Question

Find the value of divergence theorem for the field D = 2xy i + x^2 j for the rectangular parallelepiped given by x = 0 and 1, y = 0 and 2, z = 0 and 3.

(a) 10

(b) 12

(c) 14

(d) 16

This question was addressed to me in a job interview.

Question is from Surface Integral topic in portion Vector Calculus of Electromagnetic Theory

Answer 1

Correct option is (b) 12

To explain I would say: While evaluating surface integral, there has to be two variables and one constant compulsorily. ∫∫D.ds = ∫∫Dx=0 dy dz + ∫∫Dx=1 dy dz + ∫∫Dy=0 dx dz + ∫∫Dy=2 dx dz + ∫∫Dz=0 dy dx + ∫∫Dz=3 dy dx. Put D in equation, the integral value we get is 12.