In the circuit shown in Figure 18.108, two thick copper...

In the circuit shown in Figure $18.108,$ two thick copper wires connect a $1.5 \mathrm{V}$ battery to a Nichrome wire. Each thick connecting wire is $17 \mathrm{cm}$ long and has a radius of $9 \mathrm{mm}$. Copper has $8.4 \times 10^{28}$ mobile electrons per cubic meter and an electron mobility of $4.4 \times 10^{-3}(\mathrm{m} / \mathrm{s}) /(\mathrm{V} / \mathrm{m}) .$ The Nichrome wire is $8 \mathrm{cm}$ Iong. and has a radius of $3 \mathrm{mm}$. Nichrome has $9 \times 10^{28}$ mobile electrons per cubic meter and an electron mobility of $7 \times 10^{-5}$ $(\mathrm{m} / \mathrm{s}) /(\mathrm{V} / \mathrm{m})$ (a) What is the magnitude of the electric field in the thick copper wire? (b) What is the magnitude of the electric field in the thin Nichrome wire?

In the circuit shown in Figure $18.108,$ two thick copper wires connect a $1.5 \mathrm{V}$ battery to a Nichrome wire. Each thick connecting wire is $17 \mathrm{cm}$ long and has a radius of $9 \mathrm{mm}$. Copper has $8.4 \times 10^{28}$ mobile electrons per cubic meter and an electron mobility of $4.4 \times 10^{-3}(\mathrm{m} / \mathrm{s}) /(\mathrm{V} / \mathrm{m}) .$ The Nichrome wire is $8 \mathrm{cm}$
Iong. and has a radius of $3 \mathrm{mm}$. Nichrome has $9 \times 10^{28}$ mobile electrons per cubic meter and an electron mobility of $7 \times 10^{-5}$ $(\mathrm{m} / \mathrm{s}) /(\mathrm{V} / \mathrm{m})$ (a) What is the magnitude of the electric field in the thick copper wire? (b) What is the magnitude of the electric field in the thin Nichrome wire?

Key Concepts

Drift Velocity

Drift velocity is the average velocity attained by charged particles, such as electrons, in a material in response to an electric field. It is given by the product of the mobility and the electric field (v_d = ?E). Understanding drift velocity helps in relating the microscopic motion of carriers to the macroscopic current that is observed.

Charge Carrier Mobility

Mobility is a measure of how quickly charge carriers (such as electrons) can move through a material when subjected to an electric field. It directly influences the drift velocity of the carriers and thus the current in the conductor, making it a crucial parameter in understanding and calculating conduction properties.

Series Circuits and Current Continuity

In a series circuit, the current remains constant throughout all elements, despite variations in material properties or geometrical dimensions. This principle of current continuity is essential when analyzing circuits with different conductors, as it ensures that the same current passes through every segment, allowing the calculation of different electric fields or potential drops along each component.

Electric Field in Conductors

The electric field in any conducting segment is defined as the potential difference divided by the length over which that drop occurs. This concept is key in determining the driving force for charge carriers within different parts of a circuit and is essential in analyzing how voltage divides among various components.

Ohm's Law and Its Microscopic Form

Ohm's law, in its microscopic form, relates the current density to the electric field through the material’s conductivity. This relation is represented by j = ?E, where conductivity is connected to the density and mobility of the charge carriers. It provides a bridge between macroscopic observations (voltage, current, resistance) and microscopic properties (charge carrier density and mobility).

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