k^2 = (4 \[Rho]*r*Sin [\[Theta]])/(\[Rho]^2 + r^2 +
2 \[Rho]*r*Sin[\[Theta]]);
V[r_, \[Theta]_] :=
Integrate[-\[Rho]/Sqrt[r^2 + \[Rho]^2 + 2 \[Rho]*r*Sin[\[Theta]]]*
Integrate[1/Sqrt[
1 - k^2*Sin[\[Psi]]^2], {\[Psi], -(\[Pi]/2), \[Pi]/2}], {r, 0,
1}]
Plot[V[r, 0], {r, -3, 3}, PlotRange -> All,
AxesLabel -> {"z", "V"}, AxesStyle -> Thickness[0.003],
PlotStyle -> Thickness[0.004]]
RevolutionPlot3D[V[r, \[Theta]], {r, 0, 10}, {\[Theta], 0, \[Pi]/2},
PlotRange -> All, PlotPoints -> 50,
AxesStyle -> {"r", "\[Theta]", "V"},
AxesStyle -> Thickness[0.003],
PlotStyle -> None]
FindMinimum[V[r, 0], {r, R}]
FindMaximum[V[r, 0], {r, -R}]
field = -D[V[r, 0], r];
Plot[field, {r, -3, 3}, PlotRange -> All,
AxesLabel -> {"r", "E"}, AxesStyle -> Thickness[0.003],
PlotStyle -> Thickness[0.004]]