Question

If a function is said to be harmonic, then

(a) Curl(Grad V) = 0

(b) Div(Curl V) = 0

(c) Div(Grad V) = 0

(d) Grad(Curl V) = 0

The question was asked at a job interview.

The doubt is from Laplacian Operator in division Vector Calculus of Electromagnetic Theory

Answer 1

Correct option is (c) Div(Grad V) = 0

The explanation is: Though option Curl(Grad V) = 0 & Div(Curl V) = 0 are also correct, for harmonic fields, the Laplacian of electric potential is zero. Now, Laplacian refers to Div(Grad V), which is zero for harmonic fields.