Magnetism Intro mages/type_effects/Electro_Magnet.gif

Magnetism

Intro

http://www.adobe.com/products/aftereffects/images/type_effects/Electro_Magnet.gif

http

://w

ww

.fun

nyfr

ank.

com

/imag

es/m

agne

t.gi

f



http://www.funnyfrank.com/images/magnet.gif

Magnets

• About three thousand years ago, the Greeks discovered rocks which would attract iron or similar rocks (a mineral ore we call magnetite). They were found in Magnesia, an area in Asia Minor

http://www.dimitris.gr/images/collections/maps/map_magnesia.jpghttp://resourcescommittee.house.gov/subcommittees/emr/usgsweb/photogallery/images/Magnetite%202_jpg.jpg

http://www.mchenry.edu/depts/EAS/courses/eas170/Minerals/images/Magnetite.jpg

http://resourcescommittee.house.gov/subcommittees/emr/usgsweb/photogallery/images/Magnetite%202_jpg.jpg

http://resourcescommittee.house.gov/subcommittees/emr/usgsweb/photogallery/images/Magnetite%202_jpg.jpg




Lodestones

• The Chinese later used these naturally occurring magnets, called lodestones, for ocean navigation.

• The first recorded description of a compass was in the Chinese Book Dream Pool Essays (1086) by Shen Kuo in the Song Dynasty, about 100 years earlier than its first record in Europe by Alexander Neekam in 1190.

• Source: http://www.booyard.com/chinese/china%20culture/Four%20Great%20Inventions.htm

http://www.eglassplace.com/lodestones.jpghttp://www.infowest.com/life/auction/20lodestone1b.jpg

http://www.booyard.com/chinese/china%20culture/culture%20pic/Great%20Inventions3.jpg

http://images.google.com/imgres?imgurl=http://www.booyard.com/chinese/china%20culture/culture%20pic/Great%20Inventions3.jpg&imgrefurl=http://www.booyard.com/chinese/china%20culture/Four%20Great%20Inventions.htm&h=142&w=175&sz=9&tbnid=i5qQJ_nNyGsJ:&tbnh=77&tbnw=95&hl=en&start=19&prev=/images?q=Ancient+chinese+compass&svnum=10&hl=en&lr=&safe=active&sa=G

http://images.google.com/imgres?imgurl=http://www.booyard.com/chinese/china%20culture/culture%20pic/Great%20Inventions3.jpg&imgrefurl=http://www.booyard.com/chinese/china%20culture/Four%20Great%20Inventions.htm&h=142&w=175&sz=9&tbnid=i5qQJ_nNyGsJ:&tbnh=77&tbnw=95&hl=en&start=19&prev=/images?q=Ancient+chinese+compass&svnum=10&hl=en&lr=&safe=active&sa=G

Magnets

• William Gilbert (a physician to Queen Elizabeth I) made many discoveries about magnets – including that the Earth itself is a giant magnetic sphere!

• He also discovered that he could make his own magnets, and coined the term “magnetic pole”.

http://www.wonderquest.com/bar-magnet.jpg

Magnets

• Magnetism is caused by the

movement of electrons within an atom. • Magnets are surrounded by magnetic fields• Electrons produce magnetic fields because

they– orbit the nucleus – spin on their own axis.

http://lep694.gsfc.nasa.gov/lepedu/siteimg/bar_magnet.gif

!!! Chemistry Flashback !!!

• Electrons pair up two per orbital – one spins clockwise, the other counter clockwise.

• Direction of spin determines the “pole” of the electron.• Diamagnetic materials – have paired electrons where

the fields cancel out because all the electrons are in pairs and have opposite spins. – Material will be repelled by a magnetic field (weak effect).

(1/1,000,000 weaker than iron). – The electric fields required to levitate

these materials are extremely large.• Source:http://www.hfml.sci.kun.nl/froglev.html

Magnetic Frog

• Paramagnetic materials - have unpaired electrons.

• Iron (Fe) electron configuration 4 s2 3 d6

– In d cloud electrons occupy 5 orbitals.– Auf bau principle – electrons must enter an empty orbital

before they pair up.

– The magnetic fields of the unpaired electrons combine to make each Fe atom a tiny magnet.

!!! Chemistry Flashback !!!

But not all iron is magnetic…right? Why not?

• The unpaired electrons give areas in these elements small magnetic fields.

