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Let T be the part of the paraboloid surface that lies between the cylinders 2 = (x + 1)² + y² - 5 x² + y² = 1 and Assume T is oriented with downward unit normal. Let x² + y² = 3. F(x, y, z)i + (z+€³)j + 2y(e¹ – 4)k be a magnetic field. (a) Determine whether or not F is a conservative vector field. (b) Determine the magnetic flux through the surface, i.e, the flux of F across T. (c) Check your answer to part (b) using the MATLAB symbolic toolbox.

Let T be the part of the paraboloid surface that lies between the cylinders 2 = (x + 1)² + y² - 5 x² + y² = 1 and Assume T is oriented with downward unit normal. Let x² + y² = 3. F(x, y, z)i + (z+€³)j + 2y(e¹ – 4)k be a magnetic field. (a) Determine whether or not F is a conservative vector field. (b) Determine the magnetic flux through the surface, i.e, the flux of F across T. (c) Check your answer to part (b) using the MATLAB symbolic toolbox.

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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Let T be the part of the paraboloid surface that lies between the cylinders 2 = (x + 1)² + y² - 5 x² + y² = 3. x² + y² = 1 and Assume T is oriented with downward unit normal. Let F(x, y, z) = i + (z + eª)j + 2y(eª – 4)k be a magnetic field. (a) Determine whether or not F is a conservative vector field. (b) Determine the magnetic flux through the surface, i.e, the flux of F across T. (c) Check your answer to part (b) using the MATLAB symbolic toolbox.
Transcribed Image Text:Let T be the part of the paraboloid surface that lies between the cylinders 2 = (x + 1)² + y² - 5 x² + y² = 3. x² + y² = 1 and Assume T is oriented with downward unit normal. Let F(x, y, z) = i + (z + eª)j + 2y(eª – 4)k be a magnetic field. (a) Determine whether or not F is a conservative vector field. (b) Determine the magnetic flux through the surface, i.e, the flux of F across T. (c) Check your answer to part (b) using the MATLAB symbolic toolbox.
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