2006-4-29 1
(Electromagnetism)
2006-4-29 2
820M
í
?+è
@¥Hr?
? ?è
@MoT¨?
p
1831ME ??
èH??C`
1785M o
e?
L
è ?¥üZQ1?
p
èHD
èHD
t ?D
N
?=Qv8?
t ?D
N
?=Qv8?
1865M
? X
?3
èH? ?
?
2006-4-29 3
èHD
èHD
=
=
?
?
áè?
?ú
?? ?
ú
?? ?
?ì
^? ?
ì
^? ?
×?H?
? ?ú
?? ?
?ú
?? ?
???? ?
??? ?
èH?
?
? X
?3
?
?
?
?
2006-4-29 4
áè?
áè?
M?43?á?
M?43?á?
¥è?
?á
3¥è?
¥è?
?á
3¥è?
(Electrostatic Field)
2006-4-29 5
?8-1 è?
è?
o
?
p
o
?
p
?è? aμè?
?è? aμè?
è?
0?
è?
0? é0
é0
(+e) è0
è0
(-e)
è?
o?
è?
o?
(charge conservation)
B aè? (electric charge)
q X
e
3
1
± e
3
2
±
2006-4-29 6
?á?
?á?
?è?
?è?
W¥MoT¨
W¥MoT¨
1
r
v
2
r
v
21
r
v
21
F
v
12
F
v
1
q
2
q
y
z
x
O
21
3
21
21
21
r
r
qq
kF
v
v
=
= a o
?
p
= a o
?
p
(Coulomb’s Law)
2006-4-29 7
229
/CmN1099.8 ?×≈k
0
4
1
πε
=k
? boèè
21
3
21
21
0
21
4
1
r
r
qq
F
v
v
πε
=
)m/(NC1085.8
2212
0
?×=
?
ε
21
3
21
21
21
r
r
qq
kF
v
v
=
2006-4-29 8
1?üZQ1¥)
?
1?üZQ1¥)
?
21
3
21
21
21
r
r
qq
kF
v
v
=
? ? ?
?
? ? ?
?
1760M
M
um ?
um ?
Y
a<
bW¥ (
(
?? ò_]?
1759M
M
?1à
06.0,
1
2
=∝
+
δ
δ
r
F
·
?êμ
·
?êμ
δ
2006-4-29 9
1773M
M
5ó°
I
02.0≤δ
1785M
M
o
o
04.0=δ
δ+
∝
2
1
r
F
1759M
M
?1à
06.0=δ
?
1
04.2
r
F ∝ ?
1
96.1
r
F ∝
-5
105< ×δ
? X
?3
1971M
M
-16
102.7< ×δ
;0á?é
g102<
-47
0
×m
2006-4-29 10
[ è
è
1]1?_e0?è0Dé0-Wáè ?
1?_e0?è0Dé0-Wáè ?
?£μ? ? b
?£μ? ? b
r = 5.29×10
-11
m
G = 6.67×10
-11
N?m
2
/kg
2
kg1011.9
31?
×=
e
m
2
2
0
4
1
r
e
F
e
πε
=
N1022.8
8?
×=
3
3
kg1067.1
27?
×=
p
m
2
r
mm
GF
pe
g
=
N1063.3
47?
×=
39
g
e
1027.2 ×=
F
F
2006-4-29 11
?8-2 è?<
è?<
è?
è?
?
? T¨
è? è?
è
è
?
?
electronic
field
1. {è8μT¨ ?
2 {è8è??M?
Hè? ?S?
3.áè???C`
2006-4-29 12
B
B
.è?<
è?<
(electric field intensity)
kè?
kè?
Llè
l
0
q
F
v
0
q
F
E
v
v
=
?ê N/C
1.è?<
^
O
vl???ê
è??
s?è? ?
Z_1?
è???
s?¥è? ?¥Z_
2.è?<D
kè?í1
2006-4-29 13
=
=
.?Fe ?
?Fe ?
(superposition principle)
+
0
q
+
1
q
?
2
q
01
r
v
02
r
v
F
v
01
F
v
02
F
v
0201
FFF
vvv
+=
n
FFFF
00201
v
L
vvv
+++=
1.áè ?¥?Fe ?
áè ?¥?Fe ?
2006-4-29 14
2.?<?Fe ?
?<?Fe ?
0
00201
0
q
FFF
q
F
E
n
v
L
vvv
v
++
==
n
FFFF
00201
v
L
vvv
+++=
∑
=
=+++=
n
i
in
EEEEE
1
21
vv
L
vvv
2006-4-29 15
1.?è?¥?<
?è?¥?<
0
2
0
0
4
1
r
r
qq
F
v
v
πε
=
0
q
F
E
v
v
=
0
2
0
4
1
r
r
q
v
πε
=
+
?
? ?<9
?