• When the individual areas or domains all line up, the piece of metal has a BIG magnetic field

http://www.physics.carleton.ca/~watson/1000_level/Magnetism/1008_Perm_mags.html




Magnetic Materials

• Ferromagnetic – an element which is attracted to magnets and can be made into temporary magnets.– Iron, nickel and cobalt.– All are paramagnetic elements

http://neil.fraser.name/news/2004/iron.gif

http://neil.fraser.name/news/2004/iron.gif

• Hard magnetic materials - require a strong external magnetic field to orient their domains. – Once oriented the domains stay aligned.– Permanent magnets– Alnico, an alloy of aluminum, nickel, cobalt,

iron and copper common permanent magnet.– Heating or hitting can move the domains out of alignment

• Soft magnetic materials (nails & paper clips) are easily magnetized but demagnetized when the external field is removed.– Domains become random again when

the magnet is removed.– Temporary magnetism


Magnetic Materials

http://www.harcourtschool.com/glossary/science/images/gr1/magnetize1.gif



http://www.harcourtschool.com/glossary/science/images/gr1/magnetize1.gif

Magnetic Poles

• Magnets have polarity (different parts of a magnet experience different forces)

• Poles of a magnet are called north and south• Opposite poles attract, like poles repel.

• Magnetic poles always come in pairs (north

and south) not possible to have only one pole– Magnetic dipole.

• Breaking a magnet in half forms two new magnets.

Magnetic Field

Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.


• The space around a magnet has an invisible magnetic field that exerts magnetic forces

• This field is represented by drawing magnetic field lines or lines of magnetic flux

• Greater magnetic flux density (stronger field) is shown with more flux lines– closer lines stronger the magnetic field. – the flux density is the greatest at the POLES!

• arrows show the direction (out of the north pole and into the south pole)

• pass through the magnet to form loops.Earth’s Field

Drawing Magnetic Fields


Compass Method• If we could scatter tiny compass needles over a

piece of paper and bring a bar magnet underneath them, the needles would line up in the bar magnet’s magnetic field

Iron Filing Method• Sprinkling iron files near a magnet will cause the

filings to line up along the magnetic flux lines

Magnetic Fields

Bar Magnet

Two Like Magnets Two Unlike Magnetshttp://www.ece.neu.edu/faculty/nian/mom/work.html

http://www.ece.neu.edu/faculty/nian/mom/work.htmlhttp://www.ece.neu.edu/faculty/nian/mom/work.html

Magnetic Field

• Between two like poles.

http://my.execpc.com/~rhoadley/motion02.htm


Magnetic Field

• Between two opposite poles.



Magnetic Field

• Around a rotating pole.



Magnetic Field

• Field Variations.



Earth’s Magnetism

The earth has a magnetic field! • Scientists theorize it is caused by electric currents

circulating in the liquid outer core.• The earth has both a north and a south magnetic

pole, like a magnet.Notice the earth’s magnetic field lines!• Same shape as a bar magnet Is the Earth’s North Pole a North or a South magnetic pole?

www.edumedia.fr


http://www.edumedia.fr/

Compass

• If suspended, a magnet’s north pole will point toward the earth’s geographic north.

• A compass is a magnetic needle on a pivot.


North Pole Fallacy

Is the Earth’s North Pole a North or South magnetic pole?

• You already know that like poles

_______and that unlike poles _______.

But think about this…• The north end of a magnet is attracted to the south

end of a second magnet.• The north end of a compass needle points to the

geographic NORTH pole of the earth….• So…the earth’s geographic NORTH pole must be a

magnetic SOUTH pole.


Earth’s Magnetic Field

• Since the earth is tilted, the magnetic poles of the earth don’t line up exactly with the geographic poles.

• This discrepancy is called magnetic declination.

Copywrited by Holt, Rinehart, & Winston

http://www.globalsecurity.org/military/library/policy/army/fm/3-25-26/ch11.htm

Angle of declination

Importance of Earth’s Magnetic Field

• Navigation– Animal migration– Navigational systems

• Protects the earth from solar winds– Charged particles from the sun– Aurora Borealis – Northern Light– Aurora Australis – Southern Lights

http://www.elasmoresearch.org/education/topics/topic_images/magnet.gif

http://science.nasa.gov/newhome/headlines/images/core_plasma/magnetosphere.jpg

Earth’s Core





http://solidearth.jpl.nasa.gov/IMAGES/mag2.gif


• Over the past 150 years, the main component of the Earth's magnetic field has decayed by nearly 10%, a rate ten times faster than expected

• This is centered around an area in the south Atlantic Ocean that has a field 35% weaker than expected.

• source: http://solidearth.jpl.nasa.gov/images/mag2.gif

http

://s

cien

ce.n

asa.

gov/

new

hom

e/he

adlin

es/a

st07

sep9

9_1.

htm


http://solidearth.jpl.nasa.gov/IMAGES/mag2.gif

http://solidearth.jpl.nasa.gov/images/mag2.gif

http://science.nasa.gov/newhome/headlines/ast07sep99_1.htm

Are Magnetism and Electricity Connected?

