Trouble with VectorPlot function

[byoung (Bill Young)]

Good morning everyone. I am a newbie to the world of Mathematica. I’m a math tutor with a B.S. in electrical engineering, so the mathematics is not the problem. I have a calculus 3 student that is studying vector calculus. I’m having problems plotting using the VectorPlot script. When I type: VectorPlot[{-5y/(x^2+y^2),5x/(x^2+y^2)},{x,-2,2},{y,-2,2}], I get an incorrect graph (an x-y plane with a few dots on it, and a single vector).

If I change this to a 3D plot: VectorPlot3D[{-5y/(x^2+y^2),5x/(x^2+y^2),0},{x,-2,2},{y,-2,2},{z,-2,2}] then the graph is perfect except it is multiple layers.

Obviously this 3D plot uses the z-magnitude of 0 so any single layer of this plot is exactly what the first 2D plot should look like.

I truly copied & pasted my VectorPlot function to be the VectorPlot3D function, and then added the z-magnitude. I can’t figure out why the VectorPlot 2D isn’t working correctly. Can any of you please offer your suggestions? Thank you!
Bill Young
Denver, CO

[mthiel (Marco Thiel)]

Hi,

I think that this might be because of the way that Mathematica scale the vectors. The function drops off quickly as you move away from the origin. It appears that you might want to change the scaling manually using VectorScale:

VectorPlot[{-1. y/( x^2 + y^2), 1. x/( x^2 + y^2)}, {x, -2, 2}, {y, -2, 2}, VectorScale -> {0.1, 0.8, Automatic}]

or

VectorPlot[{-1. y/( x^2 + y^2), 1. x/( x^2 + y^2)}, {x, -2, 2}, {y, -2, 2}, VectorScale -> {0.1, 0.8, None}]

Cheers,

Marco