P
+
r
v
q
F
v
0
q
2006-4-29 16
2.?è?"¥?<
?è?"¥?<
∑
=
=
n
i
i
EE
1
vv
∑
=
=
n
i
i
i
i
r
r
q
1
0
2
0
4
v
πε
0
2
0
4
1
r
r
q
E
v
v
πε
=
1
q
2
q
3
q
1
r
v
3
r
v
2
r
v
1
O
YF
O
YF
2006-4-29 17
è}0
è}0
?′s|è?
?′s|è?
F?¥"d
q q
e
r
v
?+
+= EEE
vvv
ee
rqp
vv
=
è}
2006-4-29 18
2006-4-29 19
2
0
)2/(4
1
e
rx
q
E
?
=
+
πε
[ è
è
2]pè} ¥è?
pè} ¥è?
:(1)
è?üé
è?üé
L
?B?¥è?<
L
?B?¥è?<
(2)
è? ?
è? ?
L?<L
?B?¥è?< b
3
3
(1)
e
r
v
A x
x
q?
q+
O
?
E
v
+
E
v
2
0
)2/(4
1
e
rx
q
E
+
=
?
πε
2006-4-29 20
?+
?=∴ EEE
A
?
?
?
?
?
?
+
?
?
=
22
0
)2/(
1
)2/(
1
4
ee
rxrx
q
πε
2
0
)2/(4
1
e
rx
q
E
+
=
?
πε
e
r
v
A
x
x
q?
q+
O
?
E
v
+
E
v
2
0
)2/(4
1
e
rx
q
E
?
=
+
πε
2006-4-29 21
224
0
)2/1()2/1(4
2
xrxrx
qxr
ee
e
+?
=
πε
?
?
?
?
?
?
+
?
?
=
22
0
)2/(
1
)2/(
1
4
ee
A
rxrx
q
E
πε
p
e
=qr
e
x>>r
e
3
0
2
4
1
x
qr
E
e
A
πε
=
Z_ x?_
3
0
2
4
1
x
p
e
πε
=
1
4
2
2
<<
x
r
e
2006-4-29 22
3
0
2
4
1
x
p
E
e
A
πε
=
e
r
v
A
x
x
q?
q+
O
?
E
v
+
E
v
O
T
3
0
2
4
1
x
p
E
e
A
v
v
πε
=
Dè ¥Z_Bá
Dè ¥Z_Bá
2006-4-29 23
(2)
)4/(4
1
22
0 e
ry
q
EE
+
==
?+
πε
q?
q+
O
y
B
y
?
E
v
+
E
v
θ
B
E
v
θθ coscos
?+
+= EEE
B
θcos2
+
= E
4/
2/
cos
22
e
e
ry
r
+
=θ
2006-4-29 24
[]
2/3
22
0
4/
4
1
e
e
B
ry
qr
E
+
?=
πε
?
?
y>>r
e
H
3
0
4
1
y
qr
E
e
B
πε
=
3
0
4
1
y
p
e
πε
=
Z_ xμZ_
μZ_
)4/(4
1
22
0 e
ry
q
E
+
=
+
πε
θcos2
+
= EE
B
4/
2/
cos
22
e
e
ry
r
+
=θ
q?
q+
O
y
B
y
?
E
v
+
E
v
θ
B
E
v
2006-4-29 25
O
T
3
0
4
1
y
p
E
e
B
v
v
πε
?=
Dè ¥Z_MQ
Dè ¥Z_MQ
3
0
2
4
1
x
p
E
e
A
v
v
πε
=
e
r
v
A x
x
q?
q+
O
?
E
v
+
E
v
q?
q+
O
y
B
y
?
E
v
+
E
v
θ
B
E
v
3
0
4
1
y
p
E
e
B
πε
=
2006-4-29 26
Q
dq¥?<
¥?<
3. ??s?è?¥?<
??s?è?¥?<
qd
P
r
v
0
2
0
d
4
1
d r
r
q
E
v
v
πε
=
0
2
0
4
1
r
r
q
E
v
v
πε
=
?è?
?è?
??{è8¥?<
??{è8¥?<
EE
Q
vv
d∫=
0
2
0
d
4
1
r
r
q
Q
v
πε
∫=
E
v
d
O
s
2006-4-29 27
z35e5
35e5
:5s3
5s3
,as
as
kEjEiEE
zyx
vvvv
++=
kEjEiEE
zyx
vvvv
dddd ++=
EE
Q
vv
d∫=
0
2
0
d
4
1
r
r
q
Q
v
πε
∫=
Q
qd
P
r
v
E
v
d
xx
EE d∫=
yy
EE d∫=
zz
EE d∫=
O
s
S
s
2006-4-29 28
EE
Q
vv
d∫=
0
2
0
d
4
1
r
r
q
Q
v
πε
∫=
Q
qd
P
r
v
E
v
d
O
s
S
s
dd Vq ρ=
8s?
?s?
dd sq σ=
Ls?
dd lq λ=
zè?í
è?í
2006-4-29 29
è 3.
