 # Drift Velocity Derivation

Drift velocity is defined as the average velocity attained by the particles (electrons) of a given material due to an electric field that is proportional to current. Ohm’s law can be expressed in terms of drift velocity as follows:

u=μE

Where,

u: drift velocity (m/s)

μ: material’s electron mobility (m2/V.s)

E: electric field (V/m)

## Derivation of Drift velocity

Following is the derivation of drift velocity:

$$F=-\mu E$$ $$a=\frac{F}{m}=\frac{-\mu E}{m}$$ $$u=v+at$$

Here,

v = 0

t = T (relaxation time that is the time required by an electron to return to its initial equilibrium value)

$$u=aT$$ (substituting for v and u)

$$∴ u=(\frac{-\mu E}{m})T$$ (substituting for a)

This is the final equation explaining drift velocity.

But as the temperature increases, the drift velocity of electrons increases in a metallic conductor.

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