Rascunho Do Tcc
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Letra A
In[1]:=
Manipulate@ParametricPlot3D @885 * Cos@tD, 5 * Sin@tD, 0<, 8z * t, 0, 0<, 80, z * t, 0<, 80, 0, z * t<, 8r * H1 + tL * Cos@ΦD, r * H1 + tL * Sin@ΦD, z * t<, 8r * H1 - tL * Cos@ΦD, r * H1 - tL * Sin@ΦD, z * t<, 8r * Cos@tD, r * Sin@tD, 0<< , 8t, - Π, Π< , PlotStyle ® 8White, Blue, Blue, Blue, 8Red, Thick, Dashed<, 8Red, Thick, Dashed<, 8Black, Thick<<, Boxed ® False, Mesh ® None, Axes ® FalseD, 8Φ, 0, 2 Π<, 88r, 1, "Raio"<, 0, 10<, 88z, 1, "Para todo z"<, 0, 10
Φ Raio Para todo z
Out[1]=
Letra C :
1 In[2]:=
Out[2]=
In[3]:=
Out[3]=
dE = 4 Π * Ε0 :
x ∆0
4 Π Ix2 + y2 +
Out[4]=
Ix2 + y2 + 32 z2 M
32 z2 M
∆0 * y
,
Ix2 + y2 + y ∆0
, Ε0
4 Π Ix2 + y2 +
32 z2 M
32 z2 M
- ∆0 * z
Ix2 + y2 + z2 M
,
32
,-
>
4 Π Ix2 + y2 + z2 M
32
Ε0
>
z ∆0
Ε0
Integrate@dE, zD :
x z ∆0 4Π
In[4]:=
∆0 * x
Ix2
+
y2 M
y z ∆0 ,
x2
+
y2
+
z2
Ε0
4Π
Ix2
+
y2 M
>
∆0 ,
x2
+
y2
+
z2
Ε0
4Π
x2
+
y2
+
z2
Ε0
Imp = Out@3D :
x z ∆0 4 Π Ix2 + y2 M
y z ∆0 ,
x2 + y2 + z2 Ε0
4 Π Ix2 + y2 M
∆0 ,
x2 + y2 + z2 Ε0
4Π
x2 + y2 + z2 Ε0
>
2
Oficial.nb
In[5]:=
Out[5]=
Limit@Imp, z ® InfinityD - Limit@Imp, z ® - InfinityD :
x ∆0
4Π In[6]:=
Out[6]=
In[7]:=
Out[7]=
Ix2
+
y2 M
x ∆0
+ 4Π
Ε0
y ∆0
, x2
Ε0 + 4 Π
y2
Ε0
4Π
Ix2
+
y2 M
y ∆0
+ Ε0
, 0> 4Π
x2
Ε0 + 4 Π y2 Ε0
Simplify@Out@5DD :
x ∆0
y ∆0 ,
2Π
x2
Ε0 + 2 Π
y2
Ε0
, 0> 2Π
x2
2Π
x2
Ε0 + 2 Π y2 Ε0
EP = Out@6D :
x ∆0
y ∆0 ,
2Π
x2
Ε0 + 2 Π
y2
Ε0
, 0> Ε0 + 2 Π y2 Ε0
Letra D In[8]:= Out[8]=
P = 8x, y, 0< 8x, y, 0<
g H ^ PL = P In[9]:=
8x, y, z< = 8a * Cos@ΘD, a * Sin@ΘD, 0<
Out[9]=
8a Cos@ΘD, a Sin@ΘD, 0<
In[10]:=
EP
Out[10]=
:
a Cos@ΘD ∆0
a Sin@ΘD ∆0 ,
2
a2
2
Π Cos@ΘD Ε0 + 2
a2
2
Π Sin@ΘD Ε0
, 0> 2
a2
Π Cos@ΘD2 Ε0 + 2 a2 Π Sin@ΘD2 Ε0
P In[11]:=
dotP = EP . Norm@PD a2 Cos@ΘD2 ∆0
Out[11]= 2
2
Abs@a Cos@ΘDD + Abs@a Sin@ΘDD
I2
a2
2
Π Cos@ΘD Ε0 + 2
a2
Π Sin@ΘD Ε0 M
+
2
2
a2 Sin@ΘD ∆0 Abs@a Cos@ΘDD2 + Abs@a Sin@ΘDD2 I2 a2 Π Cos@ΘD2 Ε0 + 2 a2 Π Sin@ΘD2 Ε0 M In[12]:=
Integrate@dotP * Norm@PD, 8Θ, 0, 2 Π
