Question

If a function is described by F = (3x + z, y^2 − sin x^2z, xz + ye^x5), then the divergence theorem value in the region 0<x<1, 0<y<3 and 0<z<2 will be (a) 13 (b) 26 (c) 39 (d) 51 I had been asked this question by my college professor while I was bunking the class. Asked question is from Gauss Divergence Theorem topic in chapter Vector Calculus of Electromagnetic Theory Select the correct answer from above options Electromagnetic Theory questions and answers, Electromagnetic Theory questions pdf, Electromagnetic Theory question bank, Electromagnetic Theory questions and answers pdf, mcq on Electromagnetic Theory pdf,electromagnetic theory book pdf,electromagnetic theory pdf notes,electromagnetic theory lecture notes,electromagnetic theory of light,maxwell electromagnetic theory,electromagnetic theory proposed by,electromagnetic theory engineering physics,electromagnetic theory nptel

Answer 1

The correct option is (c) 39 To explain I would say: Div (F) = 3 + 2y + x. By divergence theorem, the triple integral of Div F in the region is ∫∫∫ (3 + 2y + x) dx dy dz. On integrating from x = 0->1, y = 0->3 and z = 0->2, we get 39 units.