Question

Electric field E can be written as _________

(a) -Gradient of V

(b) -Laplacian of V

(c) Gradient of V

(d) Laplacian of V

The question was posed to me in exam.

My question comes from Gradient of a Function and Conservative Field in section Vector Differential Calculus of Engineering Mathematics

Answer 1

The correct option is (a) -Gradient of V

The best explanation: Potential difference decreases in the direction of increase in Electric field. Hence Electric field is nothing but the negative of the gradient of potential difference.