Laplace’s equation — UPSC CSE 2020 Physics PYQ

Write expressions for divergence and curl of an electrostatic field. From these, obtain Poisson and Laplace equations. Two concentric conducting spherical shells having radii r_1 and r_2 (r_1<r_2) are charged to potentials V_1 and V_2, respectively. What are the electric potential and hence electric field in the space between the shells? Also find the charge on the inner shell.