Use the surface integral in Stokes Theorem to calculate the circulation of the field F around the
Question:
Use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around the curve C in the indicated direction.
F = x2i + 2xj + z2k
C: The ellipse 4x2 + y2 = 4 in the xy-plane, counterclockwise when viewed from above
Transcribed Image Text:
THEOREM 6-Stokes' Theorem Let S be a piecewise smooth oriented surface having a piecewise smooth boundary curve C. Let F = Mi + Nj + Pk be a vector field whose components have continuous first partial derivatives on an open region containing S. Then the circulation of F around C in the direction counterclockwise with respect to the surface's unit normal vector n equals the integral of the curl vector field VX F over S: fF.dr = [[ S Counterclockwise circulation VXF ndo Curl integral (4)
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To apply Stokes Theorem we need to find the curl of F curl F Fy Fz i Fz Fx j Fx Fy k 2yi 0j 2zk Now ...View the full answer
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Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
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