3. Let S be the part of the paraboloid surface that lies between the cylinders z = (x + 1)² + y² - 5 x² + y² = 3. x² + y² = 1 and Assume S 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 S. (c) Check your answer to part (b) using the MATLAB symbolic toolbox.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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3. Let S be the part of the paraboloid surface
that lies between the cylinders
z = (x + 1)² + y² – 5
x² + y²
and
Assume S is oriented with downward unit normal. Let
= 1
x² + y² = 3.
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 S.
(c) Check your answer to part (b) using the MATLAB symbolic toolbox.
Transcribed Image Text:3. Let S be the part of the paraboloid surface that lies between the cylinders z = (x + 1)² + y² – 5 x² + y² and Assume S is oriented with downward unit normal. Let = 1 x² + y² = 3. 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 S. (c) Check your answer to part (b) using the MATLAB symbolic toolbox.
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