!? b?μB ({è°Lé1 L ,
9è
1
Q
L?μB
P
? ? 7°L¥
<° ?1 d ,
P
??°L
¥ ?L-W
¥C?sY1 θ
1
θ
2
?m
?
Up P?
¥?< .
1
1
θ
2
θ
E
2006-4-29 30
1
1
θ
2
θ
E
r
θ
E
v
d
y
θ
qd
x
x
1 y ?US"
y ?US"
2.êè?í
êè?í
L
Q
xq
=
=
λ
λ dd
2
0
d
4
1
d
r
x
E
λ
πε
=
2006-4-29 31
1
1
θ
2
θ
E
r
θ
E
v
d
y
θ
qd
x
x
2
0
d
4
1
d
r
x
E
λ
πε
=
)cos(dd θπ ??= EE
x
θcosd E=
)sin(dd θπ ?= EE
y
θsind E=
θθ
πε
λ
dcos
4
d
0
d
E
x
=
θθ
πε
λ
dsin
4
d
0
d
E
y
=
dBsM
θ
πθ
cot
)2/(tan
d
dx
?=
?=
θθ dcscd
2
dx =∴
θ
22222
cscdxdr =+=
2006-4-29 32
θθ
πε
λ
dcos
4
d
0
d
E
x
=
θθ
πε
λ
dsin
4
d
0
d
E
y
=
∫
=
2
1
dcos
4
0
θ
θ
θθ
πε
λ
d
E
x
∫
=
2
1
dsin
4
0
θ
θ
θθ
πε
λ
d
E
y
)sin(sin
4
12
0
θθ
πε
λ
?=
d
)cos(cos
4
21
0
θθ
πε
λ
?=
d
1
1
θ
2
θ
E
r
θ
E
v
d
y
θ
qd
x
x
2006-4-29 33
1
1
θ
2
θ
E
r
θ
E
v
d
y
θ
qd
x
x
)sin(sin
4
12
0
θθ
πε
λ
?=
d
E
x
)cos(cos
4
21
0
θθ
πε
λ
?=
d
E
y
H∞→L ).1(
πθθ →→
21
,0
d
EE
yx
0
2
,0
πε
λ
==∴
2006-4-29 34
(2).?íKé?L
??
?íKé?L
??
E )
)
d
v
E
x
v
E
y
P
2/0
21
πθθ →→ ?m
d
E
d
E
yx
00
4
,
4
πε
λ
πε
λ
==∴
1
1
θ
2
θ
E
r
θ
E
v
d
y
θ
qd
x
x
)sin(sin
4
12
0
θθ
πε
λ
?=
d
E
x
)cos(cos
4
21
0
θθ
πε
λ
?=
d
E
y
2006-4-29 35
[ è
è
4]B??1
B??1
R a ({è1
({è1
q ¥%?ì
¥%?ì
p (1)àL
B?
àL
B?
P ¥?<
¥?<
(2)àL
'
àL
'
B?)¥?<v$ipvl b
B?)¥?<v$ipvl b
3
3
y ??mUS"
y ??mUS"
l
R
q
q d
2
d
π
=
x
x
P
x
E
v
d
⊥
E
v
d
θ
R
O
E
v
d
r
ld
0
2
0
d
4
1
d r
r
q
E
v
v
πε
=∴
2006-4-29 36
x
EE
vv
d∫=
???μ
???μ
iE
v
θcosd∫=
il
rR
q
l
v
d
cos
24
1
2
0
θ
ππε
∫=
0
2
0
d
4
1
d r
r
q
E
v
v
πε
=
x
x
P
θ
R
O
E
v
d
r
x
E
v
d
⊥
E
v
d
l
R
q
q d
2
d
π
=
2006-4-29 37
rx=θcosQ
222
Rxr +=
Rl
l
π2d =
∫
i
Rx
qx
E
vv
2/322
0
)(4
1
+
?=∴
πε
x
x
P
θ
R
O
E
v
d
r
x
E
v
d
⊥
E
v
d
il
rR
q
E
l
vv
d
cos
24
1
2
0
θ
ππε
∫=
2006-4-29 38
?è?¥è?
?è?¥è?
(1)?
?
x>>R
H
i
x
q
E
vv
2
0
4
1
πε
=
x
x
P
θ
R
O
E
v
d
r
x
E
v
d
⊥
E
v
d
i
Rx
qx
E
vv
2/322
0
)(4
1
+
?=
πε
(2) x =0
H
0=E
v
2006-4-29 39
(3) E ¥′ê?
¥′ê?
0
)(4
1
d
d
d
d
2/322
0
=
?
?
?
?
?
?
+
=
Rx
qx
xx
E
πε
Rx
2
2
±=
x
x
P
θ
R
O
E
v
d
r
x
E
v
d
⊥
E
v
d
i
Rx
qx
E
vv
2/322
0
)(4
1
+
?=
πε
R
2
2
R
2
2
?
E
o
x
2006-4-29 40
?mX?????1
?mX?????1
R
L
á1 λ
p??)?<