According to what I was taught, if current was dispersed “uniformly,” current density would remain constant. So, in a conductor, the 'current density should be the same at all points.' But, given that electrons flow at random (their time between collisions differs from that of other electrons), how can current density be the same everywhere?
Every electron's drift velocity is different. And I am not talking about the average drift velocity here. Rather, specific drift velocities.
An electron's drift velocity differs from that of other electrons, so the j vector should differ as well, right?
Why, then, is the j vector the same everywhere?
I believe I am missing something crucial.
Please correct me and explain your reasoning.
Please review the changes.
I get that we're smoothing out the fluctuations by averaging current densities, but the actual question is, "Are there any fluctuations at all in reality?" or "Are current densities truly different at all points?" (If the electric field is consistent)
This is because the equation
Eσ = J*
(E=electric field,σ - conductivity, j=current density)
implies that if E is uniform (the same at all points of the conductor), then J is uniform at all "points." As a result, the last question is —
How is this possible that j has the same value at each position when each electron's drift velocity varies(as time between two subsequent collision varies) ?
How can q in j= q/(Δt*dA) be the same at all places for a given amount of time Δt and very small area dA(point),where q is charge crossing that point?
Please assist me in resolving my confusion.