| Author |
Comment/Response |
Michael
|
 08/01/12 07:05am
The norm of the vector field goes to infinity at the origin. By scaling, vectors elsewhere will have a length that will appear to be close to zero.
See
Plot3D[Norm[{(3 x y)/(x^2 + y^2)^5, (-x^2 + 2 y^2)/(x^2 + y^2)^5}], {x, -1, 1}, {y, -1, 1}, PlotRange -> {0, 10^20}]
Play with VectorScale (change the value of $NormCutOff for instance) or the LightingAngle to see better what's going on:
$NormCutOff = 10;
VectorDensityPlot[{(3 x y)/(x^2 + y^2)^5, (-x^2 + 2 y^2)/(x^2 + y^2)^5}, {x, -1, 1}, {y, -1, 1}, LightingAngle -> {0.5, 0}, MaxRecursion -> 3, VectorColorFunction -> (Yellow &), VectorScale -> {Automatic, Automatic, If[#5 > $NormCutOff, None, #5] &}]
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