Question

The given equation satisfies the Laplace equation.

(a) V = x^2 + y^2 – z^2. State True/False.

(b) True

(c) False

This question was addressed to me in an international level competition.

My question is taken from Poisson and Laplace Equation in section Electrostatic Boundary Value Problem of Electromagnetic Theory

Answer 1

The correct choice is (a) V = x^2 + y^2 – z^2. State True/False.

To explain I would say: Grad (V) = 2xi + 2yj – 4zk. Div (Grad (V)) = Del^2(V) = 2+2-4 = 0. It satisfies the Laplacian equation. Thus the statement is true.