Download - Lecture 13: June 19 th 2009

Physics for Scientists and Engineers II , Summer Semester 2009

1

Lecture 13: June 19th 2009

Physics for Scientists and Engineers II


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Ampere’s Law

current. thegsurroundin circle a tol tangentiaare lines field Magnetic

B

I

a I

B

Top View

sd

Irr

IsdBsdB 0

0 22


3

Ampere’s Law

path.different a Picking

I

Top View

sd

semicircleleft semicircleright tionstraighttionstraight

sdBsdBsdBsdBsdBsecsec

1r2r

Bsd

sd


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Ampere’s Law

III

sdr

Isd

r

I

sdBsdBsdBsdBsdB

rr

semicircleleft semicircleright tionstraighttionstraight

000

02

0

01

0

secsec

22

02

02

21

IsdB

IsdB

0

0

path. closed by the

bounded surfaceany through passingcurrent steady total theis I

where,equalspath closedany around integral line The


5

Ampere’s Law

path.different a Picking

I

Top View

sd

semicircleinner semicircleright tionstraighttionstraight

sdBsdBsdBsdBsdBsecsec

1r

2r

B

sdsd

B


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Ampere’s Law

022

02

02

00

02

0

01

0

secsec

21

II

sdr

Isd

r

I

sdBsdBsdBsdBsdB

rr

semicircleinner semicircleright tionstraighttionstraight

IsdB

IsdB

0

0

path. closed by the

bounded surfaceany through passingcurrent steady total theis I

where,equalspath closedany around integral line The


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Example Application of Ampere’s Law

I2

I1 r

r

r

3

32

21

1

r:Outside

rr:conductorOuter

rr :(air)Insulator

rr :conductorInner

1

10100

21

21

10

22

1

100

1

r22

rrr :Insulator

r2r

r2

rr :conductorInner

IBIrBIsdB

rI

BI

rBIsdB

inside

inside


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Example Application of Ampere’s Law

r2

2

rr :Outside

r

2

r2

rrr :conductorOuter

210

2100

3

22

23

22

2

210

22

23

22

2

2100

32

IIB

IIrBIsdB

rr

rII

rB

rr

rIIrBIsdB

inside

inside


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Preventing Pitfalls

I

page). theofout (comingpath thelar toperpendicu is B

Rather, path. blue thealong 0B that know wefact,In

0By that necessarilnot but 00

sdBsdB

sd


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Preventing Pitfalls

I

laws. sAmpere' from sconclusionright thedraw

path to thealongconstant B of magnitude that theand field magnetic theof

direction theetc.symmetry from know toneedalready You :Conclusion

path. red thealong 0

IμsdB

sd


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A Long Solenoid (Wire wound in the form of a helix)

interior"."in their fields magnetic uniform reasonably produce solenoids Long

I

small. isit but coil, theoutside0B

0

IμsdB

!!!! 0Bmean that t Doesn'

0

sdB


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A Long Solenoid (Wire wound in the form of a helix)

internalexternal B B that assumption theMake

length)unit per turnsofnumber theis

loop) blue theinside turnsofnumber (N

000

0

L

N(n

InμIL

NμBINμLB

INμsdB

externalB

internalB

L


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Problem 33 in the book

L

density.current linear a is

direction)-yin paper of(out J s

x

z

.2

and lar toperpendicu

sheet, the toparallel is that Show

0s

s

JμBJ

B


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Problem 33 in the book

sJμL

IμBIμLB

IμsdB

000

0

2

1

2

12

L

density.current linear a is

direction)-yin paper of(out J s

x

z .J lar toperpendicu

andsheet the toparallel is B that showsSymmetry

s


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Gauss’s Law in Magnetism

(weber).1Tm 1 :flux magnetic of Units

Ad:surface ah flux thoug Magnetic

Add :Adelement surfaceh flux thoug Magnetic

2

B

B

Wb

B

B

0Ad

:zero always is

surface closedany gh flux throu magnetic The :magnetismin law sGauss'

B


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Gauss’s Law Comparison

0Ad B0

Adinsideq

E

Electric flux through closed surfaceis proportional to the amount of electriccharge inside (electric monopoles).

Isolated magnetic monopoles have never been found.


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Magnetism in Matter

We now know how to build “electromagnets” (using electric current through a wire).We also found that a simple current loop produces a magnetic field / has a magneticdipole moment.

How about the “current” produced by an electron running around a nucleus?Let’s use a classical model (electron is a point charge orbiting around a positively charged nucleus.

-+ r

direction of motion of electronI

The tiny current loop produces a magnetic moment

L Orbital angular momentum of electron


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Magnetism in Matter

-+ r

I

L

)(22

1

2

1

2

22

2

LLm

e

m

Le

m

LrvrvmL

rverr

veIA

r

vee

T

e

t

qI

ee

ee

L = “orbital angular momentum”


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Quantization

class). thisof scope thebeyond is ...thisdirection. onein only that

fromdifferent is which momentum,angular orbital total"" with do tohas 2factor (the

22

2: of valuenonzerosmallest

constant). sPlank' 100512

of multiplesin occursonly it :(means

quantized"" is L momentumangular Orbital :Physics Quantum

34

ee m

eL

m

e

hJs.π

h


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Spin

magnetonBohr thecalled is2

1027.92

:spin toduemoment Magnetic

2

3S :momentumangular spin of Magnitude

electron.an ofmoment magnetic total the toscontribute that electrons ofproperty intrinsicAn :Spin

B

24spin

e

e

m

e

T

J

m

e

0existmust electron unpairedan electrons ofnumber uneven with atomsFor

0paired"" are electrons all whereatomsFor

spin

spin

spinorbitaltotal

electronnucleus electrons. and protons sit' toduemoment magnetic a has also atoman of nucleus The