Why Does Drift Velocity Calculation Differ for One Electron vs Many?

In summary, the average drift velocity, v_d, of many electrons in a conductor due to an electric field is equal to the acceleration, a, multiplied by the mean time between collisions, t. This is also equivalent to v_d = at/2 for a single electron and v_d = at for many electrons.
  • #1
conquerer7
26
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If a is the acceleration of an electron in a conductor due to an electric field, and t is the mean time between collisions, than v_d, the average drift velocity, is

v_d = at

1. There should be a 1/2 there! If you followed one electron, its average v_d would be at/2 by kinematics.
2. Book says: We're averaging over many electrons. For each one, at some instant, v_d = aT where T is the time since the last collision. And what's the average of that? Just v_d = at.

Which one is right? They both sound correct to me...
 
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  • #2
Both are correct. 1/2 is the average drift velocity of a single electron, while at is the average drift velocity of many electrons.
 

FAQ: Why Does Drift Velocity Calculation Differ for One Electron vs Many?

What is drift velocity?

Drift velocity is the average velocity at which charged particles, such as electrons, move in a particular direction under the influence of an electric field.

How is drift velocity calculated?

Drift velocity can be calculated by dividing the current density by the charge density and the charge on the particle.

Why is the 1/2 missing in the equation for drift velocity?

The 1/2 is missing because it accounts for the random motion of charged particles, also known as thermal motion. This motion is not influenced by the electric field and therefore does not contribute to the overall drift velocity.

Is drift velocity the same for all materials?

No, drift velocity varies depending on the material's resistivity and the strength of the electric field. Materials with higher resistivity will have a lower drift velocity.

What is the practical application of drift velocity?

Drift velocity is important in the study of electrical currents and is used in the design and analysis of electronic devices such as transistors, diodes, and integrated circuits. It also plays a role in understanding the behavior of charged particles in materials, such as in the field of semiconductor physics.

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