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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 16 "Charged Cylinder" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "with(plots):with(plottools):
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Radius of the cylinder." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "R:=" }{TEXT -1 0 "" }
{MPLTEXT 1 0 2 "1;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Parametriza
tion of the cross-section" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
18 "z:=R*exp(I*theta);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Define \+
the potential on the boundary" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 44 "chi:=(a,b,x)->Heaviside(x-a)*Heaviside(b-x):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 43 "g:=theta->chi(-Pi,0,theta)-chi(0,Pi,theta);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(g(theta),theta=-Pi
..Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Obtain complex potentia
l via the Cauchy Integral formula" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 67 "f:=w->(1/(2*Pi*I))*int(g(theta)*diff(z,theta)/(z-w),t
heta=-Pi..Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Plot equipotent
ial and flow lines (note that they are orthogonal)" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 50 "a:=3:win:=-a*R..a*R:opts:=x=win,y=win,conto
urs=40:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "circ:=plot([Re(z
),Im(z),theta=-Pi..Pi],color=blue):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "equi:=contourplot(Re(f(x+I*y)),opts):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "flow:=contourplot(Im(f(x+I*y)),opts
):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "display(equi,flow,cir
c);" }}}}{MARK "18" 0 }{VIEWOPTS 1 1 0 1 1 1803 }