songs to solve electrodynamics tofma.if.usp.br › ~nickolas › rt › 2019 ›...
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Songs to Solve Electrodynamics to
Níckolas Alves
Departamento de Física-MatemáticaInstituto de Física
Universidade de São Paulo
Recepção Tensorial 2019
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Blank SpaceTaylor Swift
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
All Star - Smash Mouth
∇ ·E =ρ
ϵ0∇×E = 0
⇓
E =1
4πϵ0
∫ρ
r 2 r̂rr dτ ′
{∇ ·B = 0∇×B = µ0J
⇓
B =µ04π
∫J× rrrr 2 dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
All Star - Smash Mouth
∇ ·E =ρ
ϵ0∇×E = 0
⇓
E =1
4πϵ0
∫ρ
r 2 r̂rr dτ ′
{∇ ·B = 0∇×B = µ0J
⇓
B =µ04π
∫J× rrrr 2 dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
All Star - Smash Mouth
∇ ·E =ρ
ϵ0∇×E = 0
⇓
E =1
4πϵ0
∫ρ
r 2 r̂rr dτ ′
{∇ ·B = 0∇×B = µ0J
⇓
B =µ04π
∫J× rrrr 2 dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
All Star - Smash Mouth
∇ ·E =ρ
ϵ0∇×E = 0
⇓
E =1
4πϵ0
∫ρ
r 2 r̂rr dτ ′
{∇ ·B = 0∇×B = µ0J
⇓
B =µ04π
∫J× rrrr 2 dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Treat You Better - Shawn Mendes
∇×E = 0
⇓
E = −∇V
⇓
∇2V = − ρϵ0
⇓
V =1
4πϵ0
∫ρ
r dτ ′
∇ ·B = 0
⇓
B = ∇×A
⇓
∇2A = −µ0J
⇓
A =µ04π
∫J
r dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Treat You Better - Shawn Mendes
∇×E = 0
⇓
E = −∇V
⇓
∇2V = − ρϵ0
⇓
V =1
4πϵ0
∫ρ
r dτ ′
∇ ·B = 0
⇓
B = ∇×A
⇓
∇2A = −µ0J
⇓
A =µ04π
∫J
r dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Treat You Better - Shawn Mendes
∇×E = 0
⇓
E = −∇V
⇓
∇2V = − ρϵ0
⇓
V =1
4πϵ0
∫ρ
r dτ ′
∇ ·B = 0
⇓
B = ∇×A
⇓
∇2A = −µ0J
⇓
A =µ04π
∫J
r dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Treat You Better - Shawn Mendes
∇×E = 0
⇓
E = −∇V
⇓
∇2V = − ρϵ0
⇓
V =1
4πϵ0
∫ρ
r dτ ′
∇ ·B = 0
⇓
B = ∇×A
⇓
∇2A = −µ0J
⇓
A =µ04π
∫J
r dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Treat You Better - Shawn Mendes
∇×E = 0
⇓
E = −∇V
⇓
∇2V = − ρϵ0
⇓
V =1
4πϵ0
∫ρ
r dτ ′
∇ ·B = 0
⇓
B = ∇×A
⇓
∇2A = −µ0J
⇓
A =µ04π
∫J
r dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Treat You Better - Shawn Mendes
∇×E = 0
⇓
E = −∇V
⇓
∇2V = − ρϵ0
⇓
V =1
4πϵ0
∫ρ
r dτ ′
∇ ·B = 0
⇓
B = ∇×A
⇓
∇2A = −µ0J
⇓
A =µ04π
∫J
r dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Treat You Better - Shawn Mendes
∇×E = 0
⇓
E = −∇V
⇓
∇2V = − ρϵ0
⇓
V =1
4πϵ0
∫ρ
r dτ ′
∇ ·B = 0
⇓
B = ∇×A
⇓
∇2A = −µ0J
⇓
A =µ04π
∫J
r dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Treat You Better - Shawn Mendes
∇×E = 0
⇓
E = −∇V
⇓
∇2V = − ρϵ0
⇓
V =1
4πϵ0
∫ρ
r dτ ′
∇ ·B = 0
⇓
B = ∇×A
⇓
∇2A = −µ0J
⇓
A =µ04π
∫J
r dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Live While We’re Young - One Direction
{∂νF
µν = µ0Jµ
∂νGµν = 0
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Take On Me - a-ha
∇ ·E = ρϵ0
∇ ·B = 0
∇×E = −∂B∂t
∇×B = µ0J+ µ0ϵ0∂E
∂t
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
One of Us - Joan Osborne
