Do equipotential lines fall on the equiprobability contours?

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.
  • #1
Mikheal
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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 σx=σy.

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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  • #2
Is NDF a Gaussian? Your question needs to be a little bit more definitive.
 

FAQ: Do equipotential lines fall on the equiprobability contours?

What are equipotential lines?

Equipotential lines are lines or surfaces in a field (such as an electric or gravitational field) where the potential is constant. In other words, if you move along an equipotential line, the potential energy at any point on that line remains the same.

What are equiprobability contours?

Equiprobability contours are lines or surfaces in a probability distribution where the probability density is constant. These contours are used in fields like statistics and quantum mechanics to represent regions of equal likelihood.

Do equipotential lines and equiprobability contours represent the same concept?

No, equipotential lines and equiprobability contours do not represent the same concept. Equipotential lines are related to fields and potential energy, while equiprobability contours are related to probability distributions and likelihood.

Can equipotential lines fall on equiprobability contours?

In general, equipotential lines do not fall on equiprobability contours because they represent different physical quantities. However, in specific contexts or under certain conditions, there might be a relationship between the two, but this is not typically the case.

What fields of study involve equipotential lines and equiprobability contours?

Equipotential lines are commonly studied in physics, particularly in electromagnetism and gravitational fields. Equiprobability contours are frequently used in statistics, quantum mechanics, and other fields that involve probability distributions.

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