Chapter 20, 21Chapter 20, 21

Magnetism and ElectromagnetismMagnetism and Electromagnetism

MAGNETISM

Arguable the oldest subject in Physics: ancient Greeks (near the City of Magnesia) and Chinese realized certain strange stones attracted iron.

Around 1600, William Gilbert proposed that the Earth itself is A gigantic magnet.

For a long time, people knew only one source of magnetism from Iron. In 1821, a Danish physicist, Oersted noticed that an electrical wire carrying current made the near-by compass reorient. First clue of inter-relation between electricity and Magnetism.

Ampere, Faraday established the nature of electricity and magnetism (all from their experimental observations).

MagnetsMagnets PolesPoles of a magnet are the ends where of a magnet are the ends where

objects are most strongly attractedobjects are most strongly attracted• Two poles, called Two poles, called northnorth and and southsouth

Like poles repel each other and unlike poles Like poles repel each other and unlike poles attract each otherattract each other• Similar to electric chargesSimilar to electric charges

Magnetic poles cannot be isolatedMagnetic poles cannot be isolated• If a permanent magnetic is cut in half repeatedly, you If a permanent magnetic is cut in half repeatedly, you

will still have a north and a south polewill still have a north and a south pole• This differs from electric chargesThis differs from electric charges• There is some theoretical basis for monopoles, but There is some theoretical basis for monopoles, but

none have been detectednone have been detected

More About MagnetismMore About Magnetism An unmagnetized piece of iron can An unmagnetized piece of iron can

be magnetized by stroking it with a be magnetized by stroking it with a magnetmagnet• Somewhat like stroking an object to Somewhat like stroking an object to

charge an objectcharge an object Magnetism can be inducedMagnetism can be induced

• If a piece of iron, for example, is placed If a piece of iron, for example, is placed near a strong permanent magnet, it will near a strong permanent magnet, it will become magnetizedbecome magnetized

S N S NS N

S NS N

S NN S

Magnets exist in pairs of N-S poles.

A theoretical prediction says that it is possible to have magnetic mono-poles but they have not been observed!!

Magnetic field cannot be defined as E-field,

FE = qEFB = qBB

Magnetic FieldsMagnetic Fields A vector quantityA vector quantity Symbolized by Symbolized by BB Direction is given by the direction a Direction is given by the direction a

north polenorth pole of a compass needle of a compass needle points in that locationpoints in that location

Magnetic field linesMagnetic field lines can be used to can be used to show how the field lines, as traced show how the field lines, as traced out by a compass, would lookout by a compass, would look

Magnetic Field Lines, sketchMagnetic Field Lines, sketch

A compass can be used to show the A compass can be used to show the direction of the magnetic field lines (a)direction of the magnetic field lines (a)

A sketch of the magnetic field lines (b)A sketch of the magnetic field lines (b)

Magnetic Field Lines, Bar Magnetic Field Lines, Bar MagnetMagnet

Iron filings are Iron filings are used to show the used to show the pattern of the pattern of the magnetic field linesmagnetic field lines

The direction of the The direction of the field is the field is the direction a north direction a north pole would pointpole would point

Magnetic Field Lines, Unlike Magnetic Field Lines, Unlike PolesPoles

Iron filings are Iron filings are used to show the used to show the pattern of the pattern of the magnetic field magnetic field lineslines

The direction of The direction of the field is the the field is the direction a north direction a north pole would pointpole would point

Magnetic Field Lines, Like PolesMagnetic Field Lines, Like Poles Iron filings are Iron filings are

used to show the used to show the pattern of the pattern of the magnetic field linesmagnetic field lines

The direction of the The direction of the field is the field is the direction a north direction a north pole would pointpole would point• Compare to the Compare to the

electric field electric field produced by like produced by like chargescharges

Magnetic and Electric FieldsMagnetic and Electric Fields An electric field surrounds any An electric field surrounds any

stationary electric chargestationary electric charge A magnetic field surrounds any A magnetic field surrounds any

movingmoving electric charge electric charge A magnetic field surrounds any A magnetic field surrounds any

magnetic materialmagnetic material

Earth’s Magnetic FieldEarth’s Magnetic Field The Earth’s geographic north pole The Earth’s geographic north pole

corresponds to a magnetic south corresponds to a magnetic south polepole

The Earth’s geographic south pole The Earth’s geographic south pole corresponds to a magnetic north polecorresponds to a magnetic north pole• Strictly speaking, a north pole should be Strictly speaking, a north pole should be

a “north-seeking” pole and a south pole a “north-seeking” pole and a south pole a “south-seeking” polea “south-seeking” pole

Earth’s Magnetic FieldEarth’s Magnetic Field The Earth’s The Earth’s

magnetic field magnetic field resembles that resembles that achieved by achieved by burying a huge bar burying a huge bar magnet deep in the magnet deep in the Earth’s interiorEarth’s interior

N S

In unifrom field, no force only torque!!!

