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前沿科技高端對(duì)話時(shí)間:2016年4月1日(週五)早上9:20-12:30地點(diǎn):N101內(nèi)容:白春禮院士、葉培建教授、ErwinNeher教授及楊芙清院士進(jìn)行演講Mid-term
examination(期中考試)時(shí)間:2016年4月8日(週五)早上10:50-12:50地點(diǎn):C301考試方式:閉卷內(nèi)容:本學(xué)期教授內(nèi)容,課件見公用郵箱(
;xpzhang)英文試卷/答題可帶計(jì)算器不可帶字典,電子詞典,手機(jī),電腦Chapter
30Induction
and
Inductance實(shí)驗(yàn)一:插入或拔出條形磁鐵Someexperimentsaboutinduction實(shí)驗(yàn)二:插入或拔出載流線圈實(shí)驗(yàn)三:接通或斷開初級(jí)線圈的電流實(shí)驗(yàn)四:導(dǎo)線做切割磁感線運(yùn)動(dòng)When
the
magnetic
fluxpassingthrough
the
loop
is
changing,
an
emf
isinduced
in
the
loop.(emf:法語,電動(dòng)勢(shì);英語:electromotive
force)當(dāng)穿過閉合導(dǎo)體回路的磁通量發(fā)生變化時(shí),回路中就產(chǎn)生電流.Faraday’s
Law
of
Induction:
Magneticflux:
F
B
=
B
dSSSI:WeberLenz’s
Law
(楞次定律):An
induced
current
has
a
direction
suchthat
the
magnetic
field
due
to
thecurrentopposes
the
change
in
the
magneticfluxthat
induces
the
current.閉合回路中感應(yīng)電流的方向,總是使得它所激發(fā)的磁場(chǎng)與引起感應(yīng)電流的磁通量的變化方向相反。The
direction
of
an
induced
emf is
that
of
theinduced
current.ΦB
Bεt(a)
Φ
>
0,
dΦ
BB
dtL>
0,
ε
<
0
Bε(b)
Φ
BL
ΦB>
0,
dΦ
B
<
0,
ε
>
0dttΦB
Bt(c)
Φ
<
0,
dΦ
BB
dtL<
0,
ε
>
0
B(d)
ΦBL
ΦB<
0,
dΦ
B
>
0,
ε
<
0dttThe
direction
of
emf
is
opposite
to
the
direction
ofchange
in
magnetic
flux.A
quantitative
treatmentAfter
accurate
experiments,
it
is
found
thatthe
magnitude
of
emf
is
proportional
to
thechange
rate
of
magnetic
flux.感應(yīng)電動(dòng)勢(shì)的大小與磁通量的變化率成正比。dte
=
-
dF
BExample
1:
A
rectangular
coil
of
N
turns
and
oflength
a
and
width
b
is
rotated
at
frequency
f
in
auniform
magnetic
field
B.
The
coil
is
connected
to
co-rotating
cylinders,
against
which
metal
brushes
slide
tomake
contact. Find
the
emf
induced
in
the
coil.
S
θ
Bw
ΦB
=
B S
=
BS
cos
θε
=
-
dΦB
=
BS
sin
θ
dθ
dt
dtε
=
BSω
sin
ωt
=
ε0
sin
ωtε0
=
BSω02effe=
e0=
0.707eEffective
emf:θ
=
ωt正弦交流電Solution:Example
2:
a
metal
rod
is
forced
to
movewith
constant
velocity
v
along
two
parallelmetal
rails,
the
magnetic
field
is
uniform.Find
the
induced
emf.Example
2:
a
metal
rod
is
forced
to
move
withconstant
velocity
v
along
two
parallel
metalrails,
the
magnetic
field
is
uniform.
Find
theinduced
emf.dtdtF
B
=
B
l
se
=
-
dF
B=
-Bl
ds
=
-Blv順時(shí)針Classwork
1:
A
square
loop
of
wire
has
sides
oflength
2.0
cm.
A
magnetic
field
is
directed
out
ofthe
page;
its
magnitude
is
given
by
B=4.0t2
y,where
B
is
in
teslas,
t
is
in
seconds,
and
y
is
inmeters.
