Area of cross-section of a copper wire is equal to area of a...

Area of cross-section of a copper wire is equal to area of a square of $2 \mathrm{~mm}$ length It carries a current of $8 \mathrm{~A}$ Find drift velocity of electrons (Density of free electrons in copper $\left.=8 \times 10^{28} \mathrm{~m}^{-3}\right)$ (A) $1.56 \times 10^{-2} \mathrm{~ms}^{-1}$ (B) $1.56 \times 10^{-4} \mathrm{~ms}^{-1}$ (C) $3.12 \times 10^{-2} \mathrm{~ms}^{-1}$ (D) $3.12 \times 10^{-3} \mathrm{~ms}^{-1}$

Area of cross-section of a copper wire is equal to area of a square of $2 \mathrm{~mm}$ length It carries a current of $8 \mathrm{~A}$ Find drift velocity of electrons (Density of free electrons in copper $\left.=8 \times 10^{28} \mathrm{~m}^{-3}\right)$
(A) $1.56 \times 10^{-2} \mathrm{~ms}^{-1}$
(B) $1.56 \times 10^{-4} \mathrm{~ms}^{-1}$
(C) $3.12 \times 10^{-2} \mathrm{~ms}^{-1}$
(D) $3.12 \times 10^{-3} \mathrm{~ms}^{-1}$

Key Concepts

Free Electron Density

Free electron density is the number of conduction electrons per unit volume in a material. It is critical for determining how many charge carriers are available to conduct current in a conductor. This concept plays an essential role in calculations involving electrical conductivity and drift velocity, as it directly influences the overall current that can flow through a material.

Cross-Sectional Area of the Conductor

The cross-sectional area of a conductor affects the current density, which is the current per unit area. In the context of drift velocity calculations, the area of the conductor is used alongside the free electron density and the drift velocity to establish the total charge flow. A larger area would allow more carriers to contribute to the current, thus influencing the derived drift velocity when a known current is present.

Drift Velocity

Drift velocity refers to the average velocity that a particle, such as an electron, attains due to an electric field. In electrical conductors, although the individual electrons move randomly at high speeds, the net movement in response to an applied potential is very slow. Drift velocity is a key concept in understanding how microscopic particle motions result in macroscopic electric current.

Electric Current and Charge Carriers

Electric current is the rate at which charge flows through a conductor. This flow is carried by charge carriers, such as electrons in metals. The relationship between current, drift velocity, the number density of charge carriers, the cross-sectional area of the conductor, and the elemental charge is fundamental in connecting microscopic particle behavior to the observed electrical current.

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