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Distance vs Displacement

Drift speed i...

Question

Drift speed is defined as v_d = Δl/Δt, where Δl is the distance drifted in a long time Δt. Why don't we define drift speed as the limit of Δl/Δt as Δt → 0?

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Solution

An electron drifts under the influence of an external electric field. During the course of this motion, an electron follows a very random path. So, we have to take the average for a very long time. Hence, we cannot define drift speed as the limit of Δl/Δt as Δt → 0 because this is a very short interval of time that is not enough to get the desired result.

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