PHYS 311 Homework Chapter 1 PDF
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Uploaded by ConciliatoryDevotion7065
2024
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Summary
This document appears to be a physics homework assignment for PHYS 311, focusing on calculations and vector analysis. The assignment includes questions on surface integrals, divergence theorem, and line integrals for a given vector field, with emphasis on unit vector and calculating using ellipsoids and a closed curve.
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Assignment/Homework (Chapter 1: PHYS 311) Due date: 5 Sept 2024 (during class) Total point: 35% "β = 2π₯π§ π₯) + (π₯ + 2)π¦) + π¦(π§ ! β 3)π§Μ over the five sides 1. Calculate the surface integral of π (e...
Assignment/Homework (Chapter 1: PHYS 311) Due date: 5 Sept 2024 (during class) Total point: 35% "β = 2π₯π§ π₯) + (π₯ + 2)π¦) + π¦(π§ ! β 3)π§Μ over the five sides 1. Calculate the surface integral of π (excluding the bottom) of the cubical box. Let βupward and outwardβ be positive direction as indicated by the arrows. (Hint: taking one side at a time) (10%) "β = π¦ ! π₯) + (2π₯π¦ + π§ ! )π¦) + (2π¦π§)π§Μ and a 2. Check the divergence theorem using the function π unit cube at the origin as shown. (10%) "! $! &! 3. The equation giving a family of ellipsoids is: π’ = #! + %! + ' !. Find the unit vector normal to each point of the surface of these ellipsoids. (Hint: find the unit vector π)) (5%) 4. Given the vector π΄β = 4πΜ + 3π7 β 2π), find its line integral around the closed path shown in Figure shown. The curved portion is the arc of a circle of radius r0 centered at the origin. Also find the surface integral of β Γ π΄β over the enclosed area and compared your results. (10%)
