2. §11.4 自感和互感
Self-Inductance and Mutual Inductance
Self-Inductance 自感
亨利 J. Henry 1829
self-induced emf
dt
d
L
Φ
ε −=
ISdB
s
∝⋅= ∫∫
rr
Φ
自感电动势
LI=Φ
L Self-Inductance自感系数
自感 退出返回
3. LI=Φ Wb/A1H1H: =SI
L is a proportionality constant that depends on the
geometry of the circuit
由回路的形状、大小及周围磁介质决定
dt
dL
I
dt
dI
L
dt
d
L −−=−=
Φ
ε
dt
dI
LL −=εIf L is constant
退出返回
4. If we establish a current I in a coil of N turns, the current
produces a magnetic flux through the coil.
magnetic flux linkage 磁链
线圈
NΦΦΦΨ +…++= 21
If the coil is tightly wound (closely packed), so that the
same magnetic flux passes through all the turns.
LI=ΨΦΨ N=
CAI
dt
dI
L
dt
d
L
−=−=
Ψ
ε
退出返回
6. 12121 IM=Φ
21212 IM=Φ
Mutual inductance of loop 2 with respect to loop 121
M
Mutual inductance of loop 1 with respect to loop 212
M
MMM == 2112 Mutual inductance 互感系数
互感
212 MI=Φ121 MI=Φ
退出返回
7. 212 MI=Φ
121 MI=Φ 0if =
dt
dM
dt
dI
M 1
21 −=ε
dt
dM
I
dt
dI
M
dt
d
1
121
21
−−=−=
Φ
ε
返回 退出dt
dM
I
dt
dI
M
dt
d
2
212
12 −−=−=
Φ
ε dt
dI
M 2
12 −=ε
8. 线圈
A magnetic flux (the flux through coil 2 associated with the
current in coil 1) links the N2 turns of coil 2.
21
Φ
21221
ΦΨ N= 1
21
dt
dI
M−=ε121 MI=Ψ
dt
dI
M 2
12 −=ε212
MI=Ψ12112
ΦΨ N=
退出返回
9. avBavB 21 −= ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
−=
bxx
Iav
00
0 11
2π
µ
∫ ⋅×=
L
ldBv
rrr
)(ε
b,a,x,I 0
(1) the loop is moving to the right with speed v at
position x0
(2) the loop is rest at x0 ，
1.
0>
dt
dI ?2 =ε
(3) the loop is moving to the right with speed v at
position x0， 0>
dt
dI
?3 =ε
?1 =ε
I a
b
v
r
0x
(1)
clockwise
返回 退出
∫∫ −=
21
1
ll
vBdlvBdlε
