Question

For a function given by F = 4x i + 7y j +z k, the divergence theorem evaluates to which of the values given, if the surface considered is a cone of radius 1/2π m and height 4π^2 m.

(a) 1

(b) 2

(c) 3

(d) 4

This question was addressed to me by my school teacher while I was bunking the class.

The question is from Gauss Divergence Theorem topic in portion Vector Calculus of Electromagnetic Theory

Answer 1

Correct option is (b) 2

For explanation: Div (F) = 4 + 7 + 1 = 12. The divergence theorem gives ∫∫∫(12).dV, where dV is the volume of the cone πr^3h/3, where r = 1/2π m and h = 4π^2 m. On substituting the radius and height in the triple integral, we get 2 units.