A silver wire of diameter 1.0 mm carries a current of 150 mA. The density of conduction electron

step 1 In this problem, we have a silver wire with a diameter of 1 millimeter, which is the same as the

A silver wire of diameter 1.0 mm carries a current of 150...

A silver wire of diameter $1.0 \mathrm{mm}$ carries a current of $150 \mathrm{mA}$. The density of conduction electrons in silver is $5.8 \times 10^{28} \mathrm{m}^{-3} .$ How long (on average) does it take for a conduction electron to move $1.0 \mathrm{cm}$ along the wire?

Key Concepts

Uniform Motion Kinematics

Uniform motion kinematics deals with motion at a constant velocity. By applying the simple relation time = distance/velocity, one can determine the time required for a particle, moving at a constant drift speed, to cover a certain distance. This concept is key when transitioning from microscopic drift velocities to macroscopic time measurements.

Charge Carrier Density

Charge carrier density refers to the number of free electrons available per unit volume in a material. This parameter is fundamental in determining how easily a material can conduct electricity, as a higher density implies more carriers to participate in current flow.

Cross-Sectional Area in Conductors

The cross-sectional area is critical because it directly affects the relationship between current and drift velocity. For a cylindrical wire, this area is calculated using the formula A = ?r², where r is the radius. This geometric concept is essential for linking the physical dimensions of a conductor to its electrical properties.

Drift Velocity

Drift velocity is the average velocity attained by charged particles, such as electrons, when they move under the influence of an electric field. In conductors, although electrons move randomly, their net motion in the direction of the field is what constitutes drift velocity, linking microscopic electron motion with macroscopic electrical conduction.

Current-Drift Velocity Relationship

This concept involves the relationship I = n e A v_d, where I is the electric current, n is the charge carrier density, e is the elementary charge, A is the cross-sectional area of the conductor, and v_d is the drift velocity. This equation connects the microscopic behavior of conduction electrons with the macroscopic current observed in a circuit.

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