Question

Determine the divergence of F = 30 i + 2xy j + 5xz^2 k at (1,1,-0.2) and state the nature of the field. (a) 1, solenoidal (b) 0, solenoidal (c) 1, divergent (d) 0, divergent This question was posed to me at a job interview. I need to ask this question from Divergence topic in section 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

Right option is (b) 0, solenoidal The best explanation: Div(F) = Dx(30) + Dy(2xy) + Dz(5xz^2) = 0 + 2x + 10xz = 2x + 10xz Divergence at (1,1,-0.2) will give zero. As the divergence is zero, field is solenoidal. Alternate/Shortcut: Without calculation, we can easily choose option “0, solenoidal”, as by theory when the divergence is zero, the vector is solenoidal. “0, solenoidal” is the only one which is satisfying this condition.