Out[12]=
Ε0
In[1]:=
Manipulate@ParametricPlot3D @885 * Cos@tD, 5 * Sin@tD, 0<, 8z * t, 0, 0<, 80, z * t, 0<, 80, 0, z * t<, 8r * H1 + tL * Cos@ΦD, r * H1 + tL * Sin@ΦD, z * t<, 8r * H1 - tL * Cos@ΦD, r * H1 - tL * Sin@ΦD, z * t<, 8r * Cos@tD, r * Sin@tD, 0<< , 8t, - Π, Π< , PlotStyle ® 8White, Blue, Blue, Blue, 8Red, Thick, Dashed<, 8Red, Thick, Dashed<, 8Black, Thick<<, Boxed ® False, Mesh ® None, Axes ® FalseD, 8Φ, 0, 2 Π<, 88r, 1, "Raio"<, 0, 10<, 88z, 1, "Para todo z"<, 0, 10
Φ Raio Para todo z
Out[1]=
Letra C :
1 In[2]:=
Out[2]=
In[3]:=
Out[3]=
dE = 4 Π * Ε0 :
x ∆0
4 Π Ix2 + y2 +
Out[4]=
Ix2 + y2 + 32 z2 M
32 z2 M
∆0 * y
,
Ix2 + y2 + y ∆0
, Ε0
4 Π Ix2 + y2 +
32 z2 M
32 z2 M
- ∆0 * z
Ix2 + y2 + z2 M
,
32
,-
>
4 Π Ix2 + y2 + z2 M
32
Ε0
>
z ∆0
Ε0
Integrate@dE, zD :
x z ∆0 4Π
In[4]:=
∆0 * x
Ix2
+
y2 M
y z ∆0 ,
x2
+
y2
+
z2
Ε0
4Π
Ix2
+
y2 M
>
∆0 ,
x2
+
y2
+
z2
Ε0
4Π
x2
+
y2
+
z2
Ε0
Imp = Out@3D :
x z ∆0 4 Π Ix2 + y2 M
y z ∆0 ,
x2 + y2 + z2 Ε0
4 Π Ix2 + y2 M
∆0 ,
x2 + y2 + z2 Ε0
4Π
x2 + y2 + z2 Ε0
>
2
Oficial.nb
In[5]:=
Out[5]=
Limit@Imp, z ® InfinityD - Limit@Imp, z ® - InfinityD :
x ∆0
4Π In[6]:=
Out[6]=
In[7]:=
Out[7]=
Ix2
+
y2 M
x ∆0
+ 4Π
Ε0
y ∆0
, x2
Ε0 + 4 Π
y2
Ε0
4Π
Ix2
+
y2 M
y ∆0
+ Ε0
, 0> 4Π
x2
Ε0 + 4 Π y2 Ε0
Simplify@Out@5DD :
x ∆0
y ∆0 ,
2Π
x2
Ε0 + 2 Π
y2
Ε0
, 0> 2Π
x2
2Π
x2
Ε0 + 2 Π y2 Ε0
EP = Out@6D :
x ∆0
y ∆0 ,
2Π
x2
Ε0 + 2 Π
y2
Ε0
, 0> Ε0 + 2 Π y2 Ε0
Letra D In[8]:= Out[8]=
P = 8x, y, 0< 8x, y, 0<
g H ^ PL = P In[9]:=
8x, y, z< = 8a * Cos@ΘD, a * Sin@ΘD, 0<
Out[9]=
8a Cos@ΘD, a Sin@ΘD, 0<
In[10]:=
EP
Out[10]=
:
a Cos@ΘD ∆0
a Sin@ΘD ∆0 ,
2
a2
2
Π Cos@ΘD Ε0 + 2
a2
2
Π Sin@ΘD Ε0
, 0> 2
a2
Π Cos@ΘD2 Ε0 + 2 a2 Π Sin@ΘD2 Ε0
P In[11]:=
dotP = EP . Norm@PD a2 Cos@ΘD2 ∆0
Out[11]= 2
2
Abs@a Cos@ΘDD + Abs@a Sin@ΘDD
I2
a2
2
Π Cos@ΘD Ε0 + 2
a2
Π Sin@ΘD Ε0 M
+
2
2
a2 Sin@ΘD ∆0 Abs@a Cos@ΘDD2 + Abs@a Sin@ΘDD2 I2 a2 Π Cos@ΘD2 Ε0 + 2 a2 Π Sin@ΘD2 Ε0 M In[12]:=
Integrate@dotP * Norm@PD, 8Θ, 0, 2 Π
Out[12]=
Ε0
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