Establish a relation between electric current and drift velocity. OR prove that the current density of metallic conductors is directly proportional to the drift speed of electrons.

The relationship between electric current and drift velocity is fundamental in understanding how electricity flows through conductors. In metallic conductors, the movement of electrons creates an electric current, which can be described mathematically.

Key Concepts

• Electric Current (I): The flow of electric charge, measured in amperes (A).
• Drift Velocity (v_d): The average velocity of charge carriers (like electrons) in a conductor when an electric field is applied.
• Current Density (J): The amount of electric current flowing per unit area of the conductor, expressed in amperes per square meter (A/m²).

Mathematical Relationship

The current density (J) can be expressed as:

J = n * q * v_d

Where:

• n: Number of charge carriers per unit volume (in m³).
• q: Charge of each carrier (for electrons, approximately -1.6 x 10^-19 coulombs).
• v_d: Drift velocity of the electrons.

Direct Proportionality

From the equation above, it is clear that current density (J) is directly proportional to drift velocity (v_d). This means that as the drift velocity increases, the current density also increases, assuming the number of charge carriers and their charge remain constant.

Conclusion

In summary, the electric current in metallic conductors is closely linked to the drift velocity of electrons. The relationship is defined by the current density, which shows that higher drift speeds lead to greater current flow, illustrating the direct proportionality between these two concepts.