3) A point mass m is located at the origin. Let F = -m (x, y, z) (where p2 = x2 + y2 + z2) be its gravitational field. Let Q be the flux of the...
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Problem is in the screenshot. Multivariable Calculus: Surface Integral

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3) A point mass m is located at the origin. Let F = -m (x, y, z) (where p2 = x2 + y2 + z2) be its gravitational field. Let Q be the flux of the gravitational field F through the cylinder x2 + y2 = R2 for a < < < b, including the top and bottom. Show that Q = -47Gm if a < 0 < b (m lies on the inside of the cylinder), and Q =0 if 0 < a < b (m lies outside the cylinder). Hint: You will need to parametrizationine the normal vector, and calculate the flux through the top, bottom and sides of the cylinder. Which of these will change, and how, depending on if a > 0 or a < 0?

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