Question

Find the value of divergence theorem for A = xy^2 i + y^3 j + y^2z k for a cuboid given by 0<x<1, 0<y<1 and 0<z<1.

(a) 1

(b) 4/3

(c) 5/3

(d) 2

This question was addressed to me in homework.

Query is from Surface Integral in chapter Vector Calculus of Electromagnetic Theory

Answer 1

Right option is (c) 5/3

The best explanation: A cuboid has six faces. ∫∫A.ds = ∫∫Ax=0 dy dz + ∫∫Ax=1 dy dz + ∫∫Ay=0 dx dz + ∫∫Ay=1 dx dz + ∫∫Az=0 dy dx + ∫∫Az=1 dy dx. Substituting A and integrating we get (1/3) + 1 + (1/3) = 5/3.