plotting – StreamDensityPlot creating an Image that doesn’t correspond to DensityPlot

I am trying to use StreamPlotDensity to find the direction of my electric field at a point x,y. My electric field is given as

ElecticField={((E^-(x^2 + y^2)^2) (x^2 + y^2) Cos(2 Pi))^2 + ((E^-(x^2 + y^2)^2) (x^2 + y^2) Cos(2 Pi))^2}

Now when I use PlotDensity for this electric field with the code

 DensityPlot({((E^-(x^2 + y^2)^2) (x^2 + y^2) Cos(2 Pi))^2 + ((E^-(x^2 + y^2)^2) (x^2 + y^2) Cos(2 Pi))^2}, {x, -3, 3}, {y, -3, 3}, PlotTheme -> "Minimal", 
 PlotRange -> All, PlotPoints -> 50, ColorFunction -> "Rainbow")

To get

enter image description here

Now when I use the following StreamDensityPlot code

StreamDensityPlot({((E^-(x^2 + y^2)^2) (x^2 + y^2) Cos(
     2 Pi)), ((E^-(x^2 + y^2)^2) (x^2 + y^2) Cos(2 Pi))}, {x, -3, 
  3}, {y, -3, 3}, PlotTheme -> "Minimal", PlotRange -> All, 
 ColorFunction -> "Rainbow")

I get the image

enter image description here

Now my issue is that the image is not showing the direction lines for all parts of the plot and that the plot is not looking how the DensityPlot one does. Can you please provide some help regarding this

Essentially what I am trying to do is create a plot of my electric field and show the direction of it at a point x,y.

Thank you for all your help