I

X

Right-handed cork-screw rule

Magnetic field can make a closed loop

(not with E-field).

Magnetic FieldsMagnetic Fields In a magnetic field, a current In a magnetic field, a current

carrying wire experiences a magnetic carrying wire experiences a magnetic forceforce• This force has a maximum value when This force has a maximum value when

the wire is perpendicularly to the the wire is perpendicularly to the magnetic field linesmagnetic field lines

• This force is zero when the wire is along This force is zero when the wire is along the field linesthe field lines

Magnetic Fields, contMagnetic Fields, cont One can define a magnetic field in One can define a magnetic field in

terms of the magnetic force exerted terms of the magnetic force exerted on current carrying wireon current carrying wire• Similar to the way electric fields are Similar to the way electric fields are

defineddefined

)( BIILFB

Units of Magnetic FieldUnits of Magnetic Field The SI unit of magnetic field is the The SI unit of magnetic field is the

TeslaTesla (T) (T)

• Wb is a WeberWb is a Weber

2)/( mWb

smCN

mANT

I

B

F

FB = ILB

Length of the section in B-field

Magnetic inductionMagnetic flux densityMagnetic field (strength)

[B] = [F/IL] = Ns/Cm = Tesla *1 Tesla = 104 gauss

FB = ILB

(1) A net force on the loop(2) A net torque on the loop(3) A net force and torque(4) nothing, zip

?Magnetic force on a current carrying loop

S N

XX

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

DC Electrical Motor

X

X

X

X

X

X

X

X

X

Magnetic Force on Magnetic Force on Moving ChargeMoving Charge

The direction of the The direction of the magnetic force is magnetic force is always perpendicular always perpendicular to both to both vv and and BB

F = qvB (vF = qvB (vB)B) Force is smaller when Force is smaller when

v is not perpendicular v is not perpendicular to Bto B

F = 0 when v is F = 0 when v is parallel to Bparallel to B

Right Hand RuleRight Hand Rule Hold your right hand Hold your right hand

openopen Place your fingers in the Place your fingers in the

direction of Bdirection of B Place your thumb in the Place your thumb in the

direction of vdirection of v The direction of the The direction of the

force on a positive force on a positive charge is directed out of charge is directed out of your palmyour palm• If the charge is negative, If the charge is negative,

the force is opposite that the force is opposite that determined by the right determined by the right hand rulehand rule

CRT TV

http://www.paikstudios.com/Nam June Paik

X x x x x

X x x x x

X x x x x

X x x x x

X x x x x

X x x x x

q

vF

F = q v B┴

Force by a magnetic field on a moving charge is always Perpendicular to the direction of motion.

NO WORK DONE BY THE FIELD!!!

q

v

F

qv

Fq

v

F

q

vF

X x x x x

X x x x x

X x x x x

X x x x x

X x x x x

B

qm

r v

FB = q v BForce by B-field

This force causes a circular motion. Centrepetal force = FB

Fc = mv2/r = q v B = FB

r = mv/qBSince there is no work done by the field, in vacuum,

The charge will make a circular motion forever!!!

Bubble Chamber

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

B = 0.36 T

A univalent ion with mass mCame into the field region with

Speed v = 6 x 105 m/s.

An object with +e chargeAnd mass m kg

r = 0.4 m

Mass m?Mass spectrometer

http://www.geo.mtu.edu/weather/aurora/images/aurora/jan.curtis/index4.htmlhttp://science.nasa.gov/headlines/y2002/23sep_auroraseason.htm

Magnetic Fields – Magnetic Fields – Long Straight WireLong Straight Wire

A current-carrying A current-carrying wire produces a wire produces a magnetic fieldmagnetic field

The compass needle The compass needle deflects in directions deflects in directions tangent to the circletangent to the circle• The compass needle The compass needle

points in the direction points in the direction of the magnetic field of the magnetic field produced by the produced by the currentcurrent

Direction of the Field of a Long Direction of the Field of a Long Straight WireStraight Wire

Right Hand Rule Right Hand Rule #2#2• Grasp the wire in Grasp the wire in

your right handyour right hand• Point your thumb in Point your thumb in

the direction of the the direction of the currentcurrent

• Your fingers will Your fingers will curl in the direction curl in the direction of the fieldof the field

Magnitude of the Field of a Long Magnitude of the Field of a Long Straight WireStraight Wire

The magnitude of the field at a The magnitude of the field at a distance r from a wire carrying a distance r from a wire carrying a current of I iscurrent of I is

µµoo = 4 = 4 x 10 x 10-7 -7 T m / AT m / A• µµo o is called the is called the permeability of free permeability of free

spacespace

r2IB o

I

x ox ox ox ox ox ox ox ox o

http://www.bugman123.com/Physics/Physics.html

For infinitely long solenoidB = onI

n: number of turns/m

A solenoid electro-magnet is energized as shown in the figures. Since current flows through wire in the presence of magnetic fields,

the solenoid will feel force. Which figure correctly describes the force actingon the solenoid?

