What is drift velocity of free electrons? Deduce I = nAEVₖ where the symbols have their usual meaning.

The drift velocity of free electrons refers to the average velocity that electrons attain due to an electric field in a conductor. When an electric field is applied, electrons move in a direction opposite to the field, resulting in a net flow of charge, which we observe as electric current.

Understanding Drift Velocity

Drift velocity can be defined as the velocity at which electrons move through a conductor when an electric field is applied. It is typically denoted by the symbol Vₖ.

Deriving the Current Formula

The electric current I in a conductor can be expressed in terms of the number density of charge carriers, the cross-sectional area of the conductor, and the drift velocity. Here’s how we can derive the formula I = nAEVₖ:

• n: This represents the number density of free electrons, or the number of electrons per unit volume.
• A: This is the cross-sectional area of the conductor through which the electrons flow.
• E: This is the elementary charge of an electron, approximately equal to 1.6 x 10^-19 C.
• Vₖ: This is the drift velocity of the electrons.

To derive the current, we consider the total charge passing through a cross-section of the conductor in a given time:

The charge Q that passes through the area A in time t can be expressed as:

Q = n \cdot A \cdot Vₖ \cdot t \cdot E

Since current I is defined as the charge per unit time, we can write:

I = Q/t = nAEVₖ

This equation shows that the current is directly proportional to the number density of electrons, the cross-sectional area, and the drift velocity, providing a clear relationship between these variables.