# RESUMEN DEL CAPITULO “ECUACIONES GENERALES”

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```RESUMEN DEL CAPITULO “CAMPOS MAGN&Eacute;TICOS ESTACIONARIOS”
LEY DE AMPER:
r r
H
∫ ⋅ dl = I encerrada
C
POTENCIAL VECTOR:
r
r
r
r
B = ∇ &times; A ya que ∇ ⋅ B = 0 y ∇ ⋅ ∇ &times; A ≡ 0
r
∇ ⋅ A = 0 Calibracion
(
)
ECUACIONES DEL POTENCIAL VECTOR:
r
r
∆A = −&micro;J
CONDICIONES DE CONTORNO DEL POTENCIAL VECTOR:
r
r
n\$ &times; A 2 − A 1
(
)
S
Medio 2
=0
Medio 1
ECUACIONES INTEGRALES Y LEY BIO-SAVART:
r r
r r
&micro;J ( r ′)dv ′
A( r ) = ∫∫∫
r r
V 4π r − r ′
r r
r r
&micro;J s ( r ′)ds′
A( r ) = ∫∫
r r
S′ 4 π r − r ′
r
r r
&micro;Idl ′
A( r ) = ∫
r r
L′ 4 π r − r ′
r r
r r
r r
&micro;J ( r ′ ) &times; ( r − r ′)dv ′
B( r ) = ∫∫∫
r r
V
4π r − r ′
r r
r r
r r
&micro;J s ( r ′) &times; ( r − r ′ )dv ′
B( r ) = ∫∫
r r
S′
4π r − r ′
r
r r
r r
&micro;Idl ′ &times; ( r − r ′)dv ′
B( r ) = ∫
r r
L′
4π r − r ′
MOMENTO MAGN&Eacute;TICO Y CAMPO LEJANO:
r 1
r r r
r r
m = ∫∫∫ r ′ &times; J ( r ′)dv ′
r r
&micro;
r&times;m
V
′
2
A( r ) =
r 1
r r r
4 πr rr 3r
r
m = ∫∫∫ r ′ &times; J s ( r ′ )ds′
r r
&micro; ⎡ 3 ( r ⋅ m) r m ⎤
2 S′
− 3⎥
B( r ) =
⎢
r
r 1
r
4π ⎣ r 5
r ⎦
m = ∫∫∫ r ′ &times; Idl ′ = ISn\$
Espira
2 L′
Plana
ENERG&Iacute;A DEL CAMPO MAGN&Eacute;TICO
r r
r r
1
H( r , t ) ⋅ B( r , t )dv
∫∫∫
2 V
r r r r
1
Wh = ∫∫∫ A( r , t )J ( r , t )dv
2 V
Wh =
COEFICIENTE DE AUTOINDUCCI&Oacute;N
1
Wh = LI 2
2
r r
&micro;
dl ⋅ dl ′
L=
r r Ley de Neumann
∫
∫
4 π L L′ ri − rj
COEFICIENTE DE INDUCCI&Oacute;N MUTUA
n\$
σ (rr, t)
r r
js ( r , t )
ε 1, &micro;1
ε 2, &micro; 2
S
N
Φ B Espira i = ∑ M ik I i
k =1
N
N
N N
1
1
1
Wh N conductores = ∑ Φ Bi I i = ∑ L i I 2i + ∑ ∑ M ik I i I k
i =1 2
i =1 2
i =1 k = 1 2
i≠ k
r r
&micro;
dli ⋅ dlk
M ik =
Ley de Neumann
r r
∫
∫
4 π Li L k ri − rk
FUERZA MAGN&Eacute;TICA:
r r
r
F = Jdv &times; B
r r
r
r r
F = ∫∫∫ J &times; Bdv = I ∫ dl &times; B
V
Espira
L
```