Current in a wire when electron accelerates Suppose electron in wire is accelerating isn't current same all over the wire? Thinking electrons as water molecule the current will be same all over the wire but the current will change as time changes. But why people say the current will not be constant over the wire if electron accelerate in wire? Why am I wrong?
 A: Edit: having read your question again,  when we say "the current is constant" we mean the current has no time dependence, aka is constant in time. You are referring to a constant spacial dependence. If electrons in the wire are macroscopically accelerating the current is not constant in time, but can be treated as constant in space as the entire wire has the same current (if the same wire ofcourse)
This is the drude model of conductivity, it models the electrons in a wire  with a resistive force proportional to its velocity
$m\frac{d\vec{v}}{dt}= q\vec{E} - \frac{m}{T}\vec{v}$
In the limit as t goes to infinity, the velocity is a constant, as the resistive force equals the electric force.
In this condition, $\frac{d\vec{v}}{dt} = 0$
Substituting into our differential equation
$0= q\vec{E} - \frac{m}{T}\vec{v}$
$\frac{m}{T}\vec{v}= q\vec{E}  $
$\vec{v}= \frac{Tq\vec{E}}{m} $
Meaning the velocity is constant.
Now substituting the definition $\vec{J} = nq \vec{v}$
We get
$\vec{J}= \frac{nTq^2\vec{E}}{m}$
Which is ohms law
Where $\frac{nTq^2}{m}= \sigma $
A: In the classical model of a conductor, the free electrons are in thermal equilibrium with the atoms and bounce rapidly and randomly off the atoms. In a uniform current carrying wire at equilibrium, the free charge density has a uniform gradient which produces a uniform electric field. This field accelerates the free electrons between each bounce giving rise to a small average drift velocity.