∇ ·B = 0
⇓
B = ∇×A
∇×E = −∂B∂t
⇓
∇×(E+
∂A
∂t
)= 0
⇓
E+∂A
∂t= −∇V
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
One of Us - Joan Osborne
∇ ·B = 0
⇓
B = ∇×A
∇×E = −∂B∂t
⇓
∇×(E+
∂A
∂t
)= 0
⇓
E+∂A
∂t= −∇V
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
One of Us - Joan Osborne
∇ ·B = 0
⇓
B = ∇×A
∇×E = −∂B∂t
⇓
∇×(E+
∂A
∂t
)= 0
⇓
E+∂A
∂t= −∇V
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
One of Us - Joan Osborne
∇ ·B = 0
⇓
B = ∇×A
∇×E = −∂B∂t
⇓
∇×(E+
∂A
∂t
)= 0
⇓
E+∂A
∂t= −∇V
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
One of Us - Joan Osborne
∇ ·B = 0
⇓
B = ∇×A
∇×E = −∂B∂t
⇓
∇×(E+
∂A
∂t
)= 0
⇓
E+∂A
∂t= −∇V
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Superman (It’s Not Easy) - Five for Fighting
∇2V + ∂∂t
(∇ ·A) = − ρϵ0(
∇2A− µ0ϵ0∂2A
∂t2
)−∇
(∇ ·A+ µ0ϵ0
∂V
∂t
)= −µ0J
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Somebody That I Used To Know - Gotye, Kimbra
∇2V − 1c2
∂2V
∂t2= − ρ
ϵ0
∇2A− 1c2
∂2A
∂t2= −µ0J
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Somebody That I Used To Know - Gotye, Kimbra
∇2V − 1∞
∂2V
∂t2= − ρ
ϵ0
∇2A− 1∞
∂2A
∂t2= −µ0J
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Somebody That I Used To Know - Gotye, Kimbra
∇2V = − ρϵ0
∇2A = −µ0J
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Feel So Close - Calvin Harris
V (r, t) =1
4πϵ0
∫ρ(r′, t)
r dτ ′
A(r, t) =µ04π
∫J(r′, t)
r dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Feel So Close - Calvin Harris
V (r, t) =1
4πϵ0
∫ρ(r′, t− rc )r dτ ′
A(r, t) =µ04π
∫J(r′, t− rc )r dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Best Day Of My Life - American Authors
E(r, t) = −∇V − ∂A∂t
B(r, t) = ∇×A
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Blank Space Taylor Swift
Best Day Of My Life - American Authors
E(r, t) =1
4πϵ0
∫ r̂rrr 2 ⌊ρ⌋+
r̂rrcr⌊∂ρ
∂t
⌋− 1
c2r⌊∂J
∂t
⌋dτ ′
B(r, t) =µ04π
∫ [1
r 2 ⌊J⌋+1
cr⌊∂J
∂t
⌋]× r̂rr dτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
A Cruel Angel’s ThesisYoko Takahashi
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
Deja Vu (Initial D) - Tsuko G
∇ ·D = ρ∇ ·B = 0
∇×E = −∂B∂t
∇×H = J+ ∂D∂t
D = ϵ0E+P
H =1
µ0B−M
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
Deja Vu (Initial D) - Tsuko G
∇ ·D = ρ∇ ·B = 0
∇×E = −∂B∂t
∇×H = J+ ∂D∂t
D = ϵ0E+P
H =1
µ0B−M
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
Deja Vu (Initial D) - Tsuko G
∇ ·D = ρ∇ ·B = 0
∇×E = −∂B∂t
∇×H = J+ ∂D∂t
D = ϵE
H =1
µB
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
Don’t Go Breaking My Heart - Backstreet Boys
∇2E− µϵ∂2E
∂t2=
1
ϵ∇ρ+ ρ∇1
ϵ−∇
(E · ∇ϵ
ϵ
)+ µ
∂J
∂t+ µ∇
(1
µ
)× (∇×E)
∇2B− µϵ∂2B
∂t2= J×∇µ− µ∇× J−∇×
[µB×∇
(1
µ
)]
+
∇×Bµϵ
− Jϵ−
B×∇(
1µ
)ϵ
× [µ∇ϵ+ ϵ∇µ]
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
I Want It That Way - Backstreet Boys
Hipóteses sobre o meio:
1 linear;2 dielétrico (µ = µ0);3 homogêneo (∇ϵ = 0).
