# Do equipotential lines fall on the equiprobability contours?

• I
Mikheal
TL;DR Summary
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 σxy.

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.

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