[UPSC IFoS 2020] Electrostatics and Magnetostatics (Q71, 8M)

Derive Poisson's equation. Under what conditions it takes the form of Laplace's equation? If \phi_1, \phi_2, \cdots, \phi_n are solutions of Laplace's equation, then show that \phi = \lambda_1 \phi_1 + \lambda_2 \phi_2 + \cdots + \lambda_n \phi_n is also a solution. Here \lambda\text{s} are arbitrary constants.