• Until 1820 everyone thought electricity and magnetism were completely separate.

• Hans Oersted discovered that a compass needle is deflected by an electric current.

• Electricity and Magnetism are just different aspects of the same thing!

http

://w

ww

.am

eric

anpi

ctur

es.c

om/

gene

alog

y/de

scen

t/ph

otos

/H

.C.O

erst

ed.1

822.

jpg

http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/images/35-wirecompass320.jpg



Magnetic Field Generation

• Moving charges create magnetic fields.

• The magnetic field of a current through a straight wire makes circles perpendicular to the current.

Magnetic Field Generation



Right Hand Rule (Grip Rule)

To calculate the direction of the magnetic field produced by a current carrying wire:

• Point your right thumb in the direction of the conventional current flow.

• Your fingers curl in the direction of the magnetic field.

Current Convention:



RHR Practice

What direction would the magnetic field be around a current coming out of the screen?

• A. Clockwise• B. Counterclockwise• C. Into the screen• D. Out of the screen

The magnetic field of a straight, current-carrying wire is

A. parallel to the wire.B. perpendicular to the wire.C.around the wire.D. inside the wire.E. zero.

Slide 24-4

Checking Understanding

Point P is 5 cm above the wire as you look straight down at it. In which direction is the magnetic field at P?

Slide 24-19


Slide 24-20


Point P is 5 cm above the wire as you look straight down at it. In which direction is the magnetic field at P?

Magnetic Force

• A charge moving in a magnetic field feels a force.

• The force on the charge is a “sideways” force - perpendicular to the field line and to the charge’s velocity.

http://www.sr.bham.ac.uk/xmm/images/fmc/lhr_340_287.gif

http://www.sr.bham.ac.uk/xmm/images/fmc/lhr_340_287.gif

Magnetic Force

• Charge not moving?

• Charge moving with field line? • The charge must move ACROSS the

field lines to feel a force

• NO FORCE

• NO FORCE


Experiments show that:• F ~ the current, I• F ~ the length of conductor in the field, • F = (a constant) I x

• the constant is called the magnetic flux density (B) when current flows at 90° to the field.

• B is a measure of the strength of the magnetic field• B units are NA-1m-1 or Teslas (T)

Magnetic Force

Cut

nell

& J

ohns

on,

Wil

ey

Pu

bli

shin

g,

Phy

sics

5th E

d.

• Flux density is the force per unit

length acting on a conductor

placed at 90° to the field.• If the conductor is placed at an angle θ to the

field, then the force is given by:

Magnetic Force

Cut

nell

& J

ohns

on,

Wil

ey

Pu

bli

shin

g,

Phy

sics

5th E

d.

Right Hand Rule (Slap Rule)http://www.ph.unimelb.edu.au/~mkl/640162/prot/module1/image/RHruleI.gif

http://www.ph.unimelb.edu.au/~mkl/640162/prot/module1/image/RHruleI.gif

Magnetic Force on a Wire

• A horizontal wire carries a

current and is in a vertical

magnetic field. What is the

direction of the force on the wire?

1) left2) right3) zero4) into the page5) out of the page

B

I


B

I


Magnetic Force on a Wire

• A horizontal wire carries a current

and is in a vertical magnetic field.

What is the direction of the force

on the wire?


Magnetic Force on a Charge

• Consider a conductor of length, having n free electrons per unit volume. A current, I, is flowing through it.

• Recall, and

• This is the sum of the forces acting on all the free charges as they move through the piece of conductor.

• Therefore, force per charge, F, is given by

• On average, the charges must be moving with speed v = /t.

• Therefore,

• If the direction of the velocity is not at 90° to the flux lines, we use the component of the velocity which acts at 90° to the field.

• Therefore, and the direction of the force is at 90° (perpendicular) to both the velocity and the magnetic field.

Charged Particle in a Magnetic Field



Right Hand Rule (Slap Rule)

Force direction calculation

• Thumb direction of (+) charge• Point fingers in the direction

of the magnetic field• The palm indicates the

direction of force

Alternative method

Is there a left hand rule?• Yes, when a (–) charge is

involved

The direction of the magnetic field can be determined using the right hand rule.

What direction?

A positive charge moving with a constant velocity enters a uniform magnetic field pointing out of the paper. What way will the charge move?

A. Continue straight

B. Curve upward

C. Curve downward

D. Go into the paper

What would have happened if it was a negative charge moving into a magnetic field pointing into the paper?


