Question

Find the divergence of the vector F= xe^-x i + y j – xz k

(a) (1 – x)(1 + e^-x)

(b) (x – 1)(1 + e^-x)

(c) (1 – x)(1 – e)

(d) (x – 1)(1 – e)

The question was posed to me in an interview for job.

I would like to ask this question from Divergence in section Vector Calculus of Electromagnetic Theory

Answer 1

The correct option is (a) (1 – x)(1 + e^-x)

Easy explanation: Div(F) = Dx(xe^-x) + Dy(y)+Dz(-xz) = -xe^-x + e^-x + 1 – x =

e^-x(1 – x) + (1 – x) = (1 – x)(1 + e^-x).