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Chapter 18: Problem 9

Briefly tell what is meant by the drift velocity and mobility of a free electron.

Short Answer

Expert verified
Answer: Drift velocity is the average velocity at which free electrons move inside a conductor under the influence of an electric field, and mobility is a measure of how easily an electron can navigate through a material. They are related through the electric field: higher mobility corresponds to higher conductivity and more efficient current flow. Drift velocity can be calculated using the formula \(v_d = \frac{I}{n q A}\), and mobility can be calculated using the formula \(\mu = \frac{v_d}{E}\).

Step by step solution

01

1. Drift Velocity Definition

Drift velocity is the average velocity at which free electrons move inside a conductor under the influence of an electric field. When a potential difference is applied across a conductor, free electrons experience a force that causes them to drift against the direction of the electric field. The drift velocity is usually quite small, in the order of millimeters per second.
02

2. Drift Velocity Formula

The drift velocity (\(v_d\)) can be calculated using the following formula: \[v_d = \frac{I}{n q A}\] where: - \(v_d\) is the drift velocity (m/s) - \(I\) is the current flowing through the conductor (A) - \(n\) is the number of free electrons per unit volume (m\(^{-3}\)) - \(q\) is the charge of an electron (\(1.6 \times 10^{-19}\) C) - \(A\) is the cross-sectional area of the conductor (m\(^2\))
03

3. Mobility Definition

Mobility of a free electron refers to the ability of an electron to move through a conductor when subjected to an electric field. It is a measure of how easily an electron can navigate through a material, and it is affected by factors such as temperature, impurities, and lattice vibrations. Mobility is directly related to the electrical conductivity of a material.
04

4. Mobility Formula

The mobility (\(\mu\)) of a free electron can be calculated using the following formula: \[\mu = \frac{v_d}{E}\] where: - \(\mu\) is the mobility of a free electron (m\(^2\)/V s) - \(v_d\) is the drift velocity (m/s) - \(E\) is the electric field applied to the conductor (V/m).
05

5. Relationship Between Drift Velocity and Mobility

Drift velocity and mobility are related through the electric field. As the electric field increases, the drift velocity of free electrons inside the conductor also increases, directly affecting their mobility. Higher mobility corresponds to higher conductivity, which means less resistance and more efficient current flow through the material.

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