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Lecture 13: June 19 th 2009. Physics for Scientists and Engineers II. Ampere’s Law. Top View. Ampere’s Law. Top View. Ampere’s Law. Ampere’s Law. Top View. Ampere’s Law. Example Application of Ampere’s Law. I 2. I 1. Example Application of Ampere’s Law. Preventing Pitfalls. - PowerPoint PPT Presentation
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Physics for Scientists and Engineers II , Summer Semester 2009
1
Lecture 13: June 19th 2009
Physics for Scientists and Engineers II
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
3
Ampere’s Law
path.different a Picking
I
Top View
sd
semicircleleft semicircleright tionstraighttionstraight
sdBsdBsdBsdBsdBsecsec
1r2r
Bsd
sd
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
5
Ampere’s Law
path.different a Picking
I
Top View
sd
semicircleinner semicircleright tionstraighttionstraight
sdBsdBsdBsdBsdBsecsec
1r
2r
B
sdsd
B
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
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.
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
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”
Physics for Scientists and Engineers II , Summer Semester 2009
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
Physics for Scientists and Engineers II , Summer Semester 2009
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