A current of 10.0 A is carried by a copper wire of diameter 1.00 mm. If the density of the condu

step 1 we have i equals number of carriers times charge of an electron times area times drift speed so

A current of 10.0 A is carried by a copper wire of diameter...

A current of $10.0 \mathrm{A}$ is carried by a copper wire of diameter $1.00 \mathrm{mm}$. If the density of the conduction electrons is $8.47 \times 10^{28} \mathrm{m}^{-3},$ how long does it take for a conduction electron to move $1.00 \mathrm{m}$ along the wire?

Key Concepts

Drift Velocity

Drift velocity is the average velocity attained by charged particles, such as electrons, when subjected to an electric field. Although electrons move randomly at high speeds due to thermal energy, the net movement in one direction (their drift) is slow and governs the flow of electric current in a conductor.

Relationship between Current and Drift Velocity

The relationship between current and drift velocity is given by the equation I = n q v_d A, where I is the current, n is the conduction electron density, q is the charge of an electron, v_d is the drift velocity, and A is the cross-sectional area of the conductor. This formula connects the microscopic behavior of charge carriers to the macroscopic measurable electric current.

Conduction Electron Density

Conduction electron density refers to the number of free electrons available per unit volume within a material. This parameter is crucial in determining a material's ability to conduct electric current, as a higher density generally leads to higher conductivity given the same applied electric field.

Time-Distance-Velocity Relationship

The time-distance-velocity relationship is a basic kinematic principle that relates the distance traveled to the product of velocity and time. In the context of drift velocity, this relationship is used to determine the time it takes for electrons to travel a particular length of the conductor by rearranging the equation to time = distance/velocity.

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