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
I Want It That Way - Backstreet Boys
Hipóteses sobre o meio:
1 linear;2 dielétrico (µ = µ0);3 homogêneo (∇ϵ = 0).
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
I Want It That Way - Backstreet Boys
Hipóteses sobre o meio:
1 linear;2 dielétrico (µ = µ0);3 homogêneo (∇ϵ = 0).
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
I Want It That Way - Backstreet Boys
Hipóteses sobre o meio:
1 linear;2 dielétrico (µ = µ0);3 homogêneo (∇ϵ = 0).
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
Happier - Marshmello, Bastille
∇2E− µ0ϵ∂2E
∂t2=
1
ϵ∇ρ+
����0
ρ∇1ϵ−∇
(E ·��*
0∇ϵϵ
)
+ µ0∂J
∂t+ µ0
��
���>
0
∇(
1
µ0
)× (∇×E)
∇2B− µ0ϵ∂2B
∂t2= J×��
�*0∇µ0 − µ0∇× J−∇×
µ0B×�
��
��>0
∇(
1
µ0
)
+
∇×Bµ0ϵ − Jϵ −B×
�����*
0
∇(
1µ0
)ϵ
× [µ0��*0∇ϵ+ ϵ���*0∇µ0]
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
Happier - Marshmello, Bastille
∇2E− µ0ϵ
∂2E
∂t2=
1
ϵ∇ρ+ µ0
∂J
∂t
∇2B− µ0ϵ∂2B
∂t2= −µ0∇× J
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
Wouldn’t It Be Nice - The Beach Boys
E(r, t) =1
4πϵ0
∫V0
solução no vácuodτ ′ + 14πϵ1
∫V1
solução no meiodτ ′
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
God Only Knows - The Beach Boys
Propriedades esperadas de uma solução:
1 reflexão e refração;2 mudanças de velocidade;3 presença de um dielétrico afeta a solução;4 et cetera.
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
God Only Knows - The Beach Boys
Propriedades esperadas de uma solução:
1 reflexão e refração;2 mudanças de velocidade;3 presença de um dielétrico afeta a solução;4 et cetera.
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
God Only Knows - The Beach Boys
Propriedades esperadas de uma solução:
1 reflexão e refração;2 mudanças de velocidade;3 presença de um dielétrico afeta a solução;4 et cetera.
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
God Only Knows - The Beach Boys
Propriedades esperadas de uma solução:
1 reflexão e refração;2 mudanças de velocidade;3 presença de um dielétrico afeta a solução;4 et cetera.
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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A Cruel Angel’s Thesis Yoko Takahashi
God Only Knows - The Beach Boys
Propriedades esperadas de uma solução:
1 reflexão e refração;2 mudanças de velocidade;3 presença de um dielétrico afeta a solução;4 et cetera.
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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In The EndLinkin Park
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Everybody (Backstreet’s Back) Backstreet Boys
Everybody (Backstreet’s Back)Backstreet Boys
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Everybody (Backstreet’s Back) Backstreet Boys
You Found Me - The Fray
Voltar
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Everybody (Backstreet’s Back) Backstreet Boys
Don’t Matter - Akon
Voltar
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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Everybody (Backstreet’s Back) Backstreet Boys
Stop - Spice Girls
Voltar
N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
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N. Alves (DFMA-IFUSP) Songs to Solve Electrodynamics to Recepção Tensorial 2019
Blank SpaceTaylor Swift
A Cruel Angel's ThesisYoko Takahashi
Everybody (Backstreet's Back)Backstreet Boys