At
t=2.5s,
what
are
the
(a)
magnitude
and(b)
direction
of
the
emf
induced
in
the
loop?30lBF
=SF =
2
·
2.52
·
0.023
=
10-4
WebB
B
dS
=
4t
2
yldy
=
2t
2
ldte
=
-
dF
B=
-4tl
3e
=
-4
·
2.5·
0.023
=
-8·10-5
VSolution:Magnetic
flux:emf:順時(shí)針
f
=
iL
·
Bemf:ε
=
BLvi·
·
·
·
·
·
·
··
·
·
·
·
·
·
··
·B··
·
·
·
·
·
·
·
·
·
f
·
·
·v
-+-ε
=
BlvCDInduction
and
energy
transfersWhen
the
conducting
rodis
moving
in
the
magneticfield,
it
will
feel
theAmpere
’s
forceCurrent:i
=
e
=
BLvR
RB2
L2vRf
=
iBL
=B2
L2vRFex
=
f
=
iBL
=RB2
L2v2
e2P
=
Fex
v
==
RThe
external
force
equals
to
the
Lorentz’s
forcei.e.,
P
=
i
2
RThe
work
done
by
the
external
force
equals
to
thethermal
energy,
conversion
of
mechanical
energy
tothermal
energy.v
B
lLε
=
(
·
)
d
In
general, the
emf
for
a
moving
conductorrod
isExample
3:de
=
(v
·
B)
dl
=
vBdl
=
Bw
ldl
A
??v
=
w
·
l
L
B
O
2012LBw
Le
=de
=
Bw
ldl
=
2ABU
-U
=
1
Bw
L2
>
0Induced
electric
field(感生電場(chǎng))According
to
Faraday’s
law,
the induced
emfin
a
conducting
loop
depends
only
on
thechange
rate
of
the
magnetic
flux.The
induced
emf
is
due
to
the
inducedelectric
field. (感生電場(chǎng))A
new
description
of Faraday’s
Law:A
changing
magnetic
field
produces
anelectric
field.BdtdF=
-
Induced
emf:
e
=
E
i
dl
Total
electric
field
:
e
=
(
Es
+
Ei
)
dl
=
E
dldl
=
(
·
Es
)
dS
=
(
·(
V
))
dS
”
0
EsE
=
Es
+
EiFor
statisticfield
d
dt
S
E
dl
=
-
B
dS
LThenFor
a
given
loop,
S
?B?t
dS
E
dl
=
-
Ldt
d
dte
=
-
dF
B
=
-
S
B
dSOn
the
otherhand,iL
=
N
F
BInductor
and
InductanceInductor(電感):任何線圈均可視為電感,通常有N匝。Inductance(電感系數(shù)):B
=
m0niInductance
of
a
long
solenoidL
=
N
F
B
=
NBSi
iL
=
Nm
nS
=
m
n2V0
0N
F
B
=
LiSelf-induced
emf:e
=
-
d
(
N
F
B
)
=
-L
didt
dtLC
oscillator
circuit (LC振蕩電路):L
di
+
q
=
0dt
Cdti
=
dqd
2q
qL
+ =
0dt
2
Cq
=
q0
cos(w
t
+j0
)1LCw
=LC
振蕩電路K12εEnergy
stored
in
a
magnetic
fielddte
=
L
di
+
iRdtei
=
Li
di
+
i
2
RAccording
to
the
conservation
of
energy,
theenergy
delivered
to
the
conductor
is
stored
inthe
magnetic
field.BdUBdtdt=
Li
di
dU=
Lidi2BU
=
1
Li
2thenBUuV=
B
Energy
density2B2VLi
2
m
n2Vi
2
m
n2i
2u
==
0
=
0
2VB
=
m0niUsingWe
obtain0B2uB
=
2mIt
is
the
generalexpression
ofmagnetic
fieldenergy.02e2u
=
e
EClasswork
1:
What
must
be
the
magnitude
of
a
uniformelectric
field
if
it
is
to
have
the
same
energy
density
as
thatpossessed
by
a
0.50
T
magnetic
field?Exercise:
A
long
solenoid
has
a
diameter
of
12.0
cm.When
a
current
i
exists
in
its
windings,
a
uniform
magneticfield
of
magnitude
B
=
30.0
mT
is
produced
in
its
interior.By
decreasing
i,
the
field
is
caused
to
decrease
at
the
rateof
6.50
mT/s.
Calculate
the
magnitude
and
direction
of
theinduced
electric
field
(a)
2.20
cm
and
(b)
8.20
cm
from
theaxis
of
the
solenoid.L
Sd
E
dl
=-
dt
B
dSClasswork
1:
What
must
be
the
magnitude
of
a
uniformelectric
field
if
it
is
to
have
the
same
energy
density
as
thatpossessed
by
a
0.50
T
magnetic
field?E20=
1
B2B
20u
=
1
e
E
2
=
umB0.50Te0
m0E
==(8.85·10-12
F
m)(4p
·10-7
H
m)=1.5·108
V m
.Exercise:L
Sd
E
dl
=
-
dt
B
dSFor
a
given
loop,L?t
S
?B
dS
E
dl
=-
L
LLAccording
to
symmetry
E
dl
=
Edl
=
E
dl
=
E(2p
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