Induced emfInduced emf A current can be produced by a changing A current can be produced by a changing

magnetic fieldmagnetic field• First shown in an experiment by Michael First shown in an experiment by Michael

FaradayFaraday A primary coil is connected to a batteryA primary coil is connected to a battery A secondary coil is connected to an ammeterA secondary coil is connected to an ammeter

Faraday’s ExperimentFaraday’s Experiment The purpose of the secondary circuit is to The purpose of the secondary circuit is to

detect current that might be produced by detect current that might be produced by the magnetic fieldthe magnetic field

When the switch is closed, the ammeter When the switch is closed, the ammeter deflects in one direction and then returns deflects in one direction and then returns to zeroto zero

When the switch is opened, the ammeter When the switch is opened, the ammeter deflects in the opposite direction and then deflects in the opposite direction and then returns to zeroreturns to zero

When there is a steady current in the When there is a steady current in the primary circuit, the ammeter reads zeroprimary circuit, the ammeter reads zero

Faraday’s ConclusionsFaraday’s Conclusions An electrical current is produced by a An electrical current is produced by a

changingchanging magnetic field magnetic field The secondary circuit acts as if a The secondary circuit acts as if a

source of emf were connected to it source of emf were connected to it for a short timefor a short time

It is customary to say that It is customary to say that an an induced emf is produced in the induced emf is produced in the secondary circuit by the changing secondary circuit by the changing magnetic fieldmagnetic field

INDUCTION

Michael Faraday (1791 – 1867)

…it appeared very extraordinary, that as every electric current was accompanied by a corresponding intensity of magnetic action at right angles to the current, good conductors of electricity, when placed within the sphere of this action, should not have any current induced through them, or some sensible effect produced equivalentin force to such a current.

Primary Coil Secondary coil

G

?

Summary of Experimental Findings

EMF is induced in the secondary coil Only when the magnetic field through it changes.

EMF induced is bigger if the area of coil is bigger.

EMF is induced always in the opposite direction of change in magnetic field.

= A B : magnetic flux

Vind = (B/t)A-= - /t

Lenz’s Law

Magnetic FluxMagnetic Flux The emf is actually induced by a The emf is actually induced by a

change in the quantity called the change in the quantity called the magnetic fluxmagnetic flux rather than simply by a rather than simply by a change in the magnetic fieldchange in the magnetic field

Magnetic flux is proportional to both Magnetic flux is proportional to both the strength of the magnetic field the strength of the magnetic field passing through the plane of a loop passing through the plane of a loop of wire and the area of the loopof wire and the area of the loop

B

A = A B┴

B

B//

B┴

0.3 m

0.2 m

B = 0.175 T

40

= (0.3 x 0.2)(0.175 sin(40))= 0.06 x 0.112= 0.0067 T.m2

Vind = - /t

Vt = -3 /tNet number of loops

5 Ohm

Example 23.2

150 turn loop with a 0.75 cm2 cross-sectionMagnetic field: 0 T 0.25 T in 3.6 s

What is the induced current in the coil?

+ -++

-

+

Faraday’s Law and Faraday’s Law and Electromagnetic InductionElectromagnetic Induction

The instantaneous emf induced in a The instantaneous emf induced in a circuit equals the time rate of change of circuit equals the time rate of change of magnetic flux through the circuitmagnetic flux through the circuit

If a circuit contains N tightly wound If a circuit contains N tightly wound loops and the flux changes by loops and the flux changes by Φ during Φ during a time interval a time interval t, the average emf t, the average emf induced is given by induced is given by Faraday’s Law:Faraday’s Law:

tN B

Faraday’s Law and Lenz’ LawFaraday’s Law and Lenz’ Law The change in the flux, The change in the flux, ΔΦ, can be produced ΔΦ, can be produced

by a change in B, A or by a change in B, A or θθ• Since Since ΦΦBB = B A cos θ = B A cos θ

