Question

Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the sphere given by x^2 + y^2 + z^2 = 9. (a) 120π (b) 180π (c) 240π (d) 300π This question was addressed to me during a job interview. My enquiry is from Gauss Divergence Theorem topic in division 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

Correct answer is (b) 180π To elaborate: We could parameterise surface and find surface integral, but it is wise to use divergence theorem to get faster results. The divergence theorem is given by ∫∫ F.dS = ∫∫∫ Div (F).dV Div (3x i + 2y j) = 3 + 2 = 5. Now the volume integral will be ∫∫∫ 5.dV, where dV is the volume of the sphere 4πr^3/3 and r = 3units.Thus we get 180π.