解析函数已知,但是因为太复杂无法直接作图。如何才能做出函数图像呢?
程序如下:
a = 1; q = 1; (*输入参数*)
Potential[r_, \[Theta]_, \[Phi]_] := If[
r < a,
q/a \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(l = 0\), \(\[Infinity]\)]\(
\*SuperscriptBox[\((\(-1\))\), \(l\)]
\*FractionBox[\(\((2 l)\)!\), \(
\*SuperscriptBox[\(2\), \(2 l\)]\ \(l!\) \(l!\)\)]
\*SuperscriptBox[\((
\*FractionBox[\(r\), \(a\)])\), \(2 l\)] LegendreP[2 l,
Cos[\[Theta]]]\)\), q/a \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(l = 0\), \(\[Infinity]\)]\(
\*SuperscriptBox[\((\(-1\))\), \(l\)]
\*FractionBox[\(\((2 l)\)!\), \(
\*SuperscriptBox[\(2\), \(2 l\)]\ \(l!\) \(l!\)\)]
\*SuperscriptBox[\((
\*FractionBox[\(a\), \(r\)])\), \(2 l + 1\)] LegendreP[2 l,
Cos[\[Theta]]]\)\)
] (*利用所给解析公式*);
ElectricField =
Grad[Potential[r, \[Theta], \[Phi]], {r, \[Theta], \[Phi]},
"Spherical"] (*计算电势梯度求出电场*)
V0 = TransformedField["Spherical" -> "Cartesian",
Potential[
r, \[Theta], \[Phi]], {r, \[Theta], \[Phi]} -> {x, y,
z}] (*坐标系变换*)
Ele = Grad[V, {x, y, z}] (*求出笛卡尔坐标系中的电场*)
之后怎么作图呢?
程序如下:
a = 1; q = 1; (*输入参数*)
Potential[r_, \[Theta]_, \[Phi]_] := If[
r < a,
q/a \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(l = 0\), \(\[Infinity]\)]\(
\*SuperscriptBox[\((\(-1\))\), \(l\)]
\*FractionBox[\(\((2 l)\)!\), \(
\*SuperscriptBox[\(2\), \(2 l\)]\ \(l!\) \(l!\)\)]
\*SuperscriptBox[\((
\*FractionBox[\(r\), \(a\)])\), \(2 l\)] LegendreP[2 l,
Cos[\[Theta]]]\)\), q/a \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(l = 0\), \(\[Infinity]\)]\(
\*SuperscriptBox[\((\(-1\))\), \(l\)]
\*FractionBox[\(\((2 l)\)!\), \(
\*SuperscriptBox[\(2\), \(2 l\)]\ \(l!\) \(l!\)\)]
\*SuperscriptBox[\((
\*FractionBox[\(a\), \(r\)])\), \(2 l + 1\)] LegendreP[2 l,
Cos[\[Theta]]]\)\)
] (*利用所给解析公式*);
ElectricField =
Grad[Potential[r, \[Theta], \[Phi]], {r, \[Theta], \[Phi]},
"Spherical"] (*计算电势梯度求出电场*)
V0 = TransformedField["Spherical" -> "Cartesian",
Potential[
r, \[Theta], \[Phi]], {r, \[Theta], \[Phi]} -> {x, y,
z}] (*坐标系变换*)
Ele = Grad[V, {x, y, z}] (*求出笛卡尔坐标系中的电场*)
之后怎么作图呢?