Magnetic Force

1) out of the page2) into the page3) downward4) to the right5) to the left

A positive charge enters a

uniform magnetic field as

shown. What is the direction

of the magnetic force?

x x x x x x x x x x x x x x x x x x

v

q


1) out of the page2) into the page3) downward4) upward5) to the left

x x x x x x x x x x x x x x x x x x

vq

Magnetic Force






1) out of the page2) into the page3) zero4) to the right5) to the left

® ® ® ® ®

® ® ® ® ®

® ® ® ® ®

® ® ® ® ®

v

q

Magnetic Force






Charge Paths in a Magnetic Field

Three possible paths followed by a charged particle moving through a uniform magnetic field:

1. if q = zero the path is a straight line

2. if q = 90° the path is circular

3. if 0 < q < 90° the path is a helix.


Cut

nell

& J

ohns

on,

Wil

ey P

ub

lish

ing

, P

hysi

cs 5

th E

d.

http://www.sr.bham.ac.uk/xmm/images/fmc/magcir_6k_240_180.jpgCutnell & Johnson, Wiley Publishing, Physics 5th Ed.

http://www.sr.bham.ac.uk/xmm/images/fmc/magcir_6k_240_180.jpg




Flux Density due to Current Flowing in a Long, Straight Wire

The flux density, B, at point p is directed out of the plane of the diagram.

• The magnitude of B depends on– The current, I– The perpendicular distance, r– The medium in the space around the wire

• Assumption: if r is small compared with the length of wire, then B does not depend on the length of the wire.

Therefore,

• where µ is the permeability of the medium • µo represents air or a vacuum and has units of NA-2 or

Henrys per meter (Hm-1).

Force per Unit Length between Two Long Parallel Conductors Carrying Current

• Flux density, B, near conductor 2 due to I1 is

• So, the force (F=I B) which acts on length of conductor 2 is given by

• Therefore, the force per unit length is given by

• Also, by Newton’s third law we can say that there is an equal but opposite force acting on conductor 1.

• Now, if F/ .= 2 × 10-7 Nm-1 and r = 1m and I1 = I2, then the current in each conductor is 1 Amp.

Derivation source:http://www.saburchill.com/physics/chapters

Formal Amp Definition

One Amp is that current which, when flowing in each of two

straight, parallel, infinitely long wires, separated by 1m, in a

vacuum, produces a force per unit of 2 ×10-7Nm-1.

Attraction or Repulsion

What will happen if two long parallel wires are carrying currents, I1 and I2, flowing in the same direction are placed next to each other?

a. They attract each other

b. They repel each other

c. No interaction

Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Copywrited by Holt, Rinehart, & Winston


Attraction or Repulsion

What will happen if two long parallel wires are carrying currents, I1 and I2, flowing in the opposite direction are placed next to each other?

a. They attract each other

b. They repel each other

c. No interaction



Flux Density inside a Long Coil (Solenoid) • Current flowing through a conductor

produces a magnetic field. • For a long straight wire, then the field is

distributed over a large region of space. • If the wire is used to make a coil, the

magnetic field is concentrated into a smaller space and is therefore stronger.


Wire Loop

• Bending a current carrying wire into a circle gives a magnetic field like this:


Solenoid

• Winding many turns makes a solenoid coil with a magnetic field like a bar magnet.


Right Hand Rule (Coil Rule)

Current Loop

P

I

What is the direction of

the magnetic field at the

center (point P) of the

square loop of current?



Magnetic Strength of a Coil

• Theory suggests that the flux density, Bc, at the center of a long coil, is

• Where N = # of turns• = length• Measurements shows that if the solenoid’s

length ≥ 10 times its diameter, the flux density inside is uniform over most of its length.

• The graph shows the variation of B along the axis of a long solenoid.

Electromagnet

• A coil of wire with a current passing through it creates a magnetic field just like a bar magnet.

• Can be turned on/off or reversed by controlling the current flow.

http://www.reprise.com/host/electricity/images/magnetism.gif


Electromagnet

How can you strengthen an electromagnet?• Putting an iron core in the center of the

coil strengthens the magnetic field. • Adding more coils makes the magnetic

field stronger.• Increasing the current through the wire

strengthens the magnetic field.



Simple Electric Motors• A coil, with current flowing through it, placed

in a magnetic field, can experience a torque.

• When a current-carrying loop is placed in a magnetic field, the loop tends to rotate such that its normal becomes aligned

with the magnetic field.

Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.

Cut

nell

& J

ohns

on,

Wil

ey P

ub

lish

ing

, P

hysi

cs 5

th E

d.

Simple Electric Motors

Torque (τ): • magnitude of the torque ~ I• depends on the angle, θ, between the field and the

coil. • Torque ~ sin θτ =F x d for a loop of wire • d = w/2 sinΦ

where w = width of the loopΦ is the angle between the normal to the plane of the loop and the direction of the magnetic field.