The negative sign in Faraday’s Law is The negative sign in Faraday’s Law is included to indicate the polarity of the included to indicate the polarity of the induced emf, which is found by induced emf, which is found by Lenz’ Law Lenz’ Law • The polarity of the induced emf is such that it The polarity of the induced emf is such that it

produces a current whose magnetic field opposes produces a current whose magnetic field opposes the change in magnetic flux through the loopthe change in magnetic flux through the loop

• That is, the induced current tends to maintain the That is, the induced current tends to maintain the original flux through the circuitoriginal flux through the circuit

AC Generator

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/motorac.html#c2

James Clerk MaxwellJames Clerk Maxwell Electricity and Electricity and

magnetism were magnetism were originally thought to originally thought to be unrelatedbe unrelated

in 1865, James Clerk in 1865, James Clerk Maxwell provided a Maxwell provided a mathematical theory mathematical theory that showed a close that showed a close relationship between relationship between all electric and all electric and magnetic phenomenamagnetic phenomena

Maxwell’s Starting PointsMaxwell’s Starting Points Electric field lines originate on positive Electric field lines originate on positive

charges and terminate on negative charges and terminate on negative chargescharges

Magnetic field lines always form closed Magnetic field lines always form closed loops – they do not begin or end anywhereloops – they do not begin or end anywhere

A varying magnetic field induces an emf A varying magnetic field induces an emf and hence an electric field (Faraday’s Law)and hence an electric field (Faraday’s Law)

Magnetic fields are generated by moving Magnetic fields are generated by moving charges or currents (Ampcharges or currents (Ampère’s Law)ère’s Law)

Maxwell’s PredictionsMaxwell’s Predictions Maxwell used these starting points and a Maxwell used these starting points and a

corresponding mathematical framework to corresponding mathematical framework to prove that prove that electric and magnetic fields play electric and magnetic fields play symmetric roles in naturesymmetric roles in nature

He hypothesized that a changing electric field He hypothesized that a changing electric field would produce a magnetic fieldwould produce a magnetic field

Maxwell calculated the speed of light to be Maxwell calculated the speed of light to be 3x103x1088 m/s m/s

He concluded that visible light and all other He concluded that visible light and all other electromagnetic waves consist of fluctuating electromagnetic waves consist of fluctuating electric and magnetic fields, with each varying electric and magnetic fields, with each varying field inducing the otherfield inducing the other

Hertz’s Confirmation of Hertz’s Confirmation of Maxwell’s PredictionsMaxwell’s Predictions

Heinrich Hertz was Heinrich Hertz was the first to the first to generate and generate and detect detect electromagnetic electromagnetic waves in a waves in a laboratory settinglaboratory setting

James Clerk Maxwell’s Equations(1867)

Pre-Maxwell

JBtBE

B

E

o

o

0

tEJB

tBE

B

E

ooo

o

0

E-field comes out from p-charge andterminates at negative charge.

B-field cannot do like E-field.No magnetic monopole!

Faraday’s law

Ampere’s law

The velocity of transverse undulations in our hypothetical medium, calculated from the electromagnetic experiments, agrees so exactly with the velocity of light calculated fromthe optical experiments, that we can scarcely avoid the inference that light consists in the transverse undulation of same medium which is the cause of electric and magnetic Phenomena.

)/104)(2/1085.8(11

27212 ANmNCv

oo

2.9986 x 108 m/s

Hertz’s Experiment(1887)

Hertz’s Experimental ApparatusHertz’s Experimental Apparatus An induction coil is An induction coil is

connected to two connected to two large spheres large spheres forming a capacitorforming a capacitor

Oscillations are Oscillations are initiated by short initiated by short voltage pulsesvoltage pulses

The inductor and The inductor and capacitor form the capacitor form the transmittertransmitter

Hertz’s ExperimentHertz’s Experiment Several meters away from the Several meters away from the

transmitter is the receivertransmitter is the receiver• This consisted of a single loop of wire This consisted of a single loop of wire

connected to two spheresconnected to two spheres• It had its own inductance and It had its own inductance and

capacitancecapacitance When the resonance frequencies of When the resonance frequencies of

the transmitter and receiver the transmitter and receiver matched, energy transfer occurred matched, energy transfer occurred between thembetween them

Hertz’s ConclusionsHertz’s Conclusions Hertz hypothesized the energy Hertz hypothesized the energy

transfer was in the form of wavestransfer was in the form of waves• These are now known to be These are now known to be

electromagnetic waveselectromagnetic waves Hertz confirmed Maxwell’s theory by Hertz confirmed Maxwell’s theory by

showing the waves existed and had showing the waves existed and had all the properties of light wavesall the properties of light waves• They had different frequencies and They had different frequencies and

wavelengthswavelengths