Let J = 25/ρaρ − 20/(ρ2 + 0.01) az A/m2. (a) Find the total current crossing the plane z = 0.2 in the az direction for ρ<0.4. (b) Calculate ∂ρv/∂t. (c) Find the outward current crossing the closed surface defined by ρ = 0.01, ρ = 0.4, z = 0, and z = 0.2. (d) Show that the divergence theorem is satisified for J and the surface specified in part (c).
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