Net torque = τ = ILB(1/2 w sin Φ) + ILB(1/2 w sin Φ) = IAB sin Φ

• Wire is wrapped to form a loop of N loops

= tNIABsinf

Simple Electric MotorsA simple d.c. electric motor

consists of a coil of wire placed in a magnetic field.

• When current flows through the coil, a torque is produced.

• The brushes and commutator conduct the current from the supply to the coil.

• Each of the carbon brushes makes contact with one half of the commutator.

• The commutator rotates with the coil.

• This arrangement ensures that the torque produces a constant sense of rotation.



• In the diagram below, the force on side a – b of the coil will be directed downwards so the rotation is counter-clockwise (viewed from the front).

• When the coil has rotated 180°, side d – c is on the left but, as the commutator has also rotated, the torque is still in the same sense.

DC Motors






Magnetic Flux

• If B is at 90° to the area, A, then the total magnetic flux, Φ "passing through" A is defined to be

• Φ greek letter phi• The units of flux are Tm²

1 Tm² = 1 Weber

• If B is not at 90° to the area: the component of B which acts at 90° to A is B cos α.

• So, the flux passing through the area is

f = AB

Flux Linkage

• a flux, Φ, "passes through" a coil of N turns then the coil is said to be linked to the flux so we define the quantity "flux linkage" as

N = # of turns,

B = magnetic field strength

A = cross sectional area of coil

θ = angle to normal of coil– Associated with a multiple turned coil or solenoid

Φ = NBA cosθ

Flux linkage = # of turns x magnetic flux

Can a Magnetic Field produce a Current?

• For 12 years after Oersted’s discovery that electric current creates a magnetic field, scientists looked for a way for magnetic fields to create a current.

• In 1832, Michael Faraday made a suggestion: “Move the Magnet!”

• Doing so “induced” an electric current!!!! The result of Faraday’s work became known as electromagnetic induction.

http://www.peoplephysics.com/images/leggifisiche/induzionean.gif

http

://s

cien

cew

orld

.wol

fram

.com

/bio

grap

hy/F

arad

ay.h

tml

http://www.peoplephysics.com/images/leggifisiche/induzionean.gif

http://scienceworld.wolfram.com/biography/Faraday.html

http://scienceworld.wolfram.com/biography/photo-credits.html#Faraday

http://scienceworld.wolfram.com/biography/photo-credits.html#Faraday

Electromagnetic Induction

• Thrusting a magnet into a loop of wire induces current.

• Holding the magnet still does not!

• It doesn’t matter whether the magnetic field moves or the wire moves. It works either way!

• Faraday described this by saying that electromotive forces are generated in the wire whenever field lines cut across the wire.

• When the magnet is thrust into the loop, its field lines cut across the wire generating EMF that produces current.

• Ditto when the loop is moved over themagnet.

http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/images/c01347.jpg

http://www.houghtonmifflinbooks.com/booksellers/press_release/studentscience/gif/induction1.gif

http://www.slcc.edu/schools/hum_sci/physics/tutor/2220/em_induction/

http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/images/c01347.jpg

http://www.houghtonmifflinbooks.com/booksellers/press_release/studentscience/gif/induction1.gif

http://www.slcc.edu/schools/hum_sci/physics/tutor/2220/em_induction/

EMF Clarification

Warning: The term EMF can be misleading!!!!!• The electromotive forces that are generated

are not really “forces”.• They are actually increases in electrical

potential (voltage) and are therefore measured in VOLTS!

• IB defines EMF – work done per unit charge– Circuit EMF –in moving charge from one terminal

of the battery to the other.– Motional EMF – induced as a result of the motion

of a conductor in the magnetic field

But WHY??!?!?!?!

EMF Generation

No relative motion between the conductor and the magnetic field no emf.

Cop

ywrit

ed b

y H

olt,

Rin

ehar

t, &

Win

ston

Therefore the work done per unit charge is

and, work done per unit charge is the induced emf .

EMF Induced in a Conductor Moving through a Magnetic Field

• A conductor moves a distance, Δs, at 90° to a magnetic field of flux density B, in time Δ t.

• The free electrons in the conductor will experience a force causing them to move through the conductor.

• Suppose that a total charge Δ Q moves past any point in the conductor in time Δ t.

• The work done by the force F is given by

• This work is equal to the energy given to the charge Δ Q.

W = FDs

F Δ s/ Δ Q

EMF Induced in a Conductor Moving through a Magnetic Field

• If the conductor moves at constant speed, the force F must be equal but opposite to the force acting on it due to the current, I, induced in it.

• Therefore,

• So,

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elevol.html#c3Derivation source:http://www.saburchill.com/physics/chapters

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elevol.html#c3

EMF Generation

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/genwir.html#c1

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/genwir.html#c1

EMF generation

• In the case of TWO wire loops, when current is first turned on in one loop, magnetic field lines build up, cutting across the other loop – producing EMF.

