# Do equipotential lines fall on the equiprobability contours?

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• Mikheal
However, in summary, the conversation is discussing the relationship between 2D charge distributions and the contours with equal probability. It is suggested that near the core of the distribution, the equipotential surfaces will be similar, but as the distance from the core increases, they will become circles for certain distributions such as 2D Gaussian with different standard deviations. It is also mentioned that the normalized probability density function (PDF) with a peak at (0,0) and standard deviations σ x and σ y may not always be a Gaussian distribution.
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.

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

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