,

Lenz’s law: the magnetic field

produced by the induced current opposes

the changing magnetic flux.

• Electric generator, back emf


WileyPLUS Assignment 2 Next Week Midterm Test Faraday's Law ...

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