(a) A flux density field is given as F1 = 5az. Evaluate the outward flux of F1 through the hemispherical surface, r = a, 0 < θ < π/2, 0 < ϕ < 2π.
(b) What simple observation would have saved a lot of work in part a?
(c) Now suppose the field is given by F2 = 5zaz. Using the appropriate surface integrals, evaluate the net outward flux of F2 through the closed surface consisting of the hemisphere of part a and its circular base in the xy plane. (d) Repeat part c by using the divergence theorem and an appropriate volume integral.
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