000513431.pdf

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PHY 2054C – College Physics B

q,v

R

B

F

F

q,v

q,v

L6—Ch21spring 2013

Fs

FN

( Faraday’s Law

),

Transformers

magnetic induction

Today’s Lecture: purpose & goals

1) Induced Voltage

2) Lenz s Law

3) Generators and

Chapter 21

Electricity, Magnetism, Light, Optics and Modern Physics

WÜ Wtä|w ` _|Çw

F 1 I a B , F 2 I a B

F 1b

2sin F 2

b

2sin

I a b B sin

Torque on a Coil due to

Magnetic Field

N I A Bsin between coil face andB

Current loop “coil” on the right; Left and Right wire have different

current directions;

RHR-> F1 into page,

F2 out of page

If the coil has N windings, and area A=ab

Result: simple DC motor A coil is pivoted to rotate freely inside a magnetic

field. current thru coil, causes a torque.

When the coil has turned by 90° , switch currentdirection, so that it continues to turn (commutator)

F I l B sin

Hur sluta röka cold turkey

http://www.halsanet.com/14/2014/04/Hur-sluta-roka-cold-turkey.html

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Very Simple Motors

….including Michael Faraday’sfirst demonstration of motioninduced by the flow of current

Strong magnet

wire …feels a force!

I

B

outward

Important Pointsfrom last Lecture 1) Magnetic Fields are generated by

moving charges, currents

straight wire:

current in long coil:

2) Effect of Magnetic Field;Force on moving charges

Force on current

Torque on coil area A

B0

2

I

r , 0 4 10

7 T m

A

B 0

N

l I

“First” Right-Hand Rule

F q v B sin

F I l B sin N I A B sin

“Second” Right-Hand Rule

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Intro: Induced Voltage Michael Faraday thought: “If current produces a magnetic

field, why can't a magnetic field produce a current?”

When switch is closed, coil X builds up a magnetic field inmagnet core

Galvanometer shows negative current through coil Y

When switch is opened, the magnetic field disappears, and a positive current is shown

[Notice that the effect is transient; it only happens for a short timeright after the opening or closing]

Intro: Induced Voltage

B A cos

“Faraday’s Law” Inserting a magnet into

a coil also produces

an induced voltage ( ind

)

or current.

[the key here is change!! ] The faster speed of

insertion/retraction, the higher the inducedvoltage.

What we change here is called the “magneticflux”, the amount of field B that passes throughan area A:

ind N t

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Magnetic Flux , cont.

If the field is perpendicular to the surface, B = B A

If the field makes an angle θ with the normal to thesurface, B = B A cosθ

If the field is parallel to the surface, B = 0 “How strong the magnetic field is in that region of space”

Section 21.2

Faraday’s Law , Summary

Only changes in the magnetic flux matter Rapid changes in the flux produce larger values of emf

than do slow changes This dependency on frequency means the induced emf

plays an important role in AC circuits

The magnitude of the emf is proportional to the rateof change of the flux If the rate is constant, then the emf is constant In most cases, this isn’t possible and AC currents result

The induced emf is present even if there is no currentin the path enclosing an area of changing magneticflux

Section 21.2

ind N t

ind V

=IR

ind

B 0

N

l I

ind

BAcos

changing

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Lenz's Law Sometimes it is hard to figure out the sign of the induced

voltage; There is a simple rule:

A change in flux gives rise to an induced current

whose magnetic field always opposes theoriginal change.

(No formula) – this is the minus sign

in Faraday’s law

ΔB1

At the time of closing the switch

Primary current

Induced Current

B2

ind N t

ind N t

ind V

=IR

ind

B 0

N

l I

ind

Opposite directions!!

Lenz's Law2 and Example “Induced current opposes the

change that caused it”

dropping a strong magnetthrough a copper tube:

Induced currents - B aboveact attractively

Induced current's - B belowmagnet act repulsively

Magnet will fall, but very slowly!

N

S

Induced Current

Induced Current

“Eddy Currents”

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Question 1

If we send the same magnet through a pipe with a

slit along the side, we would expect the magnet to

a) fall at the same, slow rate as in the solid pipe

b) fall even slower

c) fall much faster

Lenz's Law Sometimes it is hard to figure out the sign of the induced

voltage; There is a simple rule:

A change in flux gives rise to an induced current

whose magnetic field always opposes theoriginal change.

(No formula) – this is the minus sign

in Faraday’s law

ΔB1

At the time of closing the switch

Primary currentInduced Current

B2

ind N t

ind N t

ind V

=IR

ind

B 0

N

l I

ind

Opposite directions!!

R e v i e w

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Question 1

When do you expect to see the

lightbulb turn on?

a) when it’s at the top

b) when it’s at the bottom

c) on one side or the other

solenoid coil

lightbulb

pole face ofmagnet

Anything special about the lightbulb flash?

a) it turns on a very short time b) it turns on twice per revolution

c) it stays on for most of the revolutuion

Lenz's Law: An induced emf gives rise to a currentwhose magnetic field opposes the original change inmagnetic flux.

Lenz’ Law

Magnetic Flux is reduced,

Induced currenttries to add to Flux

Magnetic Flux is increased,

Induced currenttries to reduce Flux

The direction of the induced current comes from “right-hand rule”1: fingers: curled B, thumb: I:

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B A cos

ind N t

B A cos

ind N t

Problem Solving with Lenz’s Law

I

B(out)

Lenz's Law: An induced emf gives rise to a currentwhose magnetic field opposes the original change inmagnetic flux.

