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Cell["\<\
Definimos el potencial exacto. Para esto seteamos \[Lambda]=1, o sea, el \
potencial se mide en unidades de \[Lambda]. Fijamos tambi\[EAcute]n a=1, o \
sea, las longitudes se miden en unidades de la separaci\[OAcute]n entre los \
planos\
\>", "Subsection",
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Cell["\<\
Definimos a su vez el potencial aproximado, como una suma parcial hasta el \
valor \[OpenCurlyDoubleQuote]n\[CloseCurlyDoubleQuote] a partir del resultado \
que obtuvimos con la primer separaci\[OAcute]n de variables.\
\>", "Subsection",
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Cell["\<\
En tercer  lugar definimos el potencial aproximado como una integral num\
\[EAcute]rica a partir del resultado que obtuvimos con la segunda separaci\
\[OAcute]n de variables. Notemos que definimos el potencial de a pedazos (as\
\[IAcute] fue nuestro resultado)\
\>", "Subsection",
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Cell["\<\
Aqu\[IAcute] graficamos el perfil del potencial con x corriendo entre 0 y 1 \
(entre una pared y la otra) y variando \[OpenCurlyDoubleQuote]y\
\[CloseCurlyDoubleQuote] con y=0.1, 0.3, 0.4, 1, 2. Vemos que el potencial va \
de 0 a 0 entre las paredes (como corresponde a la condici\[OAcute]n de \
contorno que impusimos) y es m\[AAcute]ximo en el centro. A su vez, el m\
\[AAcute]ximo es m\[AAcute]s alto cuanto m\[AAcute]s cerca del hilo estemos \
(y->0)\
\>", "Subsection",
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Cell["\<\
Si nos paramos en y=0 y nos movemos en x, encontramos una divergencia en \
x=1/2, que es donde est\[AAcute] el hilo cargado:\
\>", "Subsection",
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Cell["\<\
Pasemos a estudiar el error de la expresi\[OAcute]n de la transformada de \
Fourier num\[EAcute]rica. Nos paramos en valores de y fijos (y=0, 0.5, 1, 2) \
y variamos x entre 0 y 1. Vemos que a lo sumo cometemos un error de 10^(-9). \
Observar que cuando x=1/2 e y=0 obtenemos \[Infinity] pero esto es esperable \
pues el potencial explota all\[IAcute] en presencia del hilo infinito como \
vimos en el gr\[AAcute]fico anterior\
\>", "Subsection",
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Cell["\<\
Ahora queremos estudiar cu\[AAcute]n r\[AAcute]pido converge la serie parcial \
de Fourier variando el n\[UAcute]mero de t\[EAcute]rminos que \
inclu\[IAcute]mos en la suma \[OpenCurlyDoubleQuote]n\[CloseCurlyDoubleQuote] \
(la \[UAcute]ltima entrada de \[Phi]n[x,y,n]). Si tomamos un valor fijo de y \
lejos del centro, digamos y=1, y=2, y nos movemos en x vemos que todos los gr\
\[AAcute]ficos se solapan. Es decir, lejos del hilo, alcanza con 1 o 2 t\
\[EAcute]rminos en la serie para tener mucha precisi\[OAcute]n\
\>", "Subsection",
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Cell["\<\
En cambio, si hacemos lo mismo para un valor de y cercano al hilo, por \
ejemplo y=0.1, vemos que necesitamos varios t\[EAcute]rminos de la serie para \
obtener una aproximaci\[OAcute]n aceptable.\
\>", "Subsection",
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Cell["\<\
Por \[UAcute]ltimo graficamos el perfil de la densidad superficial de carga \
de las paredes a tierra. Como se ve en el gr\[AAcute]fico, casi toda la carga \
est\[AAcute] concentrada en el centro, cerca de y=0 (y extendida \
uniformemente a lo largo de z)\
\>", "Subsection",
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