Formulario electromagnetismo

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FORMULÁRIO DE ELECTROMAGNETISMO
Electrostática
−→
F21 =
1
4π�0
q1q2
r2
r̂12, �0=8,85×10−12 F/m
−→
E =
1
4π�0
N∑
i=1
qi
r2i
r̂i
−→
E =
1
4π�0
ˆ
dq
r2
r̂
V =
1
4π�0
N∑
i=1
qi
ri
V =
1
4π�0
ˆ
dq
r
Ep =
i,j∑
i<j
qiqj
4π�0rij
Ep =
1
2
ˆ
V dq WE =
1
2
˚
V
�0E
2dV
Circuitos eléctricos
−→
J = σc
−→
E R ≡ ∆V
I
C ≡ Q
∆V
L ≡ φT (
−→
B )
I
Magnetostática
−→
FL = q
(−→
E +−→v ×
−→
B
)
, µ0=4π×10−7 H/m
−→
B =
µ0
4π
ˆ
I
−→
d`×r̂
r2
−→
B =
µ0
4π
˚
V
−→
J ×r̂
r2
dV
−→m ≡ 1
2
ˆ
−→r ×
(
I
−→
d`
)
Ep =
1
2
i,j∑
i6=j
Iiφij WB =
1
2
˚
V
B2
µ0
dV
FORMULÁRIO DE MATEMÁTICA
Coordenadas cilíndricas
dS = r dr dθ dS = r dθ dz dS = dr dz dV = r dr dθ dz
∇U = ∂U
∂r
r̂ +
1
r
∂U
∂θ
θ̂ +
∂U
∂z
k̂
∇ ·
−→
C =
1
r
∂
∂r
(rCr) +
1
r
∂Cθ
∂θ
+
∂Cz
∂z
∇×
−→
C =
(
1
r
∂Cz
∂θ
− ∂Cθ
∂z
)
r̂+
(
∂Cr
∂z
− ∂Cz
∂r
)
θ̂+
1
r
[
∂
∂r
(rCθ)−
∂Cr
∂θ
]
k̂
∇2U = 1
r
∂
∂r
(
r
∂U
∂r
)
+
1
r2
∂2U
∂θ2
+
∂2U
∂z2
Coordenadas esféricas
dS = r2 sin θ dθ dϕ dV = r2 sin θ dr dθ dϕ
∇U = ∂U
∂r
r̂ +
1
r
∂U
∂θ
θ̂ +
1
r sin θ
∂U
∂ϕ
ϕ̂
∇ ·
−→
C =
1
r2
∂
∂r
(
r2Cr
)
+
1
r sin θ
∂
∂θ
(sin θCθ) +
1
r sin θ
∂Cϕ
∂ϕ
∇×
−→
C =
1
r sin θ
[
∂
∂θ
(sin θCϕ)−
∂Cθ
∂ϕ
]
r̂ +
+
[
1
r sin θ
∂Cr
∂ϕ
− 1
r
∂
∂r
(rCϕ)
]
θ̂ +
1
r
[
∂
∂r
(rCθ)−
∂Cr
∂θ
]
ϕ̂
∇2U = 1
r2
∂
∂r
(
r2
∂U
∂r
)
+
1
r2 sin θ
∂
∂θ
(
sin θ
∂U
∂θ
)
+
1
r2 sin2 θ
∂2U
∂ϕ2