What is the relation between drift velocity and electric field?

Finding the relation between drift velocity and electric field:

1. A drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field.
2. The magnitude of drift velocity per unit electric field is mobility (m)

$$\begin{gathered} \mathrm{m}=\frac{\left|{\mathrm{V}}_{\mathrm{d}}\right|}{\mathrm{E}} \\ =\frac{{\mathrm{q}}_{\mathrm{t}}}{\mathrm{m}} \end{gathered}$$

Here,

$\mathrm{m}$ is the mobility.

${\mathrm{V}}_{\mathrm{d}}$ is the drift velocity.

$\mathrm{E}$ is the electric field.

The S.I unit of mobility is ${\mathrm{m}}^2/{\mathrm{V}}_{\mathrm{s}}$ and is a positive quantity.

${\mathrm{V}}_{\mathrm{d}}=\mathrm{mE}$

2. The above expression represents the relationship between an electron's drift velocity as well as the applied electric field. Drift velocity changes with electric field intensity and has been determined by the formula:

${\mathrm{V}}_{\mathrm{d}}\propto \mathrm{E}$

Therefore, the relation between drift velocity and an electric field is ${\mathrm{V}}_{\mathrm{d}}\propto \mathrm{E}$.