A copper wire of cross-sectional area 1.00 mm^2 has a current of 2.0 A flowing along its length.

step 1 As we all know that number of electrons per unit volume n is equal to 1 .3 multiplication row n

A copper wire of cross-sectional area 1.00 mm^2 has a...

A copper wire of cross-sectional area $1.00 \mathrm{mm}^{2}$ has a current of $2.0 \mathrm{A}$ flowing along its length. What is the drift speed of the conduction electrons? Assume 1.3 conduction electrons per copper atom. The mass density of copper is $9.0 \mathrm{g} / \mathrm{cm}^{3}$ and its molar mass is $64 \mathrm{g} / \mathrm{mol}$.

Key Concepts

Electric Current

Electric current is the flow of electric charge through a conductor. It is driven by an applied electric field, causing charged particles (typically electrons in metals) to move, and its rate is measured in amperes, representing the amount of charge passing through a cross-sectional area per unit time.

Drift Velocity

Drift velocity is the average velocity at which conduction electrons move through a conductor under the influence of an electric field. Although electrons move randomly due to thermal energy, the electric field superimposes a small net velocity, which is essential for relating microscopic electron motion to macroscopic current flow.

Charge Carrier Density

Charge carrier density is the number of free charge carriers per unit volume in a material. In conductors like copper, it is determined by the material's mass density, molar mass, and the number of conduction electrons available per atom. This concept is crucial for calculating how many electrons contribute to conduction and thus the overall current.

Relationship Between Current, Drift Velocity, and Material Properties

The equation I = n q A v_d links the macroscopic measurement of current (I) with the microscopic drift velocity (v_d) of electrons, where n is the charge carrier density, q is the elementary charge, and A is the cross-sectional area of the conductor. This relationship allows one to solve for drift velocity by using known material properties and measured current.

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