Unformatted text preview: , , 0) → (0 , 1 , 0) → (1 , 1 , 0) (b) the path from (0 , , 0) → (1 , , 0) → (1 , 1 , 0) (c) the path from (0 , , 0) → (1 , 1 , 0) along the parabola y = x 2 6. (a) Sketch a picture of the vector ﬁeld F = x ˆ x . (b) Calculate directly the ﬂux of F outward through the surface of the unit cube deﬁned by ≤ x, y, z ≤ 1. (c) Calculate the ﬂux using the divergence theorem. 7. For the following problem work in rectangular coordinates . (a) Sketch a picture of the vector ﬁeld F = ˆ z × x ˆ x (b) Calculate directly the line integral of F around a circle in the xy plane, centered at 0 with a radius a . (c) Calculate the line integral by using Stokes’ theorem. 8. Rewrite F from the problem above in cylindrical coordinates and rework the problem in cylindrical coordinates. 1...
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 Fall '09
 STAFF
 Vector Calculus, Magnetism, Work, Vector field, Stokes' theorem, cylindrical coordinates, following problem work

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