A high-voltage transmission line with a diameter of 2.00 cm and a length of 200 km carries a ste

step 1 So in this problem we are given diameter of wire is equal to 2 cm then radius will be equal to 1

A high-voltage transmission line with a diameter of 2.00 cm...

A high-voltage transmission line with a diameter of $2.00 \mathrm{cm}$ and a length of $200 \mathrm{km}$ carries a steady current of $1000 \mathrm{A}$ If the conductor is copper wire with a free charge density of $8.49 \times 10^{28}$ electrons/m $^{3}$, how long does it take one electron to travel the full length of the line?

Key Concepts

Drift Velocity

Drift velocity is the average velocity at which charge carriers, such as electrons, move through a conductor when subjected to an electric field. It is a central concept in understanding electrical conduction and is calculated by relating the current flowing through the conductor to the number density of free electrons, the charge of an electron, and the cross-sectional area of the conductor.

Free Electron Density

Free electron density refers to the number of conduction electrons available per unit volume in a conducting material. This parameter is essential for determining the drift velocity because it directly impacts how the current is distributed among the electrons. A higher free electron density implies that, for a given current, individual electrons need to move more slowly.

Electric Current

Electric current is the rate at which charge flows through a conductor, typically measured in amperes. In the context of drift velocity, the current quantifies how many electrons are passing through a cross-sectional area per unit time, thereby linking the macroscopic observable of current to the microscopic movement of charge carriers.

Cross-Sectional Area

The cross-sectional area of a conductor is the area of its cross-section perpendicular to the flow of current. It is a key parameter that affects the drift velocity of electrons, as it determines how spread out the current is over the material. A larger cross-sectional area means the same current is distributed over more electrons, resulting in a slower drift velocity.

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