Math 208 (Lutz) - Quiz #12, 11/22/13 Name: Directions: This quiz has 4 questions, for a total of 26 points. Solve each problem carefully. You must show ALL of your work in order to earn full credit. 1. (5 points) Calculate the flux of the vector field F! = !i − !j + 3!k through the disk of radius 2 in the xy-plane, centered at the origin, oriented upward. 2. (7 points) Compute the flux of the vector field F! through the surface S, where F! (x, y, z) = 2x!j + y!k, and S is the part of the surface z = −y + 1 above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, oriented upward. 3. (7 points) Compute the flux of the vector field F! through the surface S, where F! (x, y, z) = x!i+y!j +z!k, and S is the cylinder of radius 2 centered on the z-axis, with −3 ≤ z ≤ 3, oriented outward. 4. (7 points) Compute the flux of F! = z!k through S, where S is the upper hemisphere of the sphere of radius 2 centered at the origin, oriented outward.
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