• When the current is switched off, the field lines collapse, again cutting across the loop.

Electrical Induction

Cut

nell

& J

ohns

on,

Wil

ey P

ub

lish

ing

, P

hysi

cs 5

th E

d.

Faraday’s Law of Electro-Magnetic Induction

• The induced emf is directly proportional to the rate of change of magnetic flux linking the conductor.

• and, if the conductor is a coil having N turns, we have:

• In the case of a straight conductor moving at 90° to a uniform field, we found

• If the conductor moves a distance Δs in time Δt, then the speed, v, is given by v = Δ s/ Δ t.

• So, in this case, the two statements are equivalent.

Derivation source:http://www.saburchill.com/physics/chapters

http://www.saburchill.com/physics/chapters


Generators

Generator action requires a conductor, a magnetic field, and relative motion. • Generators and motors are

almost identical in construction.• Both consist of wire loops wrapped

around an iron form - the armature - placed in a strong magnetic field.

• Convert energy in opposite directions.– Electric generators convert

mechanical energy to electric energy.

– Electric motors convert electrical energy into mechanical energy.

Cop

ywrit

ed b

y H

olt,

Rin

ehar

t, &

Win

ston

Generator vs Motor

• In a generator, as the armature turns, current is induced in the wire. This current cuts across the magnetic field lines and produces an EMF (voltage).

• In a motor, a voltage is placed across an armature coil that is in a magnetic field. The voltage causes current to flow in the coil creating a magnetic force which causes the armature to turns (torque)

http

://p

hysi

cs.u

sc.e

du/~

bars

/135

/fig

ures

/ch2

1fig

s_fil

es/im

age0

20.jp

g

http://physics.usc.edu/~bars/135/figures/ch21figs_files/image020.jpg

Generator

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/genhow.html#c1

AppliedInduction

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/genhow.html#c1

The Laws of Electro-Magnetic Induction

No current No effect

Short circuited• current flows due to

induced emf• coil is repelled from

the magnet Similarly, if the

magnet is moved the opposite way, the coil "tries" to follow it.

http://www.saburchill.com/physics/chapters/0058.html

Lenz’s Law

When an induced current flows in a wire, it creates a magnetic field. This magnetic field must resist the magnet’s motion, so work is done in moving it.

• When the north pole of a magnet is thrust into the loop, the current must flow in a direction to make a north pole repelling the magnet.


Lenz’s Law

Induced current flows in a direction to oppose the change that produced it.

law of conservation of energy electro-magnetic induction.

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

http://courses.science.fau.edu/~rjordan/rev_notes/movies/MFA07AN1.MOV

http://courses.science.fau.edu/~rjordan/rev_notes/movies/MFA07AN1.MOV

Cop

yrig

ht ©

2007

Pea

rson

Pre

ntic

e H

all,

Inc.

Lenz’s Law

• This circuit is completed by the falling conducting rod. As it falls the magnetic flux decreases inducing a current.

• The force due to the induced current is upward, slowing the fall of the rod.

Cop

yrig

ht ©

2007

Pea

rson

Pre

ntic

e H

all,

Inc.

Eddy Currents

• Induced currents in bulk conductors.– Desired Effect: used as powerful brakes.

– Undesired Effect: source of energy loss (heat)

Copyright ©2007 Pearson Prentice Hall, Inc.

Eddy Currents in Motors

• As DC motor begins to rotate, an emf (back emf) will be induced in the loop due to the changing magnetic flux in the loop.

• Lenz’s law states that this emf will oppose the change in the flux that created it.

• The induced current will flow in the loop in the opposite direction to the direction of the current fed by the battery.

• The current in the loop when it is rotating will be lower than initially before the loop has started to rotate.– Lights dimming when the refrigerator motor turns on

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/imgmag/motgen.gif

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/imgmag/motgen.gif

AC GenerationCopywrited by Holt, Rinehart, & Winston

AC Generator – coil of wire is made to rotate in a magnetic field causing the magnetic flux in the wire to change with its rotation producing an alternating EMF.


AC Generation

Flux Linkage =where N is number of coils, B is magnetic

field, and θ is the angle between the magnetic field and the normal of the coil.


If the coil turns at a constant angular speed,Therefore,

Faraday’s Law

Substituting,

AC Generation

where represents

the slope of a graph of cos (ωt) against t.

• Slope is (calculus)

• EMF becomes

(max EMF)

Note: EMF is zero when the flux is a max or min and flux is zero when the EMF is a max or min

AC Generation

How does the speed of the coil rotation in a generator effect the output power?

