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In a circuit, electric field exerts force on electrons, so they must accelerate. Every text book I have read, points that electrons move with a constant drift velocity. How can this happen? Does Newton's law not apply there?

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Yes Newton's law is applied here, and the electrons accelerate in response to the electric field. However, the electrons also undergo collisions with the atoms of the conductor, so on an average, they acquire an initial velocity of zero just after each collision. The electrons then acquire a final velocity $\vec v_f$ before the next collision and the average value of this final velocity is termed as the drift velocity, which is found to be a constant value, simply because the average time interval τ between each collision (called the relaxation time) is very small

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  • $\begingroup$ A minor point. I think the drift velocity is the average velocity of the electrons parallel to the electric field, not the average final velocity just before collision. $\endgroup$ May 22 at 14:21
  • $\begingroup$ @MathKeepsMeBusy From the sources I've read, the average value of the vector $\vec v_f$ is the vector $\vec v_d$ that is directed parallel/antiparallel to the electric field, but you may be right. The Drude model for electrical conduction has it's flaws anyway, especially because the particles in consideration are very small. $\endgroup$
    – Cross
    May 22 at 14:26
  • $\begingroup$ As an analogy, one may think of electronic drift velocity as something similar to terminal velocity of an object falling through a fluid. The latter also exists despite the gravitational force that would accelerate indefinitely if not the collisions with atoms of the fluid. $\endgroup$
    – Ruslan
    May 22 at 22:40
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Newton's law does apply but the electrons in the circuit aren't moving in a straight line like a car on a straight road for example. The motion of the electron is rather chaotic, they bounce around in the crystal and their average velocity is considered to be proportional to the Electric field.

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