Mathematica中2d函数的矢量图

Question

I am trying to plot 1/r (r-hat) using VectorPlot in Mathematica by decomposing r-hat into x-hat and y-hat.

I am using:

[Chi][x_, y_] := Sqrt[x^2 + y^2]

[Phi][x_, y_] := ArcTan[y/x]

and then plotting the above function in x,y plane.

But, for x<0 and y<0 , the vectors do not have the correct sign because the unit vectors have different sign in each of the quadrants. I tried defining a piecewise function to get around this without success.

Answer 1

VectorPlot[ 1/Sqrt[x x + y y] {Cos[ArcTan[x, y]], Sin[ArcTan[x, y]]}, 
          {x, -2, 2},  {y, -2, 2},
          RegionFunction -> Function[{x, y, vx, vy, n}, Sqrt[x x + y y] > 1/3], 
          VectorPoints -> 10]