What is Drift Velocity in Physics?

Definition: Drift velocity is defined as the average, constant velocity with which free electrons get 'drifted' towards the positive end of a conductor under the influence of an external electric field.

• Without a Battery: In a normal copper wire, free electrons move randomly in all directions at very high thermal speeds. They constantly collide with atoms, and their average net movement is zero (so, no current flows).
• With a Battery: When you connect a battery, an electric field is created. This field pushes the electrons. They still collide randomly, but they now slowly 'drift' in one specific direction (towards the positive terminal). This slow, steady drift is the drift velocity.

The formula for drift velocity ($v_d$) is derived from the relation between current ($I$) and the properties of the conductor:

$v_d = \frac{I}{n e A}$

Where:

• $I$ = Electric current flowing through the conductor
• $n$ = Number density of free electrons (electrons per unit volume)
• $e$ = Charge of a single electron ($1.6 \times 10^{-19} C$)
• $A$ = Cross-sectional area of the wire

Alternatively, drift velocity can be expressed in terms of the applied electric field ($E$) and relaxation time ($\tau$): $v_d = -\frac{e E}{m} \tau$ (Where $m$ is the mass of the electron, and $\tau$ is the average time between two successive collisions).