P=ε IR

tNABI

)sin(

)(sin 2

2

tR

NABP

• If the speed is doubled what will be the change in output power?

AC Generation

• If an identical light was burning with the same intensity in the DC and AC circuits shown below, would the average current be the same?

Physics for the IB Diploma 5th Edition (Tsokos) 2008

• From Ohm’s Law:• So,

or• But, average IAC is zero

• Average or mean AC

Power must be the

same as the DC Power

for the light to have the

same intensity.

AC Generation

Root Mean Square

• Since P = I2R, then• Where, or

This is called the root mean square (rms)

The r.m.s. value of an a.c. supply is analogous to the steady d.c.value which would convert heat at the same rate in a given resistance.

AC Notation


Transformer

A device used to change voltage in an alternating current from one value to another.

Constructed with two sets of independent coils (primary and secondary) of wire around a common iron core.

Copywrited by Holt, Rinehart, & Winston Copyright ©2007 Pearson Prentice Hall, Inc.


The Ideal Transformer

Assumptions of an ideal transformer:

• the coils have zero resistance

• all the magnetic flux, Φ, produced by the primary current, Ip, is linked with the secondary coil

• When Ip changes, Φ changes.

• From Faraday’s law, we have:

• Combining these two statements gives

Cop

ywrit

ed b

y H

olt,

Rin

ehar

t, &

Win

ston

Transformers

Transformer

• Power in both the primary and secondary circuit of the transformer is the same.

• Transformer Equations

p

s

s

p

s

p

I

I

V

V

N

N

P = primary quantities

S = secondary quantities

Challenges: • Eddy currents are produced in the iron

core because the electrons in the iron move due to the magnetic field.

• These cause the material to heat up. • By laminating the core into thin

sandwiches of iron these are eliminated.

http

://w

ww

.sa

yeds

aad

.co

m/f

undm

ent

al/1

9_

TR

AN

SF

OR

ME

RS

%20

_file

s/im

age0

03.g

if

Transformer Example

A TV contains a transformer with primary windings of 200 turns and a secondary winding of 50 turns. If 120 V is supplied to the primary winding what is the secondary output voltage?

What is the secondary output current?


TransformerExamples

AC vs DC Power Distribution

AC vs DC Power – Current Wars

DC – Thomas Edison• Invented the light bulb• Owned the patents for DC

Power Distribution• Provided DC Power to 59

customers in NYC, September 4, 1882

• Company became General Electric

AC – Nikola Tesla• Invented the AC Motor, radio

(Marconi given credit), radio control.• Owned the patents for AC Power

Distribution• Worked for Edison then went to

work for George Westinghouse• Won contract to provide electricity

to Chicago World Fair in 1893

What if Edison had won the current wars?

If so• Homes powered

with DC Power.– Power plants needed

to be within a few miles of home.

• Currently, power plants are far from homes. Why?

• Long power lines• Feasibility?

power planthomeappliance

long transmission line

Rload

Rwire

Rwire

X

looks like:

Estimate resistance of power lines: • ~ 0.001 Ohms per meter• length 200 km

Calculate current required by a single bulb• 120 W light bulb• 12 Volt connection box using

Calculate power lost in transmission line • Recall, Plost = I2R

120 WattLight bulb

12 Volt Connection Box

Power Plant on Colorado River

150 miles

DC Power Distribution – Feasibility?

0.001 W/m 2105 m = 20 Ohms

P = VI so I = P/V I = 120 W/12 V = 10 A

Plost = I2R = (10A)2 x 20Ω = 2000 W

Calculate Total Power Required• Total Power = Power Lost + Power Required

• Calculate the efficiency ( )? = e e Pout/Pin

• What could we change in order to do better?

120 WattLight bulb

12 Volt Connection Box


150 miles


Rload

Rwire

Rwire

X

=e Po/Pi= 120 W/4120 W = 0.3%

Total Power = 2 (2000) + 120 = 4120 W

The Tradeoff

• Major Problem: high current through the (fixed resistance) transmission lines

• Need less current– Power Loss is I2R I2 increases exponentially

with current• Appliances require minimum amount of power

– P = VI so less current demands higher voltage• Solution: High Voltage transmissionRepeat the power calculation for a 120 W light bulb with 12,000 Volts or 12kV delivered to the house.

Calculate • Current• Power Lost in Transmission Line• Total Power Required• Efficiency ( )? = e e Pout/Pin

More Power Delivered More Profit!

