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, divergentThis 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

Determine the divergence of F = 30 i + 2xy j + 5xz^2 k at (1,1,-0.2) a

1.	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, divergentThis 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
Answer» 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.

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