Do equipotential lines fall on the equiprobability contours?

[Mikheal]

TL;DR

Are equipotential lines fall on the equiprobability contours of charge distribution?

For 2D charge distribution ρ(x,y)=Ne PDF(x,y), where PDF is the normalized probability density function with its peak on (0,0) and has standard deviations σ _x. and σ _y. Are the contours with the equal probability "PDF(x,y)=const" the same as the equipotiential contours?, I tend to think that near the core of the distribution, they will be similar, and as the distance from the core increases, the equipotential surfaces will be circles for σ_x=σ_y.

Edit 1: I am speaking in general, not about certain particle distribution functions, such as 2D Gaussian with different σ _x and σ _y, 2D bi-Gaussian, 2D super-Gaussian, Flat-top, ....

Edit 2: I know that for 2D Gaussian with σ _x = σ _y, they fall on each other.

 

[hutchphd]

Is NDF a Gaussian? Your question needs to be a little bit more definitive.