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A particle moves along the circle x² + y² = 16 oriented counterclockwise and z = 5, under the influence of the force field: F(x,y,z) = yzi + 2xzj + exyk. Find the work done Use the divergence (Gauss') Theorem to calculate the flux of F across S where F(x,y,z) = (cos z + xy²) į + xe−² j + (sin y + x²z) k and S is the surface of the solid bounded by the paraboloid z = x² + y² and the plane z = 4 Calculate the flux of the vector field: F(x,y,z) = 4xz I + xyz j + 3z k across the outer side of the surface S, z² = x² + y²,0 ≤z ≤ 4

A particle moves along the circle x² + y² = 16 oriented counterclockwise and z = 5, under the influence of the force field: F(x,y,z) = yzi + 2xzj + exyk. Find the work done Use the divergence (Gauss') Theorem to calculate the flux of F across S where F(x,y,z) = (cos z + xy²) į + xe−² j + (sin y + x²z) k and S is the surface of the solid bounded by the paraboloid z = x² + y² and the plane z = 4 Calculate the flux of the vector field: F(x,y,z) = 4xz I + xyz j + 3z k across the outer side of the surface S, z² = x² + y²,0 ≤z ≤ 4

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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show full and complete procedure HANDWRITTEN only. Please answer a), b) and c) as they are subparts of question 1 

1. Answer the following a) A particle moves along the circle x² + y² = 16 oriented counterclockwise and z = 5, under the influence of the force field: F(x,y,z) = yzi + 2xzj + exyk. Find the work done b) Use the divergence (Gauss') Theorem to calculate the flux of F across S where -Z F(x,y,z) (cos z + xy²) į + xe` ´j + (sin y + x²z) k and S is the surface of the solid bounded by the paraboloid z =x² + y² and the plane z = 4 c) Calculate the flux of the vector field: F(x,y,z) = 4xz I + xyz j + 3z k across the outer side of the surface S, z² = x² + y²,0 ≤ z ≤ 4 =
Transcribed Image Text:1. Answer the following a) A particle moves along the circle x² + y² = 16 oriented counterclockwise and z = 5, under the influence of the force field: F(x,y,z) = yzi + 2xzj + exyk. Find the work done b) Use the divergence (Gauss') Theorem to calculate the flux of F across S where -Z F(x,y,z) (cos z + xy²) į + xe` ´j + (sin y + x²z) k and S is the surface of the solid bounded by the paraboloid z =x² + y² and the plane z = 4 c) Calculate the flux of the vector field: F(x,y,z) = 4xz I + xyz j + 3z k across the outer side of the surface S, z² = x² + y²,0 ≤ z ≤ 4 =
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