Plot with VectorPlot over a region

Questions
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1

Hello.

First time here for me.

I want to plot the vector field A,

10515CodeCogsEqn.png

over the region

4087CodeCogsEqn.png

I tried the following:

VectorPlot[{y, -x}, {x, y} \[Element] (1/4 < x^2 + y^2 && x^2 + y^2 < 9)]

But it doesn’t work, although

RegionPlot[1/4 < x^2 + y^2 && x^2 + y^2 < 9, {x, -4, 4}, {y, -4, 4}]

does return the correct region.

Can someone give me any kind of help with it? Or explain where is the syntax error?

2

It works if you add ImplicitRegion:

VectorPlot[{y, -x}, {x, y} \[Element] 
  ImplicitRegion[(1/4 < x^2 + y^2 && x^2 + y^2 < 9), {x, y}]]
3

Works. Great.

4

You can also use Annulus:

VectorPlot[{y, -x}, {x, y} \[Element] Annulus[{0, 0}, {1/2, 3}]]