The drift seed is defined as Vd = dl/dt where dl is the distance travelled in a long time dt. why don't we define the drift speed as a limit of dl/dt as dt ->0 ?

Dear nikhil

The drift velocity is the average velocity that a particle, such as an electron, attains due to an electric field.As by definition it is average velocity it is just dl/dt.if you take dt->0 then it will be instantaneous rather than average.

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