Four steps:

What is the direction of the Magnetic Flux?[Out of North magnetic pole, into South magnetic pole.]

Is the flux through the loop increasing or decreasing? Apply Lenz’s Law

if increasing, induced field will be in oppositedirection of original field.

if decreasing, induced field will be in samedirection as original field.

What direction will current be

flowing around loop? Use 1st RHR

Electric Guitars

Section 21.7

Reading computer memory

An electric guitar uses Faraday’s Lawto sense the motion of the strings

The string passes near a pickup coilwound around a permanent magnet

As the string vibrates, it produces a chang-ing magnetic flux

The resulting emf is sent to an amplifier andthe signal can be played through speakers

Magnetic read-heads on computer hard-drives and magnetic cassette tapes senseinformation stored in magnetic domainsthis same way!!

The voltage generated in the pickup coilis caused by the changing magneticflux at the boundaries between northand south-facing magnetic domains

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Bicycle Odometers

Section 21.7

Road Traffic Sensors

; only moving cars sensed!!

An odometer control unit is shown, which receives signals from a pickup coil mounted on the axle support A permanent magnet is attached to a wheel that passes the coil with

each wheel revolution.

When the magnet passes over the pickup coil, it changes themagnetic flux thru the coil, and a pulse is generated A computer keep tracks of the number of pulses

works similarly:

a pickup coil is buried in the roadway When the ferrous parts of a car (or

currents from the car’s electrical circuits)

pass over the coil, a pulse is generatedthat records the arrival of the car

The induced Voltage (emf ε) in a coil is winding number N

times the change of the magnetic flux through the coil per

time;

where the magnetic flux is defined as the magnetic fieldB passing through a loop of area A

The angle θ is measured between thenormal direction of the area andthe magnetic field direction

Faraday's Law of Induction

B A cos

ind N t

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Changing the Flux

The magnetic flux is given by a

product of B, A and cos(θ ).

Therefore there are three ways of creating a change influx and therefore an induced emf .

a) changing A

b) changing B

c) changing cos(θ )

B A cos

ind N t

Changing cos(θ)

Turning a coil in amagnetic field:

Only cos(θ ) changes

this induces an AC voltagein the coil.

ind N

B A cos

t

ind N B Acos

t

0 N B A

B Acos

ind N

B A cos

t

ind N B Acos

t

0 N B A

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Electric Generator Electric Generator:

A permanent (or electro)-magnet (rotor) with manypoles is rotating throughmany loops of wire.

The rotation keepschanging the fluxthrough each of thestationary (stator) coils,

which induces voltage on

the output.

When we use the voltage by drawing a current, themagnetic field of the induced current acts like a brake!(it’s removing energy!!)

Motor-Generator

An electric motor sends acurrent through a coil in amagnetic field, which startsto turn.

Electrical Mechanicalenergy energy

A generator turns a coil ina magnetic field, whichproduces current.

Mechanical Electricalenergy energy

Every motor is a generator

and vice versa

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Question 2

A generator, which is being turned by a hand-crank

is hooked up with a switch to a light bulb.

When the switch is closed, the cranking of thegenerator

a) gets harder

b) does not change

c) gets easier

Transformers

Transformers are devices that can increase or decreasethe amplitude of an applied AC voltage

A simple transformer consists of two solenoid coils with theloops arranged so that all or most of the magnetic fieldlines and flux generated by one coil pass through the othercoil

Section 22.9

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Changing B Primary winding uses AC current and

voltage

secondary winding produces ACcurrent and voltage

What are the voltages?

V S N S

B

t ,V P N P

B

t

V S

V P

N S

N P

B

This assembly is called a transformer. It allows us to change voltages of AC without losing power !

V o l t a g e

primary

secondary

C u r r e n t

primary

secondary

B N S I S , B N P I P I S

I P

N P

N S

What are the currents ?

B Acos

V S I S N S

N P

V P N P

N S

I P = V P I P

The electric power is the same in and out!

= PPPS =

Question

The primary winding of an electric train transformer has400 turns, and the secondary has 50. If the input voltageis 120 V(rms), what is the output voltage?

1. 480 V

2. 60 V

3. 15 V

4. 10 V

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Changing B Primary winding uses AC current and

voltage

secondary winding produces ACcurrent and voltage

What are the voltages?

V S N S

B

t ,V P N P

B

t

V S

V P

N S

N P

B

real transformers:

V o l t a g e

primary

secondary

C u r r e n t

primary

secondary

B N S I S , B N P I P I S

I P

N P

N S

What are the currents ?

B Acos

somewhat idealized: (the total magnetic flux thru the primary

coils doesn’t all pass thru the secondary): efficiency e (fraction of flux actually transferred)

I S

I P

N P

N S

e V S

V P

N S

N P

e

Stay tuned. . . .

Wednesday: problem solving (Chs. 21): Magnetismand Induction

Friday: Chapter 22 Electromagnetic Waveshttp://www.physics.fsu.edu/courses/summer2010/phy2054 c

How do you like mymagnetic

personality!!

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Another Faraday Experiment

A solenoid is positioned near a loop of wire with the lightbulb He passed a current through the solenoid by connecting it to a

battery When the current through the solenoid is constant, there is no

current in the wire When the switch is opened or closed, the bulb does light up

Section 21.1

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