(without consideration of electro spin and no matter how complex the movement of electrons)
Hamid
The answer to this question depends on three primary assumptions
Given these assumptions it can be demonstrated that the electrons will repel each other to the point where they fill the plane and be equally spaced in the two dimensions of freedom.
At the point in time where they achieve equal spacing they will then present an electrostatic field. Note this is not an electromagnetic field as an electromagnetic field requires the electrons to be moving and at the point they have filled the available space they are stationary (in macro terms - ignoring spin and quantum effects).
Because the electrons fill the homogenous space completely and have identical charges, the electrostatic field is uniform and by definition symmetric.
The value of the field depends on the density of electrons in the space concerned.
There is a fairly simple mathematical derivation of this effect which I think was first demonstrated by Faraday.
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