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


2

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


4

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


6

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


7

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


8

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


9

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


10

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


11

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


12

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


13

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


14

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


15

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


16

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.


17

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


18

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”


19

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


20

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

Date post:	07-Jan-2016
Category:	Documents
Upload:	candy
View:	42 times
Download:	3 times

Lecture 13: June 19 th 2009

Documents