- #1

Mikheal

- 5

- 0

- 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

Edit 1: I am speaking in general, not about certain particle distribution functions, such as 2D Gaussian with different σ

Edit 2: I know that for 2D Gaussian with 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.
Last edited: