Domanda del libro di testo
The electron drift speed in a 1.0-mm-diameter gold wire is 5.0 x 10⁻⁵ m/s. How long does it take 1 mole of electrons to flow through a cross section of the wire?
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Ch 27: Current and Resistance
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 27, Problema 7
The electron drift speed is 2.0 X 10⁻⁴ m/s in a metal with a mean time between collisions of 5.0 x 10⁻¹⁴. What is the electric field strength?
Guida verificata passo dopo passo1
Understand the relationship between the drift speed, electric field, and mean time between collisions. The drift speed \(v_d\) is related to the electric field \(E\) through the equation \(v_d = \mu E\), where \(\mu\) is the mobility of the electrons. Mobility \(\mu\) can be expressed as \(\mu = \frac{e \tau}{m}\), where \(e\) is the charge of an electron, \(\tau\) is the mean time between collisions, and \(m\) is the mass of an electron.
Substitute the expression for \(\mu\) into the drift speed equation. This gives \(v_d = \frac{e \tau}{m} E\). Rearrange this equation to solve for the electric field \(E\): \(E = \frac{v_d m}{e \tau}\).
Identify the known values: \(v_d = 2.0 \times 10^{-4} \ \text{m/s}\), \(\tau = 5.0 \times 10^{-14} \ \text{s}\), \(e = 1.6 \times 10^{-19} \ \text{C}\) (charge of an electron), and \(m = 9.11 \times 10^{-31} \ \text{kg}\) (mass of an electron).
Substitute the known values into the equation \(E = \frac{v_d m}{e \tau}\). This becomes \(E = \frac{(2.0 \times 10^{-4})(9.11 \times 10^{-31})}{(1.6 \times 10^{-19})(5.0 \times 10^{-14})}\).
Simplify the expression to calculate the electric field \(E\). Perform the arithmetic operations step by step to ensure accuracy, but do not compute the final value here.
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Drift Speed
Drift speed refers to the average velocity that a charged particle, such as an electron, attains due to an electric field. In conductive materials, electrons move randomly but, when an electric field is applied, they gain a net velocity in the direction of the field. This drift speed is typically very small, as seen in the given value of 2.0 x 10⁻⁴ m/s.
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Percorso guidato
07:59
Speed Distribution & Special Speeds of Ideal Gases
Mean Time Between Collisions
The mean time between collisions is the average time interval that an electron travels before colliding with an atom in the metal. This parameter is crucial for understanding the behavior of charge carriers in a conductor, as it affects their mobility and the overall conductivity of the material. In this case, the mean time is given as 5.0 x 10⁻¹⁴ seconds.
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08:20Mean Free Path
Electric Field Strength
Electric field strength, often denoted as E, is defined as the force per unit charge experienced by a positive test charge placed in the field. It is related to the drift speed and mean time between collisions through the equation E = (drift speed) / (mean time between collisions) multiplied by the charge-to-mass ratio of the electron. Understanding this relationship is essential for calculating the electric field strength in the given scenario.
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03:16Intro to Electric Fields
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