[UPSC CSE 2017] Electrostatics and Magnetostatics (Q94, 10M)

A charge q=2\,\mu\mathrm{C} is placed at a=10\,\mathrm{cm} from an infinite grounded conducting plane sheet. Find the (i) total charge induced on the sheet, (ii) force on the charge q and (iii) total work required to remove the charge slowly to an infinite distance from the plane.