Textbook Question
The current in a 2.0 mm x 2.0 mm square aluminum wire is 2.5 A. What are (a) the current density and (b) the electron drift speed?
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Ch 27: Current and Resistance
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- 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: 9780137344796Not the one you use?Change textbook
Chapter 27, Problem 15
A hollow copper wire with an inner diameter of 1.0 mm and an outer diameter of 2.0 mm carries a current of 10 A. What is the current density in the wire?
Verified step by step guidance1
Determine the cross-sectional area of the hollow wire. The cross-sectional area is the difference between the area of the outer circle and the inner circle. Use the formula for the area of a circle: A = πr², where r is the radius. Convert the diameters to radii by dividing by 2, and ensure the units are in meters.
Calculate the area of the outer circle using the outer radius (r_outer = 2.0 mm / 2 = 1.0 mm = 0.001 m). Substitute this value into the formula A_outer = πr_outer².
Calculate the area of the inner circle using the inner radius (r_inner = 1.0 mm / 2 = 0.5 mm = 0.0005 m). Substitute this value into the formula A_inner = πr_inner².
Find the cross-sectional area of the hollow wire by subtracting the inner area from the outer area: A_hollow = A_outer - A_inner.
Determine the current density (J) using the formula J = I / A_hollow, where I is the current (10 A) and A_hollow is the cross-sectional area calculated in the previous step.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Current Density
Current density is defined as the amount of electric current flowing per unit area of a cross-section of a conductor. It is represented by the symbol 'J' and is calculated using the formula J = I/A, where 'I' is the current in amperes and 'A' is the cross-sectional area in square meters. Understanding current density is crucial for analyzing how current distributes within a conductor.
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Cross-Sectional Area
The cross-sectional area of a wire is the area of a slice taken perpendicular to its length. For a hollow cylindrical wire, the cross-sectional area can be calculated by subtracting the area of the inner circle from the area of the outer circle. This area is essential for determining the current density, as it directly influences how concentrated the current is within the wire.
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Ohm's Law
Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance of the conductor. While the question focuses on current density, understanding Ohm's Law provides insight into the relationship between current, voltage, and resistance, which is fundamental in electrical circuits.
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Related Practice
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