120 WattLight bulb

12,000 Volt Connection Box


150 miles


=e Po/Pi= 120 W/120.004 W = 99.996%

Total Power = 2 (0.002W) + 120W = 120.004 W

I = P/V = I = 120 W/12,000 V = 0.01 A

Plost = I2R = (0.01A)2 x 20Ω = 0.002 W

DANGER High Voltage!• High voltage in each household is a recipe for disaster

– sparks every time you plug something in– risk of fire– not cat or kid friendly

• Need a way to step-up/step-down voltage – Transformer– not possible with DC, Why?– Works only with AC (Tesla wins)

A way to provide high efficiency, safe low voltage:

High Voltage Transmission LinesLow Voltage to Consumers

step-up to 500,000 V

step-down,back to 5,000 V

step-down to 120 V

~5,000 Volts

Power Transmission

Transmission structures

three-phase “live” wires

500,000 230,000 138,000 69,000 7–13,000long-distance neighborhood

to house

How electricity gets to your home….

Step-up transformer

Power station

National Grid

Step-down transformer Homes, businesses

and factories etc

Power Transmission


Power Transmission

Power Generated at Power Plant• Power stepped up in voltage

and sent to high voltage transmission lines

• Power stepped down in voltage through transformers prior to sending it to your home.

Example: 480kW Plant• Transmission Lines transmit

electricity at 240kV• What is the current in the line? • If the resistance of the cable is

100 Ω what is the power lost in the transmission?

• What would be the power lost if the lines transmitted power at 120kV?

UCSD: Physics 8; 2006 113Spring 2006

= 170 Volts

= -170 Volts

120 VAC is a root-mean-square number: peak-to-peak is 340 Volts!

Power Transmission

• Most U.S. voltages are 120 V. It used to be 110-V because early light bulbs couldn’t handle higher voltages.

• Most other countries have switched to 220 V, which transmits power more efficiently.


AC Receptacle• Receptacles have three

holes each• Lower (rounded) hole is

earth ground– connected to pipes.– green wire

• Larger slot is “neutral”– for current “return”– never far from ground– white wire– if wired correctly

• Smaller slot is “hot”– swings to +170 and 170– black wire– dangerous one

AC DC - Rectification• Half-wave Rectification

– A single diode convert

AC into a pulsating DC– Diode

• Electrical gate• Allows only positive current through

(forward biased)• Blocks negative current (reverse

biased)

– Output limitation• Electrical energy in AC negative

cycle not used.

AC DC - Rectification• Full-wave Rectification

– A diode bridge converts

AC into a pulsating DC signal using all the energy of the AC signal


– Positive half cycle, current flows A-C– Negative half cycle, current flows B-D


– Drawing the circuit• Diodes on parallel sides point

in the same direction• AC signal is fed to the point

where opposite ends of two diodes join.

• Positive output comes from the junction of the negative side of two diodes

• Negative output comes from the junction of the negative side of two diodes

AC DC – Smoothing Circuit• Turns the pulsating output of a rectifying circuit

into a more steady DC output.– Uses a capacitor in parallel with the output of

rectifying circuit.– Smoothed half-wave Rectification

AC DC – Smoothing Circuit• Turns the pulsating output of a rectifying circuit

into a more steady DC output.– Smoothed full-wave Rectification

AC DC – Smoothing Circuit• Output ripple – slight fluctuation

• Capacitor– Short term energy storage– Constantly charging and discharging– Slow discharge requires a large capacitance

C so the time constant

τ is significantly largeτ=RC where R = resistance

Wheatstone Bridge

• Arrangement used to estimate an unknown resistor

• Used primarily with DC circuits• Four resistors

– Two fixed resistors – One variable resistor – One unknown resistor (RX)– Variable resistor always paired with unknown resistor.

• Galvanometer (Ammeter) bridges pair of resistors

• Adjust variable resistor so galvanometer

reads 0 A

Wheatstone Bridge

• When galvanometer reads 0 A, no potential difference across BD.

• Therefore, the potential difference across R1 and R3 are identical and the same is true for R2 and RX.

– V1=I1R1=I3R3 and V2=I1R2=I3RX

– So,

Wien Bridge

• Modification of Wheatstone bridge allow identification of resistance and capacitance values for an unknown component

• Used with AC power supply• Current in center arm adjusted to zero.

– Adjusting R2, C2 and the frequency of the supply to minimize current.

– Unknown values of RX and CX can

be calculated.

Sources:

Homer, D. and Bowen-Jones, M.,(2014) Physics: Course Companion, Oxford University Press

Tsokos, K.A.,(2014) Physics for the IB Diploma,6th edition, Cambridge University Press

University of California at San Diego (2008). AC Electricity: Why AC Distribution? Retrieved from http://physics.ucsd.edu/~tmurphy/phys8/lectures/lectures.html

http://physics.ucsd.edu/~tmurphy/phys8/lectures/lectures.html



Documents

Magnetism Intro mages/type_effects/Electro_Magnet.gif