An copper wire of cross sectional area 2.5 mm^2 carries a current with a current density of 2.4

step 1 We have a copper wire that has a cross -sectional area of 2 .5 millimeters squared. To convert t

An copper wire of cross sectional area 2.5 mm^2 carries a...

An copper wire of cross sectional area $2.5 \mathrm{~mm}^{2}$ carries a current with a current density of $2.40 \times 10^{6} \mathrm{~A} / \mathrm{m}^{2}$. The density of free electrons for copper is $8.5 \times 10^{28}$ electrons per cubic meter. Calculate (a) the current in the wire and (b) the magnitude of the drift velocity of electrons in the wire.

An copper wire of cross sectional area $2.5 \mathrm{~mm}^{2}$ carries a current with a current density of $2.40 \times 10^{6} \mathrm{~A} / \mathrm{m}^{2}$. The density of free electrons for copper is $8.5 \times 10^{28}$ electrons per cubic meter. Calculate
(a) the current in the wire and (b) the magnitude of the drift velocity of electrons in the wire.

Key Concepts

Current Density

Current density is defined as the electric current per unit cross-sectional area of a conductor. It provides a measure of how densely the electric charge is flowing through a material and is typically expressed in amperes per square meter. Understanding current density is essential for analyzing the distribution of currents in various parts of a circuit or conductor.

Cross-Sectional Area

The cross-sectional area of a conductor is the portion of the material through which the current flows. It plays a crucial role in determining the current through the conductor since a larger area allows more charge carriers to pass through, thereby affecting the overall current distribution in the material.

Electric Current

Electric current refers to the rate at which charge flows through a conductor. It is typically measured in amperes, and it is calculated by multiplying the current density by the cross-sectional area. This concept is foundational in circuit analysis and helps in understanding how electrical energy is transmitted.

Free Electron Density

Free electron density is the number of conduction electrons per unit volume in a material. In metals, these electrons are responsible for electrical conduction, and knowing their density is essential in determining the electrical properties of the material, such as its conductivity and response to an applied electric field.

Drift Velocity

Drift velocity is the average velocity at which charge carriers, like electrons, move through a conductor under the influence of an electric field. It is a key concept in understanding how microscopic charge movement results in macroscopic current and is calculated using the relationship between current, free electron density, the charge of an electron, and the cross-sectional area of the conductor.

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