Domanda del libro di testo
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?
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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 2
1.0 x 10²⁰ electrons flow through a cross section of a 2.0-mm-diameter iron wire in 5.0 s. What is the electron drift speed?
Guida verificata passo dopo passo1
Determine the formula for drift speed. The drift speed \( v_d \) is given by \( v_d = \frac{I}{n \cdot A \cdot e} \), where \( I \) is the current, \( n \) is the number density of electrons, \( A \) is the cross-sectional area of the wire, and \( e \) is the charge of an electron.
Calculate the current \( I \). The current is the rate of charge flow, \( I = \frac{Q}{t} \), where \( Q \) is the total charge and \( t \) is the time. Use \( Q = N \cdot e \), where \( N \) is the number of electrons and \( e = 1.6 \times 10^{-19} \; \text{C} \).
Find the cross-sectional area \( A \) of the wire. The wire is circular, so \( A = \pi r^2 \), where \( r \) is the radius of the wire. Convert the diameter of the wire (2.0 mm) to meters and divide by 2 to find the radius.
Determine the number density of electrons \( n \). For iron, the number density of conduction electrons is approximately \( 8.5 \times 10^{28} \; \text{electrons/m}^3 \).
Substitute all known values into the drift speed formula \( v_d = \frac{I}{n \cdot A \cdot e} \) to calculate the drift speed. Ensure all units are consistent (e.g., meters, seconds, coulombs).
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Concetti chiave
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Drift Speed
Drift speed refers to the average velocity that charged particles, such as electrons, attain due to an electric field. In a conductor, this speed is typically very small, as it represents the net movement of electrons in the direction of the electric field, despite their random thermal motion. Drift speed can be calculated using the formula v_d = I/(nqA), where I is the current, n is the charge carrier density, q is the charge of an electron, and A is the cross-sectional area.
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Percorso guidato
07:59
Speed Distribution & Special Speeds of Ideal Gases
Current
Electric current is the flow of electric charge, measured in amperes (A). It represents the rate at which charge flows through a conductor. In this context, current can be calculated using the formula I = Q/t, where Q is the total charge that passes through a cross-section of the wire in time t. Understanding current is essential for determining the drift speed of electrons in the wire.
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Percorso guidato
05:38Intro to Current
Cross-Sectional Area
The cross-sectional area of a wire is the area of its circular end face, which affects how much current can flow through it. It is calculated using the formula A = π(d/2)², where d is the diameter of the wire. A larger cross-sectional area allows more electrons to flow simultaneously, influencing both the current and the drift speed of the electrons within the wire.
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Percorso guidato
08:10Calculating the Vector (Cross) Product Using Components
Pratica correlata
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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Domanda del libro di testo
The mean time between collisions for electrons in a gold wire is 25 fs, where 1 fs = 1 femtosecond = 10⁻¹⁵ s. How many times does the electron collide with an ion while moving this distance?
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Domanda del libro di testo
The mean time between collisions for electrons in a gold wire is 25 fs, where 1 fs = 1 femtosecond = 10⁻¹⁵ s. What is the electron drift speed in a 35 mV/m electric field?
147
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