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(a) Compute the flux of the field F = r i+yj-zk across the cylindrical surface a + z = 1, 0

(a) Compute the flux of the field F = r i+yj-zk across the cylindrical surface a + z = 1, 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Compute the flux of the field F = ai+yj-zk across the cylindrical surface a+z = 1, 0 <y53 with an outward pointing normal. (b) Given that the curl of F is Vx F = i+2 j+ 3 k. Find the work done by F along the oriented square path from (1, -1,3) to (2, -1,3) to (2,0, 3) to (1,0,3) and back to (1, –1,3). %3D | (c) Let M be the surface with the equation a+y* + z = 9 that is above the right triangular region with vertices (0, 0), (1,0) and (1, 2). (i) Write down the vector function r(r, y) and domain of the parameterization for surface M. (ii) For the vector field F ri+yj+ (2 + y) k, evaluate F. M (iii) For the scalar function g(x, y, z) = xz, set up but do not evaluate an iterated double integral that gives the surface integral of g over M.
Transcribed Image Text:(a) Compute the flux of the field F = ai+yj-zk across the cylindrical surface a+z = 1, 0 <y53 with an outward pointing normal. (b) Given that the curl of F is Vx F = i+2 j+ 3 k. Find the work done by F along the oriented square path from (1, -1,3) to (2, -1,3) to (2,0, 3) to (1,0,3) and back to (1, –1,3). %3D | (c) Let M be the surface with the equation a+y* + z = 9 that is above the right triangular region with vertices (0, 0), (1,0) and (1, 2). (i) Write down the vector function r(r, y) and domain of the parameterization for surface M. (ii) For the vector field F ri+yj+ (2 + y) k, evaluate F. M (iii) For the scalar function g(x, y, z) = xz, set up but do not evaluate an iterated double integral that gives the surface integral of g over M.
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